text:
\section{Introduction}
\label{sec::Introduction}
Automatic human activity recognition (HAR) is the process of automatically labeling the videos containing human movements with the corresponding action names. Johansson et al. \cite{johansson1973visual} carried out an interesting experiment where, they attached markers to human joints before recording the movement of these markers in a video. In almost all cases, human subjects could say that the tags were attached to a human body. Furthermore, they were able to correctly guess the type of activity the actor was doing. Although this experiment  clearly proves that the task of HAR is rather trivial for humans, it does not tell us whether the human brain uses 2D trajectories of these markers or creates a 3D trajectory model, before the actual recognition process.

Numerous approaches have been proposed for solving the problem of human activity recognition. The use of sparse representation, where each video is represented by a set of independent features, has gained a lot of popularity. Most of the features proposed in the literature focused on low-level features~\cite{laptev2003interest,laptev2005space,dollar2005behavior,
laptev2008learning,bregonzio2009recognising,wang2009evaluation,pervs2010histograms}, that are directly extracted from the pixel information. Other works have used higher level features, such as main joint locations~\cite{li2010object,sadanand2012action,yao2011does,jhuang2013towards}, with the assumption that high-level features would yield better results, if they were accurately known.
Unfortunately, extracting high-level features from cluttered scenes is a non-trivial task. It might require the use of specialized equipments, like color markers on human joints~\cite{ofli2013berkeley} for example, or Microsoft Kinect sensor or other active sensors, to create a depth map and to extract human skeleton from it~\cite{shotton2013real, barnachon2014ongoing}.
On the other hand, it is relatively easy to build a trajectory by tracking a set of 2D interest points across video frames.
When compared to other sparse representation methods, trajectories are mid-level features that can yield competitive results. Recently, \cite{habashi2017trajectory} proposed and compared different 2D trajectory-based HAR algorithms. In a separate work, \cite{habashi2017better} proposed a better trajectory shape descriptor to be used for HAR.

We have used disparity as another new feature to boost the performance of trajectory-based methods.
To calculate disparities, two slightly different views of the subject are required. First, 2D trajectories are extracted from the left and right videos. Then, by matching these trajectories and mapping them to the rectified image planes, a disparity-augmented trajectory is created.

This paper demonstrates that adding the disparity information to the 2D trajectories, can be beneficial for human activity recognition. In particular, disparity-augmented trajectories have improved classification rates by 2.76\% in our tests.

Both 2D and disparity-augmented trajectories are made of pixel locations across frames. To be used for classification, a descriptor, that can discriminate between different trajectories, should be defined based on the shape of trajectories. The descriptors used in this work were inspired by the ones used in \cite{habashi2017better}.

We have also improved the performance of our proposed method by limiting the
processing to the regions of interest, instead of the whole images. Our regions
of interest consist of the parts in the video frames that contain movement.
In particular, the graph connected component analysis algorithm was used to select the active areas in frames.

It is also worth noting that the use of trajectories proposed in this paper, is independent from the HAR task, and it can be applied to any other video categorization problem. However, to show the effectiveness of our proposed algorithms and compare them with the state of the art methods, we have applied and tested them on human activity recognition application.

In summary, this paper has the following contributions:

\begin{itemize}

	\item A new method to extract disparity-augmented trajectories from stereo videos
	\item Extension of the trajectory shape descriptor to higher dimensions
	\item A method to rectify stereo videos
	\item A new dataset of stereo videos
	\item Comparison of 2D trajectories versus disparity-augmented trajectories in the HAR domain
\end{itemize}

The remainder of this paper is organized as follows. Section~\ref{sec::backgroundWorks} reviews related research works and Section~\ref{sec::preprocessing} describes the method used for detecting human activity areas in video frames. Section~\ref{sec::trajectoriesForHumanActivityRecognition} provides details for three different algorithms we have used to extract 2D trajectories and describes how the disparity information is added to the 2D trajectories. Section~\ref{sec::trajectoryShapeEncoding} describes the proposed trajectory shape encoding algorithm. Details of the learning method used can be found in section~\ref{sec::learningPhase}. Section~\ref{sec::experiments} and Section~\ref{sec::conclusion} present the experimental results and the conclusion, respectively.

\section{Background works}
\label{sec::backgroundWorks}
Trajectories have proven to be useful for aligning consecutive frames before extracting low-level features~\cite{wang2011action}. Even the extraction of deep learning feature vectors benefited from trajectory alignment~\cite{wang2015action}. Trajectory shapes can also be used directly for human activity recognition.

Wang et al.~\cite{wang2013dense,wang2013action,wang2011action} exploited trajectories in separate contributions. In their works, a grid was used to dense sample video frames. Eigenvalues of the autocorrelation matrix was utilized to filter out the samples that were not easy to track. Dense optical flow field, proposed by Farnback~\cite{farneback2003two}, was applied to track these sample points in time. This flow was then employed to align the interest points neighborhoods before calculating the HOG and HOF features. They also proposed another trajectory shape descriptor, that did not outperform the other two.

Mademlis et al.~\cite{mademlis2016exploiting} used disparity information to calculate HOG, HOF and MBH in different disparity zones before encoding them for activity recognition. Although their method improves the performance, but their use of disparity is limited to few disparity zones. Arguably the disparity can be used more efficiently for encoding task.

Hadfield et al.~\cite{hadfield2017hollywood} used 3D Hollywood movies to create a challenging stereo dataset for human activity recognition. The authors estimated the calibration information using RANSAC method and repeating the process 100 times, before selecting the best estimation. Then, the extracted 3D information extracted was used to calculate 3.5D interest points. They have defined a 3D motion descriptors for each of these feature points and, they have normalized it to remove the effect of different camera rotations.

Matikainen et al.~\cite{matikainen2009trajectons} used the technique of Kanade Lucas Tomasi (KLT)~\cite{lucas1981iterative}
to track a number of points and, created a trajectory for each of these points. Then, they used K-Means method to cluster the obtained trajectories in different clusters (words). They have also proposed to augment these trajectories by adding some affine transformation information, which represents the motion of various parts of the body. Finally, they have used a standard bag of words (BOW) method and SVM for clustering.

In another similar work, Messing et al.~\cite{messing2009activity} used KLT to track keypoints of a video and created a generative model on the velocity history of these keypoints.

Sun et al.~\cite{sun2009hierarchical} proposed to track Scale Invariant Feature Transform (SIFT) points. They have used SIFT descriptors to match each keypoints across the frames. They have extracted features at different levels and used multichannel nonlinear SVM for human activity recognition.

More recently,~\cite{habashi2017trajectory,habashi2017better} demonstrated that good sparse trajectories could produce competitive results to low-level features, but with less computations. Besides, trajectories are a better choice for HAR as they encode the motion of a body, while low-level features usually encode the texture or movement within small neighborhoods in spatiotemporal space. This makes low-level features more dataset dependent.

\section{Preprocessing}
\label{sec::preprocessing}
In order to reduce the overall processing time, we have developed a simple, yet effective, method for detecting the regions of interest (moving parts in the videos). The steps below describe how we detect and remove static (stable) regions from videos.

\begin{enumerate}
	\item Estimate background with a mixture of Gaussian
	\item Subtract estimated background from current frame
	\item Highlight the moving parts of video by erosion and dilation operations
	\item Extract the contours of motion
	\item Find rectangular regions of interest as follows:
	\begin{enumerate}
		\item Find a bounding box for each contour
		\item Create a graph, where each node represents a bounding box and, if two boxes overlap or are close enough, have an edge between them

		\item Use connected component labeling algorithm similar to~\cite{vincent1991watersheds} to find the connected components of this graph
		\item Combine the boxes of each connected components. Each combined box represents a separate region of interest
	\end{enumerate}
\end{enumerate}

The above algorithm allows the extraction of all non-static (motion) areas.

\section{Trajectories for Human Activity Recognition}
\label{sec::trajectoriesForHumanActivityRecognition}

Trajectories are defined as the trail of 2D or 3D spatial feature points in time. The disparity-augmented trajectories are similar to 3D trajectories except that they have the disparity in addition to 2D information. Formally, a trajectory is defined as an ordered list of locations, sampled over $l+1$ time steps, where $l$ is the length of the trajectory. In a single video, the frame rate determines the distance between sampling times, so a trajectory $T$ in dimension $n$ can be defined as:

\begin{equation}
	\label{equ::Trajectory}
	T = (p_0, p_1, p_2, ..., p_l), p_i \in \mathbb{R}^{n}, i=0 ... l
\end{equation}

Note that throughout this paper we assume that $n\in{\mathbb{N}}$, but in practice
and in our tests, $n\in{\{2,3\}}$.

To create a disparity-augmented trajectory, the corresponding 2D trajectories from two views of a subject are extracted and combined. Section~\ref{sec::2dTrajectoryExtraction} provides details of how these 2D trajectories are extracted. Then, section~\ref{sec::3dTrajectoryExtraction} explains how disparity is added to our 2D trajectories.

\subsection{2D Trajectory Extraction}
\label{sec::2dTrajectoryExtraction}
A 2D trajectory $T$ is an ordered list of 2D spatial coordinates $p=(x,y)$ in $l+1$ consecutive frames, formally defined as:

\begin{equation}
  \label{equ::Trajectory2D}
  T=(p_0, p_1, p_2, ..., p_l), p_i \in \mathbb{R}^{2}, i=0..l
\end{equation}

Authors in \cite{habashi2017trajectory} compared three different trajectory extraction algorithms and showed that a combination of FAST corner detector and Farnback optical flow for trajectory extraction outperformed other trajectory extraction algorithms. More details are given below for each of the three methods.

\subsubsection{Interest Point Tracking}
\label{sub::interestPointTracking}
We refer to this method as \textit{``Interest Point Tracking''} (IP).
Starting from the first frame, interest points are extracted then tracked across frames to make trajectories.
When a trajectory reaches a length of $l+1$, it is considered a complete trajectory.

$T$ and $\Psi$ are two sets to keep trajectories and matched feature points, respectively.
For each frame $I_t$, the set of feature points $P_t$ and the set of next frame feature points $P_{t+1}$ are extracted.

For each member of $P_t$, a feature descriptor is calculated based on the appearance of the interest point neighborhood. Again, the algorithm could consider any feature descriptor.

We define a mapping $\Psi_t: P_t \to \mathbb{R}^k$, where

\begin{equation}
  \label{equ::FeatureDescriptors}
  \Psi_t = \{(p, v)| p \in P_t, v \in \mathbb{R}^k \}
\end{equation}
$t$ is the frame number, $v$ is the feature descriptor vector for point $p$ and $k$ is the dimension of the descriptor (e.g., for standard SIFT descriptor $k=128$).

The neighborhood of a point $p_i$ is given by
\begin{equation}
  N_{t}(p_0)=\{p~|~p \in P_{t},~\Delta_1(p, p_0) \leq \lambda_1\}
\end{equation}
where $\Delta_1(.)$ is a distance measure and $\lambda_1$ determines the radius of neighborhood.
In our implementation, we have used the Manhattan distance.

The best match for $p_0$ is found within the neighborhood $N_{t}(p_0)$, based on
the appearance of descriptors.
To do so, for each $p_i \in P_{t-1}$, a mapping $M_{t}(p_0): N_{t}(p_0) \to \mathbb{R}$ is defined as follow:

\begin{equation}
\centering
  M_{t}(p_0)=\{(p, d)| p \in N_{t}(p_0),
  d = \Delta_2(\Psi_{t-1}(p), \Psi_{t}(p_0))\}
\end{equation}
where $\Delta_2(.)$ is a distance measure in descriptors space.

In our case, we used the Euclidean distance, where the closest match is considered the best match.

\begin{equation}
  BestMatch = \argmin\{  M_{t+1}(p_i)\}
\end{equation}

An example of the obtained trajectories is displayed on Figure~\ref{fig::DifferentTrajectoryExtractionAlgorithm} left (best seen in color).

\begin{figure*}[!htbp]
	\centering
	\includegraphics[width=0.325\linewidth]{IP}
	\includegraphics[width=0.325\linewidth]{LK}
	\includegraphics[width=0.325\linewidth]{FB}
	\caption{

	2D trajectory extraction algorithms (best seen in color). The 2D trajectories obtained by the three different algorithms: IP (left), LK (middle) and FB (right). The green box is the active area, detected by the preprocessing algorithm.}
	\label{fig::DifferentTrajectoryExtractionAlgorithm}
\end{figure*}

\subsubsection{Lucas-Kanade Feature Point Tracking}
\label{sec::LucasKanadeFeaturePointTracking}
We refer to this method as \textit{``Lucas-Kanade Trajectory''} (LK), as it is based on Lucas-Kanade optical flow algorithm~\cite{bouguet2001pyramidal}. First, the feature points of each frame of the video are extracted. Then, Lucas-Kanade optical flow algorithm is used to find the location of each of these feature points in the next frames, hence creating the trajectories.

An example of the obtained LK trajectories are displayed on Figure~\ref{fig::DifferentTrajectoryExtractionAlgorithm} (middle).

\subsubsection{Farnback Feature Point Tracking}
\label{sec::FarnbackFeaturePointTracking}
This algorithm is similar to the Farnback optical flow algorithm~\cite{farneback2003two}, we refer to as \textit{``Farnback Trajectory''} (FB). Farnback optical flow algorithm is newer than Lucas-Kanade algorithm and has shown a better performance~\cite{wang2011action,farneback2003two}. Farnback optical flow algorithm is also able to provide the dense optical flow field, while Lucas-Kanade optical flow was designed to track sparse feature points. This gives FB an advantage, especially when the selected points are not good feature points.
However, our tests revealed that FB yields competitive results to LK, and both performed much better than IP.

First, the Farnback optical flow field is calculated before the feature points of each frame are extracted. Starting from the first frame, the location of each point in the next frame is predicted, using the pre-calculated optical flow field. These points are then connected as a trajectory.

The interest points of each frame are extracted using OpenCV implementation of FAST algorithm~\cite{rosten2006machine}. The dense optical flow field is obtained using Farnback motion estimation method~\cite{farneback2003two}. The trajectories created by this algorithm are shown on Figure~\ref{fig::DifferentTrajectoryExtractionAlgorithm} (right).

\subsection{Disparity-Augmented Trajectory}
\label{sec::3dTrajectoryExtraction}
After the extraction of the 2D trajectories from the left and right videos, matching these trajectories is achieved based on local descriptors (section~\ref{sec::findingMatchingTrajectories}). The matched trajectories are then mapped to their corresponding rectified planes (section~\ref{sec::estimatingTheFundamentalMatrix}). Finally, their disparity is fused with the 2D spatial information (section~\ref{sec::DisparityAugmented}).

\subsubsection{Finding Matching Trajectories}
\label{sec::findingMatchingTrajectories}
Each trajectory starting point, in the left and right videos, are encoded with a SIFT descriptor and the best match of this descriptor is found by using the method in~\cite{lowe2004distinctive}. Starting from the first frame of the video, for each descriptor in the left frame, its best match is found in the right frame. To make the matching robust, we repeat the process between the right to the left frames and, only keep the reciprocal matches.

\subsubsection{Video Rectification}
\label{sec::estimatingTheFundamentalMatrix}
The rectification is the process of mapping an image to a plane, where the y disparity becomes zero and only the x disparity remains.
If $p$ and $p'$ represent two matching points, between the left and right images, the fundamental matrix $F$ is the matrix that satisfies:

\begin{equation}
\label{equ::fundamentalMatrix}
	pFp' = 0
\end{equation}

The eight-point algorithm is used to estimate $F$~\cite{hartley1997defense} and the FAST algorithm is used to find the feature points. The same algorithm, as explained in Section~\ref{sec::findingMatchingTrajectories}, is used to match the feature points between the left and right video frames.

The calculations of $F$ and rectification matrices $H_l$ and $H_r$~\cite{hartley1999theory} depend on the quality of matched points. To address these issues, we propose the following technique to find the best estimation of $F$, $H_l$ and $H_r$. First, $m$ random frames of the stereo video are selected. For each pair $i$ of these stereo frames, $F^i$, $H_l^i$ and $H_r^i$ are calculated. If $p=(x,y,1)^T$ and $p'=(x',y',1)^T$ represent a matching point, then $q=H_l^ip=(u,v,1)^T$ and $q'=H_r^ip'=(u',v',1)^T$ represents the mapping of these corresponding points on the rectified plane, where ideally $v - v' = 0$. Considering the matched trajectories from section~\ref{sec::findingMatchingTrajectories}, the best estimate of $F$ is the one that maximizes the number of trajectories that will be rectified with an acceptable y disparity. Figure~\ref{fig::trajectorySamples} shows samples of two matching trajectories, one before rectification and the other one after rectification.
In addition, because the calculation of $F$ is susceptible to outliers, we
have also used the random sample consensus (RANSAC) method to make its
calculation robust.

\begin{figure*}[!htbp]
\centering

\begin{tikzpicture}
\begin{axis}[
    width = 0.5\linewidth,

    xlabel={Sample stereo trajectories},

    legend style={at={(0cm,2cm)},anchor=north west},
    ymajorgrids=true,
    grid style=dashed,
]

\addplot[color=red, mark=*]
	coordinates {(0.529282, 0.302554) (0.536277, 0.30275) (0.543578, 0.302267) (0.550729, 0.301873) (0.557384, 0.300724) (0.564094, 0.299299) (0.570512, 0.297437) (0.576743, 0.295539) (0.582921, 0.294298) (0.589273, 0.294611) (0.596294, 0.296409) (0.603279, 0.298644) (0.610352, 0.300977) (0.617153, 0.301959) (0.624323, 0.303037) (0.630893, 0.30179) (0.637772, 0.301413) (0.644227, 0.300913) (0.650214, 0.299864)};

\addplot[color=blue, mark=triangle]
	coordinates {((0.497238, 0.35167) (0.50393, 0.351721) (0.511314, 0.351311) (0.518454, 0.350931) (0.525235, 0.349637) (0.531665,0.347923) (0.53786, 0.345613) (0.543955, 0.34366) (0.550198, 0.342668) (0.55675, 0.343134) (0.563674, 0.34486) (0.5706, 0.347153) (0.577617, 0.349838) (0.584726, 0.351184) (0.592069, 0.352816) (0.598828, 0.352313) (0.605394, 0.35226) (0.611757, 0.351388) (0.617767, 0.350127)
};

\legend{Left,Right}
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}
\begin{axis}[
    width = 0.5\linewidth,

    xlabel={Sample rectified stereo trajectories},

    legend pos=south east,
    ymajorgrids=true,
    grid style=dashed,
]

\addplot[color=red, mark=*]
	coordinates {(4.083905696505915062e-01, 4.338906762270391959e-01) (4.128460923664530324e-01, 4.303566863055560687e-01) (4.175455350808225385e-01, 4.278649741712325372e-01) (4.228130121295593513e-01, 4.252452342611746650e-01) (4.281978586783060092e-01, 4.231155667713080160e-01) (4.338024100564202845e-01, 4.220212101234350754e-01) (4.396758753686350607e-01, 4.223456097583975222e-01) (4.460441637970914419e-01, 4.241732163734988625e-01) (4.526213828738526179e-01, 4.262759723642053356e-01) (4.592340856599764765e-01, 4.291889710551127779e-01) (4.661516333075107488e-01, 4.323922498836437756e-01) (4.739601546342224192e-01, 4.351021953978409518e-01) (4.819474846900381193e-01, 4.361141321906819024e-01) (4.894330312493821999e-01, 4.361541489028571972e-01) (4.971266800482095904e-01, 4.360592967061021619e-01) (5.040249398043920026e-01, 4.338208203460862666e-01) (5.108791425560605948e-01, 4.310740016461834800e-01) (5.172717852087800328e-01, 4.285037086127621575e-01) (5.238387279061120783e-01, 4.269142257463990897e-01)};

\addplot[color=blue, mark=triangle]
	coordinates {(4.126085621647145318e-01, 4.383011120326761323e-01) (4.170200878163817793e-01, 4.349161560264208637e-01) (4.215291028610345658e-01, 4.323320438445366620e-01) (4.268009257073381302e-01, 4.297468619085484387e-01) (4.320070069640152832e-01, 4.270153201053751846e-01) (4.374476680780373661e-01, 4.256893622602431759e-01) (4.431303032820738119e-01, 4.262406073689005703e-01) (4.493344927906778308e-01, 4.281324064677089480e-01) (4.558125279932305207e-01, 4.306005470739864283e-01) (4.623065813851148786e-01, 4.334953806326550252e-01) (4.695988180261841949e-01, 4.372111220243641294e-01) (4.771945412856147817e-01, 4.399158889782136539e-01) (4.848215927314672991e-01, 4.403503725925374535e-01) (4.929357581106532105e-01, 4.410013659359509064e-01) (5.006954567535094602e-01, 4.403354539590202399e-01) (5.081466119099244949e-01, 4.389694762542205586e-01) (5.149207272212690256e-01, 4.353305780036445527e-01) (5.217271873509317093e-01, 4.332055187301791510e-01) (5.283822536783573387e-01, 4.317608699122651439e-01)};

\legend{Left,Right}
\end{axis}
\end{tikzpicture}

\caption{
Sample stereo trajectories, unrectified (left) and rectified (right). (best seen in color)
 }
\label{fig::trajectorySamples}
\end{figure*}

\subsubsection{Calculating Disparity-Augmented Trajectories}
\label{sec::DisparityAugmented}
Having the rectification matrices $H_l$ and $H_r$, it is now easier to calculate the rectified left and right trajectories, $t_l$ and $t_r$, as

\begin{align}
	t_l &= H_l T_l \\
	t_r &= H_r T_r
\end{align}
where $T_l$ and $T_r$ are the homogeneous representation of the left and right trajectories, respectively.

Each column of $t_l$ or $t_r$ represents a rectified trajectory image plane point. Consider two corresponding points $q=(u,v,1)^T$ and $q'=(u',v',1)^T$ on left and right trajectories, respectively. The corresponding disparity
augmented point $(x_m,y_m,d)$ will be given by:

\begin{align}
	x_m &= u   \\
	y_m &= v	 \\
	d &= u - u'
\end{align}

\section{Trajectory Shape Descriptor}
\label{sec::trajectoryShapeEncoding}
The method we used to create a descriptor for trajectories is an extension of~\cite{habashi2017better}, where the locations of interest points in 2D or 3D (2D plus disparity) spaces are encoded into trajectories. The latter are considered as discrete functions, that map time values to coordinates. The first and second derivatives of such mapping function, with respect to time, represent respectively the velocity and the acceleration of the interest point. Higher order derivatives encode higher order motion information. The final descriptor is obtained by concatenating these derivatives. In our experiments, we have used derivatives up to the 7th order, for single views and up to 5th order for multiple views.

Formally, each trajectory, defined in Equation~\ref{equ::Trajectory}, can be interpreted as a function of time that map time values to locations in $\mathbb R^{n}$ space.

\begin{align}
	\label{eq::Trajectory}
		&T : time \to \mathbb R^{n} \\
		&T(t) = P(\frac{t - t_0} {\Delta t}) \\
		&P(i) = p_i \in \mathbb R^{n}
\end{align}
where $\Delta t$ is the time between two consecutive frames and $t_0$ is the starting time of trajectory $T_k$.

The first derivative of this function is given by:

\begin{equation}
      \label{eq::Differentiation}
      V(t) = \frac{dT}{dt} = \lim_{t \to 0} \frac{T(t+dt) - T(t)}{dt}
\end{equation}

Because a video typically has a fixed frame rate, the smallest value of $dt$ is the time distance between two consecutive frames ($\Delta t$). Changing the unit of measurement from seconds to frames makes $dt = 1$. Hence, the velocity equation~\ref{eq::Differentiation} can be rewritten as:

\begin{align}
\label{equ::velocityDescriptor}
	V(t) &= T(t+1) - T(t) \\
	V&= (v_0, v_1, ..., v_{l-1}) \\
	v_i&=p_{i+1} - p_{i}, i=0...{(l-2)}
\end{align}

Similarly, the acceleration is given by

\begin{align}
	\label{eq:Acceleration}
	A(t) &= \frac{dV(t)}{dt}= V(t+1) - V(t) \\
	A&= (a_0, a_1, ..., a_{l-1}) , \\
	a_i&=v_{i+1} - v_{i}, i=0...{(l-2)}
\end{align}

Higher order functions can be defined as follows:

\begin{equation}
	\label{eq::HigherOrderDrivitives}
	\nabla^{(n)} = \frac{d^nT(t)}{dt^n}
\end{equation}

The actual descriptor is created by the concatenation of these derivatives. For example, descriptor $D_1$ is given by the velocity ($\nabla^{(1)}$), descriptor $D_2$ is given by the concatenation of $\nabla^{(1)}$ and $\nabla^{(2)}$ and, descriptor $D_3$ is given by the concatenation of $\nabla^{(1)}$, $\nabla^{(2)}$ and $\nabla^{(3)}$.

\section{Learning phase}
\label{sec::learningPhase}
Our proposed trajectory shape representation, like other sparse representation methods, represents a video by a set of independent features. Formally, a video can be represented by a set of feature descriptors as:
\begin{equation}
  S=\{D_k| D_k \in \mathbb{R}^N\}
\end{equation}

where $N$ is the dimension of the local descriptors.

Existing machine learning methods in general and SVM in particular, expect data as a vector of predetermined size. As a result, each set of these features should be represented by a vector. Different methods have been proposed in the literature.
One of the conventional methods to convert sparse sets to a vector is based on the bag of words (BOW)~\cite{pang2002thumbs}\cite{zhang2010understanding}.
Another favorite technique, known as Fisher Vector Encoding (FVE)~\cite{perronnin2007fisher,perronnin2010improving}, combines the generative and discriminative methods~\cite{varol2015efficient}. Unlike BOW that uses only the first order statistics, FVE uses first and second order statistics for encoding~\cite{wang2013action}. Instead of using K-Means for clustering, Expectation Maximization (EM) is used to cluster data into K Gaussian Mixtures. Then, the created Gaussian mixture model (GMM) is used to estimate the means, variances and prior probabilities of the mixtures.

\section{Results and discussion}
\label{sec::experiments}
This section first provides details on the used datasets and on our experimental setup.

\subsection{Dataset}
\label{sec::dataset}

\begin{figure*}[!htbp]
	\centering
	\includegraphics[width=0.41\linewidth]{DS1}
	\includegraphics[width=0.41\linewidth]{DS2}

	\includegraphics[width=0.41\linewidth]{DS13}
	\includegraphics[width=0.41\linewidth]{DS4}

	\includegraphics[width=0.41\linewidth]{DS5}
	\includegraphics[width=0.41\linewidth]{DS6}

	\includegraphics[width=0.41\linewidth]{DS7}
	\includegraphics[width=0.41\linewidth]{DS8}

	\includegraphics[width=0.41\linewidth]{DS9}
	\includegraphics[width=0.41\linewidth]{DS10}

	\includegraphics[width=0.41\linewidth]{DS11}
	\includegraphics[width=0.41\linewidth]{DS12}

	\caption{

	Sample images from our dataset (best seen in color) First row: standing up, hand shaking, walking toward camera and two-hand waving. Second row: high-five, shooting the ball, pulling heavy object and picking up something from floor. Third row: jumping over gap, exchanging object, sitting up and punching
}
\label{fig::sampleImagesFromDataset}
\end{figure*}

To the best of our knowledge, the only existing stereo dataset is the Hollywood 3D dataset, which has 13 different activity classes and a special "No Action" class.
This dataset is a very challenging one for trajectory-based methods, as the lengths of some videos are too short, making it impossible to create meaningful trajectories. In addition, sporadic camera motions create unwanted trajectories, which degrades the accuracy. There are also several videos that are labeled as single activities, while other activities are going on in the background. This usually confuses methods that assume a single activity in the field of view.

We have also created our own stereo dataset with 27 different activity classes, using static cameras.

Note that despite the amount of work that has been done on human action recognition, there is no universally accepted definition of a human action.
This is especially visible in the different datasets that have been created so far.
Some actions, like walking, running and jumping, are widely accepted~\cite{schuldt2004recognizing,zelnik2001event}. A single person usually performs these activities, with some of them containing human and objects/environment interactions, like riding a bike or shooting a basketball~\cite{liu2009recognizing}, playing cello and mopping the floor~\cite{soomro2012ucf101}. Some researchers went beyond this and created datasets for cooking different recipes~\cite{rohrbach2012database}.

In our own dataset, we considered actions to be sole movements of the human body, regardless of the background, environment or tools they might be using. Besides, we studied activities that contain the whole human body movement as actions. We considered 27 different actions for this dataset. The activities were selected based on the frequency of their appearance in other human datasets. Besides, we added activities that can be performed in an office setting. We did not use  tools a lot. For example, for recording throwing, the actor does not throw anything, he/she simply acts like throwing. The only exception was for pushing/pulling objects, where a chair have been used. Our actions were performed by eleven different volunteers in an everyday office setting. Some activities were performed in different scenarios. For example, walking was performed four times by each actor: walking from left to right, walking from right to left, walking toward the camera and walking away from the camera. We used off-the-shelf cameras to record these activities. Our stereo system consisted of two cameras that were roughly at 30cm from each other.
Five hours of activities were recorded by each camera, allowing us to obtain 4076 stereo video clips, from which 1188 were selected to represents 27 different activities. Each activity was performed four times by each of the eleven actors. Table~\ref{tab::activityNames} presents information about the recorded activities and some samples of these activities are shown on Figure~\ref{fig::sampleImagesFromDataset}.

\begin{table}
\caption{The list of activity classes in our own dataset}
\label{tab::activityNames}
\centering
\begin{tabular}{ccc}
\toprule
Crossing Arms       & Exchange Object      & Hand Clapping \\
Hand Shaking        & Hand Waving          & High Five     \\
Hitting             & Jumping Over Gap     & Jumping Jack  \\
Kick the Ball       & Kicking              & Lay Down      \\
Pickup(Floor)       & Pull                 & Pointing      \\
Pickup(Table)       & Push                 & RaiseHand     \\
Running             & Scratch Head         & Sit down       \\
Sit-up               & Skipping             & Standup       \\
Throwing            & Turning              & Walking       \\
\bottomrule
\end{tabular}

\end{table}

\subsection{Experimental Setup}
Our tests were carried out on a Ubuntu machine, with eight 3.8 GHz cores and 8Gb of RAM. The video processing part, including trajectory extraction, was implemented in C++, using OpenCV library. The trajectory aligning algorithm was implemented in Python.

After obtaining a set of trajectory descriptors for each video, and since \cite{wang2013action} has shown the `effectiveness' of \emph{Fisher Vectors} over other methods, we have used  \emph{Fisher Vectors} to prepare data before passing it to a standard support vector machine (libSVM~\cite{CC01a}).

The data used for training and testing was split as follows. For each action, all videos of one actor are used for testing, while the remaining videos from other actors are used for training. A confusion matrix is calculated for each
action. The blending of these matrices represents the overall confusion matrix. The accuracy, reported in the tables, is the ratio of correctly classified instances to the total number of samples, directly calculated from the overall confusion matrix.

\subsection{2D Trajectories}
\label{sec::results}

\begin{table*}

	\centering
\caption{The accuracy(\%) measured for left, right and both cameras. Both-camera is the combination of features from left and right frames}
	\label{tab:IP_LK_FB_TrajectoryLength}
\begin{tabular}{cccccccccc}
\toprule
		& \multicolumn{3}{c}{Left Camera} &   \multicolumn{3}{c}{Right Camera}    &   \multicolumn{3}{c}{Both Cameras}      \\

	\cmidrule(lr){2-4} \cmidrule(lr){5-7} \cmidrule(lr){8-10}
	Length  &   IP    &   LK   &   FB   &   IP    &   LK    &   FB    &   IP    &   LK    &    FB     \\
	\midrule

	9 	& 77.73 & 83.87 & 82.81 & 74.75 & 81.09 & 82.92 &80.20 & 82.89 &82.97 \\
	11 	& 76.55 & 84.29 & 84.50 & 74.45 & 84.62 & 83.38 &\textbf{80.81}  &82.49 & 85.98 \\
	13	& \textbf{79.12}  & 84.71 & 85.72 & 73.54 & 82.44 &85.80 & 79.54 &83.96 & 85.04 \\
	15	& 77.68 & 86.06 & 84.37 & 72.72 & 85.04 & 84.58 &79.80 & 84.97 &86.78 \\
	17	& 78.93 & 84.54 & 84.54 & 73.54 & 86.54 & 85.31 &78.09 & 86.07 &86.08 \\
	19	& 77.33 & 85.13 & 85.46 & 73.77 & 87.12 & 86.25 &79.78 & 85.90 &87.05 \\
	21	& 77.22 & 86.74 & 85.88& \textbf{75.67} & 85.66 & \textbf{87.90} &79.45 & \textbf{86.82} & \textbf{88.19} \\
	23	& 77.42 &  \textbf{86.81} &  \textbf{87.90} &  73.34  & \textbf{87.29}  &  87.64  &  78.70  &  85.52  &   87.43   \\
	25	&  78.94  &  86.22 &  87.65 &  71.33 &  84.94  &  85.37  &  79.74 &  85.64  &   87.04  \\
	27	&  75.32 &  86.69 &  85.84 &  70.37 &  86.52 &  87.70 & 77.85  &  85.18  &   87.35   \\
	\bottomrule
\end{tabular}
\end{table*}

Table~\ref{tab:IP_LK_FB_TrajectoryLength} summarizes the obtained results of our HAR tests using 2D trajectories. Each column represents one of the algorithms proposed in this paper, with ``\emph{both cameras}'' column refers to the simple stacking of left and right descriptors, without any further processing. The descriptors of the trajectories were calculated using the algorithm proposed in~\cite{wang2013dense}.
As it can be seen, FB outperforms the other two in most cases. LK closely follows FB and beats it in some cases. The reason  why FB and LK are yielding similar results is because the selected feature points are the corners, which are easy to follow for both algorithms. Both FB and LK track pixels at subpixel accuracy, yielding smoother trajectories. On the other hand, IP algorithm uses pixel accuracy that degrades its results, as it can be seen on Figure~\ref{fig:IP_LK_FB_Accuracies}.

\begin{figure*}[!htbp]
	\centering
\begin{tikzpicture}
\begin{axis}[
    width = 0.33\linewidth,
    title={Left Camera},
	xlabel={Trajectory length [frames]},
    ylabel={Accuracy [\%]},
    xmin=11, xmax=27,
    ymin=70, ymax=95,
    xtick={5,10,15,20,25},

    legend style={at={(-0.5cm,4cm)},anchor=north west},
    ymajorgrids=true,
    grid style=dashed,
]
\addplot[
    color=blue,
    mark=square*,
    ]
    coordinates { (5,  75.79)(7,  75.03) (9,  77.73) (11, 76.55) (13, 79.12) (15, 77.68) (17, 78.93) (19, 77.33) (21, 77.22) (23, 77.42) (25, 78.94) (27, 75.32)};
\addplot[
    color=red,
    mark=*,
    ]
    coordinates { (5,  77.73) (7,  81.68) (9,  83.87) (11, 84.29) (13, 84.71) (15, 86.06) (17, 84.54) (19, 85.13) (21, 86.74) (23, 86.81) (25, 86.22) (27, 86.69)
    };
\addplot[
    color=green,
    mark=triangle*,
    ]
    coordinates { (5,  71.25) (7,  78.90) (9,  82.81) (11, 84.50) (13, 85.72) (15, 84.37) (17, 84.54) (19, 85.46) (21, 85.88) (23, 87.90) (25, 87.65) (27, 85.84) };
    \legend{IP, LK, FB}

\end{axis}
\end{tikzpicture}
\begin{tikzpicture}
\begin{axis}[
    width = 0.33\linewidth,
    title={Right Camera},
	xlabel={Trajectory length [frames]},

    xmin=11, xmax=27,
    ymin=70, ymax=95,
    xtick={5,10,15,20,25},

    legend pos=north west,
    ymajorgrids=true,
    grid style=dashed,
]

\addplot[
    color=blue,
    mark=square*,
    ]
    coordinates { (5,  73.69) (7,  71.62) (9,  74.75) (11, 74.45) (13, 73.54) (15, 72.72) (17, 73.54) (19, 73.77) (21, 75.67) (23, 73.34) (25, 71.33) (27, 70.37) };
\addplot[
    color=red,
    mark=*,
    ]
    coordinates { (5,  73.77) (7,  77.47) (9,  81.09) (11, 84.62) (13, 82.44) (15, 85.04) (17, 86.54) (19, 87.12) (21, 85.66) (23, 87.29) (25, 84.94) (27, 86.52) };
\addplot[
    color=green,
    mark=triangle*,
    ]
    coordinates { (5,  72.55) (7,  80.92) (9,  82.92) (11, 83.38) (13, 85.80) (15, 84.58) (17, 85.31) (19, 86.25) (21, 87.90) (23, 87.64) (25, 85.37) (27, 87.70) };

\end{axis}
\end{tikzpicture}
\begin{tikzpicture}
\begin{axis}[
    width = 0.33\linewidth,
    title={Both Cameras},
	xlabel={Trajectory length [frames]},

    xmin=11, xmax=27,
    ymin=70, ymax=95,
    xtick={5,10,15,20,25},

    legend pos=north west,
    ymajorgrids=true,
    grid style=dashed,
]

\addplot[
    color=blue,
    mark=square*,
    ]
    coordinates {(5,  72.62) (7,  78.25) (9,  80.20) (11, 80.81) (13, 79.54) (15, 79.80) (17, 78.09) (19, 79.78)  (21, 79.45) (23, 78.70)  (25, 79.74)(27, 77.85)};
\addplot[
    color=red,
    mark=*,
    ]
    coordinates { (5,  73.17) (7,  80.40) (9,  82.89) (11, 82.49) (13, 83.96) (15, 84.97) (17, 86.07) (19, 85.90) (21, 86.82) (23, 85.52) (25, 85.64) (27, 85.18) };
\addplot[
    color=green,
    mark=triangle*,
    ]
    coordinates { (5,  78.08) (7,  80.51) (9,  82.97) (11, 85.98) (13, 85.04) (15, 86.78) (17, 86.08) (19, 87.05) (21, 88.19) (23, 87.43) (25, 87.04) (27, 87.35) };

\end{axis}
\end{tikzpicture}

	\caption{

	2D trajectory accuracy Accuracy of 2D trajectory extraction algorithms from left video, right video and both videos for different 2D trajectories: IP, LK and FB}
	\label{fig:IP_LK_FB_Accuracies}
\end{figure*}

The optimum trajectory length was 21 or 23 for LK and FB. Figure~\ref{fig::barChartTrajectoriesLeftRightBoth} compares the best results obtained from left, right and both cameras. As it can be seen, there is no significant difference between them. In other words, adding up trajectories seen by the left and right cameras did not improve the results.

\begin{figure}[!htbp]
	\centering

\begin{tikzpicture}
\begin{axis}[
	width=0.7\linewidth,
	x tick label style={
		/pgf/number format/1000 sep=},
	ylabel={Accuracy},
	xmin=1, xmax=4,
   	ymin=70, ymax=95,
    	xticklabels={IP, LK, FB},
	ytick={70, 75, 80, 85, 90, 95},
	enlargelimits=0.05,
	legend style={at={(0.5,-0.2)},
	anchor=north,legend columns=-1},
	ybar interval=0.5,

\addplot[color=red, fill]
	coordinates {(1, 79.12) (2, 87.90) (3, 87.90) (4,90)};
\addplot [color=green, fill]
	coordinates {(1, 75.67) (2, 87.12) (3, 87.90) (4,90)};
\addplot [color=blue, fill]
	coordinates {(1, 80.81) (2, 86.82) (3, 88.19) (4,90)};
\legend{Left,Right,Both}
\end{axis}
\end{tikzpicture}
	\caption{

	The accuracy for left, right and both cameras (best seen in color). The stacking of left and right 2D trajectories barely improve the result.}
	\label{fig::barChartTrajectoriesLeftRightBoth}
\end{figure}

\subsection{Effect of Shape Descriptor}

\begin{figure}[!htbp]
\centering
\begin{tikzpicture}
\begin{axis}[
    width = 0.8\linewidth,

    xlabel={Encoding Algorithm},
    ylabel={Accuracy [\%]},
    xmin=1, xmax=7,
    ymin=70, ymax=95,
    xtick={1,2,3,4,5,6,7},
    xticklabels={$D_1$, $D_2$, $D_3$, $D_4$, $D_5$, $D_6$, $D_7$ },

    legend pos=south east,
    ymajorgrids=true,
    grid style=dashed,
]
\addplot[color=red, mark=*]
	coordinates { (1, 84.50) (2, 85.80) (3, 85.30) (4, 84.84) (5, 84.08) (6, 84.79) (7, 82.10)};
\addplot[color=blue, mark=triangle*]
	coordinates { (1, 85.72) (2, 87.46) (3, 87.95) (4, 88.42) (5, 85.68) (6, 86.18) (7, 83.15)};
\addplot[color=green, mark=square*]
	coordinates { (1, 84.37) (2, 86.48) (3, 87.07) (4, 88.55) (5, 88.21) (6, 86.44) (7, 84.96)};
\addplot[color=cyan, mark=x]
	coordinates { (1, 84.54) (2, 86.94) (3, 89.09) (4, 88.42) (5, 87.11) (6, 86.20) (7, 85.43)};
\legend{Trajectory Length 11,Trajectory Length 13, Trajectory Length 15,Trajectory Length 17}
\end{axis}
\end{tikzpicture}

\caption{
The effect of encoding on the performance of Farnback trajectories (best seen in color). The concatenation of higher order derivatives should improve performance, but after 4th derivative the noise level outperforms the benefits.}
\label{fig::encodingEffectOnPerformance}
\end{figure}

\begin{table*}
  \centering
  \caption{Results of the proposed shape descriptor algorithm on 2D Trajectory (Accuracy \%)}
  \label{tab:TrajectoryEncodingImprovementResults}
  \begin{tabular}
    {cccccccc}
    \toprule
  	& \multicolumn{7}{c}{Trajectory Shape Descriptor} \\
	 	 \cmidrule(lr){2-8}
    	Length  &   $D_1$&  $D_2$ &    $D_3$   &   $D_4$   &  $D_5$ & $D_6$& $D_7$ \\
			\cmidrule(lr){1-1}  \cmidrule(lr){2-8}

 	        11  &    84.50 &    85.80 &    85.30 &   84.84 &  84.08 & 84.79& 82.10 \\
    			13  &    \textbf{85.72} &    \textbf{87.46} &    87.95 &   88.42 &  85.68 & 86.18& 83.15 \\
    			15  &    84.37 &    86.48 &    87.07 &   \textbf{88.55} &  \textbf{88.21} & \textbf{86.44}& 84.96 \\
    			17  &    84.54 &    86.94 &    \textbf{89.09} &   88.42 &  87.11 & 86.20& \textbf{85.43} \\

    \bottomrule
  \end{tabular}
\end{table*}

The proposed trajectory shape descriptor in this paper has improved the classification results. Table~\ref{tab:TrajectoryEncodingImprovementResults} shows the effect of the new algorithm on the accuracy. In the absence of noise, higher order derivatives might provide new information. So, higher order descriptors should produce better results in general. However, in practice the effect of noise and outliers is amplified by the derivatives. Besides, human activities do not have very complex motions. As a consequence, the accuracy has a local maximum bound. Table~\ref{tab:TrajectoryEncodingImprovementResults} and Figure~\ref{fig::encodingEffectOnPerformance} illustrate this effect. As it can be seen, $D_3$ and $D_4$ produced the best accuracy for trajectories, with length 17 and 15, respectively. As expected, higher order derivatives did not improve the performance.

\subsection{Disparity-Augmented Trajectories}
\label{3dExperiments}
\begin{figure}[!htbp]
	\centering
	\begin{tikzpicture}
		\begin{axis}[
				width = 0.9\linewidth,

				xlabel={Trajectory Length },
				ylabel={Accuracy [\%]},
				xmin=9, xmax=23,
				ymin=86, ymax=92,
				xtick={9, 13, 17, 21},

				legend pos=south east,
				ymajorgrids=true,
				grid style=dashed,
				]
				\addplot[color=red, mark=*]
				coordinates {(9, 88.9815) (11, 90.0926) (13, 89.4444) (15, 90.3704) (17, 89.9074) (19, 90.6667) (21, 89.2256) (23, 90.5741)};

				\addplot[color=blue, mark=triangle*]
				coordinates {(9, 89.7222) (11, 90.8333) (13, 88.7963) (15, 90.6481) (17, 91.4815) (19, 91.3889) (21, 91.8519) (23, 90.9259)};

				\addplot[color=green, mark=square*]
				coordinates {(9, 88.8889) (11, 89.2593) (13, 86.8519) (15, 89.9074) (17, 90.5556) (19, 91.8519) (21, 90.4074) (23, 89.537)};

				\addplot[color=cyan, mark=x]
				coordinates {(9, 88.7037) (11, 89.5370) (13, 87.8704) (15, 89.7222) (17, 88.8889) (19, 91.1111) (21, 90.1852) (23, 91.3889)};

				\addplot[color=magenta, mark=o]
				coordinates {(9, 88.4259) (11, 87.4074) (13, 87.3148) (15, 89.2593) (17, 89.3519) (19, 90) (21, 90.8333) (23, 91.0185)};

				\legend{$D_1$, $D_2$, $D_3$, $D_4$, $D_5$}
		\end{axis}
	\end{tikzpicture}

	\caption{

	Disparity-augmented trajectories accuracy. The effect of trajectory length on the accuracy of different encoding algorithms. }
	\label{fig::allTrajectories}
\end{figure}

Table~\ref{tab::disparityResutFinal} summarizes the obtained results for disparity-augmented trajectories. Each row represents a trajectory length while each column represents an encoding algorithm. We have tested trajectory lengths that range between 9 and 27, and encoding up to the fifth degree. As it can be seen, the added disparity information increased the accuracy by around 2\% in all cases. The best obtained result was for trajectory length 19 and encoding degree three. The general trend is that increasing the length of trajectory increases the accuracy of the classification. This trend is more obvious on Figure~\ref{fig::allTrajectories}. The best results (91.85\%) were obtained with $D_2$ and $D_3$ encoding, at trajectory lengths of 21 and 19, respectively.

\begin{table*}
\centering
	\caption{results of disparity-augmented trajectories for human activity recognition}

\label{tab::disparityResutFinal}
\begin{tabular}{cccccc}
	\toprule
	& \multicolumn{5}{c}{Trajectory Shape Descriptor} \\
	  \cmidrule(lr){2-6}
	Length &  $D_1$  &   $D_2$  &  $D_3$   &  $D_4$  & $D_5$    \\
	\cmidrule(lr){1-1}  \cmidrule(lr){2-6}

	9 	          & 88.98\% &   89.72\%  &  88.89\%   &   88.70\%  & 88.43\%  \\
	11 	          & 90.09\% &   90.83\%  &  89.26\%   &   89.54\%  & 87.41\%  \\
	13	          & 89.44\% &   88.80\%  &  86.85\%   &   87.87\%  & 87.31\%  \\
	15	          & 90.37\% &   90.65\%  &  89.91\%   &   89.72\%  & 89.26\%  \\
	17	          & 89.91\% &   91.48\%  &  90.56\%   &   88.89\%  & 89.35\%  \\
	19	          & \textbf{90.67}\% &   91.39\%  &  \textbf{91.85}\%   &   91.11\%  & 90.00\%  \\
	21	          & 89.23\% &   \textbf{91.85}\%  &  90.41\%   &   90.19\%  & 90.83\%  \\
	23	          & 90.57\% &   90.93\%  &  89.54\%   &   \textbf{91.39}\%  & \textbf{91.02}\%  \\
	\bottomrule
\end{tabular}
\end{table*}

Figure~\ref{fig::confusionMatrix} illustrates the confusion matrix of a sample test. Each row represents an actual class and each column represents a predicted class. The number of correct classifications is normalized between zero and one. It is also worth noting that the classes in our dataset are balanced, i.e., the number of samples for each activity classes is the same for all classes. The misclassified instances from the matrix give interesting information about the behavior of trajectories for HAR. For example, the most confused classes in this figure are ``pointing'' and ``raise hand''. The fact that for pointing to something, one should raise his/her hand shows that trajectories are capable of finding this similarity, but they are unable to distinguish between them in some cases. Another example is the classes ``kicking a fixed object'' and ``kicking the ball''. These classes have very similar motions and hence, they are expected to be confused by any motion-based HAR method.

From another viewpoint, it can be assumed that human activities have no precise definitions. In particular, many human activities do have some overlaps. For example, raising hand to point to something or waving. So, it is evident that there is a conceptual overlap over the definition of these classes and it is not easy to separate them conceptually.

\begin{figure*}[!htbp]
	\centering
	\includegraphics[width=1.0\linewidth]{confusion_matrix-3}
	\caption{

	The confusion matrix. Sample confusion matrix for 27 classes (indexed a to z and A). Each row represents the actual class, and each column is the predicted class.}
	\label{fig::confusionMatrix}
\end{figure*}

\subsection{Time measurements}
Our comparisons have shown that our disparity-augmented trajectory (DAT) method is faster than trajectory aligned methods (see Table~\ref{tab::timing}).
To test the time performance, five different random samples from the dataset were selected. Each reported time is the average of ten different runs. As it can be seen, the speed up gains vary between 1.5 to 4.5 times faster, depending on the selected activity samples. Overall, our proposed method is more than twice faster than the methods based on dense trajectories, as we are using sparse features.

\begin{table*}
\centering
\caption{Time improvements obtained by using our method over trajectory aligned descriptors for different random samples, taken from our dataset.}
\label{tab::timing}
\begin{tabular}{lcccccc}
\toprule
Method	 &   S1   &  S2 & S3 & S4 & S5 & sum \\
\midrule
DAT(our method)		 &   19.67s   & 32.13s  &  7.33s & 42.70s & 13.09s & 114.92s \\
Trajectory Aligned    &  46.89s & 51.95s & 33.68s & 66.17s & 41.31s & 240.00s \\
\midrule
Speed up &  238\%	  &  161\%  &  459\%  & 155\%  & 311\% & 209\%  \\
\bottomrule
\end{tabular}
\end{table*}

\subsection{Comparison
Table~\ref{tab::comparison} shows the performance of our proposed method compared to the state of the art. The closest works to DAT are 2D dense trajectories~\cite{wang2013action} and 3D trajectories~\cite{koperski20143d}.
We applied the algorithm proposed in~\cite{wang2011action} on sparse feature points and the result reported as sparse trajectories in Table~\ref{tab::comparison}. As it can be seen, our proposed method was able to outperform both dense and sparse trajectory methods, with a good margin. Moreover, the proposed method produced better result compared to HOG, and competitive results to HOF and MBH. It should be noted that HOG, HOF and MBH need more computation time in comparison with our disparity-augmented trajectories.

Koperski et al.\cite{koperski20143d} used depth information to create 3D trajectories. They ran their tests on \emph{MSR DailyActivity 3D} dataset, which has similar setting as our dataset, but recorded with an RGB-Depth camera. Because we are using disparity and not depth, it is not possible to run their algorithm on our dataset, and we cannot run our method on their dataset as well. Just for comparison, we reported their results in Table~\ref{tab::koperski}. As it can be seen, they could not improve the performance of 2D trajectories by using 3D data only. They only improved the performance by combining 2D and 3D data. This confirms again the effectiveness of our proposed trajectory shape descriptor.

\begin{table}
\centering
\caption{Comparison of our method against other state-of-the-art methods}
\label{tab::comparison}
\begin{tabular}{rlc}
\toprule
& Method					& Accuracy  \\
\midrule
\multirow{3}{*}{Trajectory based}
& Sparse Trajectories   &   87.80\% \\
& Dense Trajectory      &	88.74\% \\
& \textbf{DAT} (Ours)	&	91.85\%	\\
\midrule
\multirow{3}{*}{Trajectory aligned}
& HOG                   &	89.54\%	\\
& HOF					&	92.72\%	\\
& MBH					&	92.22\%	\\
\bottomrule

\end{tabular}
\end{table}

\begin{table}
\centering
\caption{3D trajectories proposed by Koperski et al.~\cite{koperski20143d}.}
\label{tab::koperski}
\begin{tabular}{lc}
\toprule
Method			& Accuracy  \\
\midrule
2D TSD  		&  78\% \\
3D TSD   		&  74\% \\
2D TSD+3D TSD	&  85\%	\\
\bottomrule
\end{tabular}
\end{table}

\begin{table}
\centering
\caption{Comparisons of the obtained results on Hollywood 3D dataset. The first 5 rows are our DAT results with different trajectory lengths.}
\label{tab::hollywood3D}
\begin{tabular}{lc}
\toprule
length	& Accuracy  \\
\midrule
7		&  21.50\%  \\
9   	&  22.73\%  \\
11		&  \textbf{23.78\%}	\\
13		&  20.79\%	\\
15		&  19.80\%	\\
\midrule
\cite{wang2013dense} & 20.8\%\\
\cite{hadfield2017hollywood}    &  21.8\% \\
\bottomrule
\end{tabular}
\end{table}

We have also tested our method on Hollywood 3D dataset, but have used their disparities only. Table~\ref{tab::hollywood3D} shows our obtained results and their comparisons with the other relevant methods. Note that our proposed method was not designed to cope specifically with random camera motions and/or rotations, as they can degrade the trajectory extraction drastically.
As it can be seen, our method still yields superior results compared to the trajectory aligned descriptors proposed in \cite{wang2013dense} and reported in \cite{hadfield2017hollywood}. Our method also outperforms the method proposed by \cite{hadfield2017hollywood} in terms of accuracy.

\section{Conclusion}
\label{sec::conclusion}
We have presented and compared three popular trajectory-based human action recognition methods. We have also enhanced the conventional trajectory encoding algorithms by considering higher order derivatives of individual trajectories.
Furthermore, we have proposed a new method based on disparity-augmented trajectories for video content analysis. Because disparities carry the scene's three-dimensional clues, we anticipated an improvement in the HAR performance.
In particular, we have fused the disparity information with motion-based features.
We have obtained improved results on HAR, when compared to traditional trajectory-based methods, at a lower computational cost.

Furthermore, we have demonstrated that trajectories are useful for video content analysis in general, and for human activity recognition in particular. The proposed shape encoding algorithm has improved the accuracy of activity recognition by about 1.5\%. The disparity information added to trajectories has also enhanced the results by another 2.5\%.

We have also discussed some limitations associated with trajectory-based activity recognition. Activities that are similar, from the movement point of view, might be confused. We believe that some actions are conceptually overlapping and are hard to be distinguished, when using the human movement information only.


Protected: Quality Matters Standard 1: A Review May 20, 2014 - There is no excerpt because this is a protected post.
Open Educational Resources – Global opinions September 27, 2012 - The following video presents ideas and opinions about Open Educational Resources from educators around the globe.
Primary Sources: Free digital content from the Library of Congress May 12, 2012 - The Library of Congress American Memory Collection is a gold mine of free for educational use images, audio, video, manuscripts and more. Check out the American Memory collection with information especially for educators.
Math Open Source Resources April 10, 2012 - National Library of Virtual Manipulatives Digital manipulatives for mathematics. Maths: New Zealand Maths—Digital Learning Objects Digital learning objects for algebra, geometry, measurement, number, and statistics.


In Wire Technologies Quality is top priority. All cables and wires from Wire Technologies must meet the company's own as well as customer-specific quality standards.
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If you have special requirements or wishes, Wire Technologies also manufactures individual cables and wires. In cooperation with our customers we develop solutions and optimizations, we support you in all steps and we invest our experience.


NXT UK Takeover: Blackpool is recapped in a series of clips.
Good match. This was fun, as is usually the case with a Ligero match.
Pretty good match. There were moments when it felt like they were struggling a little to work together, but overall I enjoyed this match. Dawn got off to a good start, but after a regroup, Jinny started using her wits to mount a comeback.
Travis Banks worked for ten years for an opportunity to compete on a show like NXT UK Takeover, but Jordan Devlin took that away with his attack. Next week, Banks will have his revenge.
Great match. I think Aichner and Barthel are the tag team of the month. They looked precise and dominant in nearly everything they did. Not to be outdone, Andrews and Webster had some breathtaking moments of their own. This has been a great feud for all four men, and I think I could watch any combination of this matchup many more times.
As opposed to the usual post-Takeover shows, this wasn't just a recap of the big event with a couple of okay matches. Tonight's show was quite entertaining, and the main focus was on the matches taking place tonight. I liked it.
High flying, big powered, and a lot of fun. Great match.


South By Southwest, or SXSW, kicked off in Austin last week and four Slingshotters were there to experience the digital creativity and cutting-edge technology that the festival has become known for. SXSW provides a great chance to see how technology is changing our industry so we can be forward-thinking for our clients.
Julie Bowman and Clay Coleman attended creative-focused sessions while Whitney Redman and Kristy Ladner focused on emerging technology. Below they share some of their favorite nuggets of information.
Technology should not overpower the concept; it should bring out what's best about an already good idea. Like Ansel Adams once said, "There is nothing worse than a sharp image of a fuzzy concept".
When your message makes someone feel something (anything), they remember. Emotional advertising is powerful, but it must be authentic.
Be curious about as many subjects as possible. The power of inquisitiveness can change your life; you never know what it will inspire.
Hulk Hogan is still strong.
Nobody follows a pessimist. People want to be inspired.
In the new Talent Economy, it's not about where you go to work, it's about who you go to work with. The company is no longer enough; it's the existing people that attract new talent.
No one likes to be oversold. Explain yourself then stop talking and listen.
Body language can tell you anything you need to know. Is someone lying to you? Follow their eyes. If they look up, they're sourcing the creative part of the brain. When people look down, they're sourcing the memory part of the brain.
The idea of FOMO (Fear Of Missing Out) is actually scientific and not just a funny word to say! When we see something on social media, the feeling of FOMO disrupts the hypothalamus (the place in our brain that links the nervous system to the endocrine system via the pituitary gland) and creates adrenaline. This makes you want to go and do the same thing!
If you can take a normal task and make it at least two seconds shorter, people will latch on. Remember the simple app YO? It took alerting/contacting to a new level. It spread the word on Israeli communities in danger– in real time.
25% of users abandon a site that takes 4 seconds or longer to load. Performance matters.
While the Internet of Things is booming, it needs to become person-centric (the Things before the Internet). Solutions need to start providing actionable insights for consumers. For example, implication of taking X number of steps. Consumers don't want data from IoT devices. They want that data turned into recommended actions to better their lives!
If you want to see cool and innovative technology, find the Japanese section at the trade show.
There's no shortage of branding opportunities at SXSW.
This year's SXSW was more mind blowing for me than years past with legit presentations on artificial intelligence and mind clones, holograms, beacons, augmented reality, robots, 3D audio, drones, and virtual reality. The biggest takeaway for us as an agency is really the level of immersive storytelling that we can begin telling for our clients.
Adding touch, texture, motion, smell, etc. to Virtual Reality makes the experience that much more real. The Samsung Insurgent VR experience added vibrations and wind to make me really feel like I was there (see pic).
3D printing allows for tangible storytelling as story worlds can come to life and unlock new adventures.
Live-streaming is the next genre of mobile-social apps that will become mainstream over the next year. Apps like Meerkat and Periscope allow you to live stream wherever you are and whatever you're doing to the Twitterverse. Think of the implications for telling live stories from travel destinations, concerts, sporting events, breaking news, etc.


I am not sure what it is about Spaceship Earth, but I really enjoy taking photos of the attraction. Maybe it is the curve of the geodesic sphere, the texture of the triangles or the monorail circles around it as it arrives at EPCOT. Like most things in Disney it is amazing how different Spaceship Earth looks during the day versus the night.
This photo is of Spaceship Earth taken across the World Showcase Lagoon. It is amazing that the fireworks barges brought out in a mere few hours to the middle of the lagoon to present "IllumiNations: Reflections of Earth". The show uses fireworks, pyrotechnics, laser lights, fountains, and fire to create a visual production on the park's World Showcase Lagoon.
It was a beautiful clear sky, but that was a problem, it was too clear, not a single cloud in the sky. I took this opportunity to add the cloud effect in post production in Photoshop.


text:
package raftgorums

import (
	"errors"
	"time"

	"github.com/Sirupsen/logrus"
	"github.com/relab/raft"
)

// Config contains the configuration needed to start an instance of Raft.
type Config struct {
	ID uint64

	Servers []string
	// IDs of server which forms the initial cluster. IDs start at 1, which
	// refers to the first server in Servers.
	InitialCluster []uint64

	Storage raft.Storage

	Batch            bool
	ElectionTimeout  time.Duration
	HeartbeatTimeout time.Duration

	EntriesPerMsg uint64
	// CatchupMultiplier is how many times more EntriesPerMsg we are allowed
	// to use when doing a catch up, i.e., EntriesPerMsg*CatchupMultiplier.
	CatchupMultiplier uint64

	Logger         logrus.FieldLogger
	CheckQuorum    bool
	MetricsEnabled bool
}

func validate(cfg *Config) error {
	if cfg.ID == 0 {
		return errors.New("invalid id")
	}

	if cfg.Logger == nil {
		cfg.Logger = logrus.New()
	}

	if cfg.HeartbeatTimeout == 0 {
		cfg.HeartbeatTimeout = 50 * time.Millisecond
	}

	if cfg.ElectionTimeout == 0 {
		cfg.ElectionTimeout = 250 * time.Millisecond
	}

	if cfg.EntriesPerMsg == 0 {
		cfg.EntriesPerMsg = 64
	}

	if cfg.CatchupMultiplier == 0 {
		cfg.CatchupMultiplier = 160
	}

	return nil
}

redpajama_set_name: RedPajamaGithub


This data relates to the UK only. Stay tuned for the US version.
a new role for the policy expert?
2018 was a good time to be a populist. The year was marked by the continuing march of this movement worldwide.
The rise of the gilets jaunes in France. The election of Bolsonaro in Brazil. The Five Star Movement and the Northern League in Italy. The continuing assault on democracy in Hungary and in Poland.
In the UK, discussions around identity and immigration remain highly emotional, alongside issues like anti-Semitism, benefits, food banks, homelessness, crime, international aid or climate change.
The Brexit debate has tested the political system to breaking point. No-one has a clear vision of the way forward – but what is becoming painfully evident is that the status quo is no longer an option.
The changes in our politics and in society have prompted think tankers to reflect on their role in the 21st century. Not least of whom Robin Niblett of Chatham House, who suggested international think tanks should be more proactive in promoting the principles they believe in.
Those of you familiar with our work will know that we believe the rise of social media has irrevocably shifted the policy-making dynamic. It has turned the public into an active player that must be taken into account.
Add to this an increasingly active regulator, a probing media, and the backdrop of a new socio-political cycle coupled with a technological revolution – and the scale of the challenge emerges. In this new fluid landscape, what can the public tell us about the role for the modern think tank? We went to Watford, a key marginal seat, to establish the current state of play.
This year's research sought to explore a number of questions to help our understanding of the political and societal environment within which policy experts operate.
What are the public's expectations of policy experts?
How can policy experts be more effective communicators?
How have recent events affected public perceptions of accountability?
We interviewed n=2,000 UK adults aged 18+ by online survey. The sample was nationally representative by age, gender and region.
Two-thirds of the British public (68%) are concerned about the rise of political extremes.
4 out of 5 of those interested in politics (85%) want policy experts to challenge fake news.
Half of those who work in politics or policy (48%) trust their heart over their head on political issues.
80% of the UK public think accountability is important.
But only 41% think we have accountability over those that influence our politics.
The public want experts to challenge fake news and help them make sense of current affairs. Those that are afraid of the rise of political extremes are the most likely to want to see that expert engagement.
Our research shows that two-thirds of the UK public are concerned about the rise of political extremes. This is true across all segments of the population, but most pronounced among the politically interested, those with university degrees, and the retired.
Crucially, these same segments are also those most likely to want policy experts to challenge news stories that are not true. Over six-in-ten of the UK population want experts to challenge fake news, rising to over eight-in-ten among those interested in politics.
Beyond standing up to fake news, respondents want policy experts to engage with them.
Half of the UK public wants experts to help them understand current affairs issues – again higher among people interested in politics.
The demand exists. The question is, how do we make it constructive and meaningful?
If we truly want to encourage an informed public debate, we need to recognise the UK public as they are. Warts and all.
The reality is that we, the public, are not good at recognising our own shortcomings.
Last year, We are Flint's research explored if the UK public thought people needed to understand government policy better. Just under three-in-four agreed. This year, we tested whether they were including themselves in this assessment.
Only one-in-four said they did not have a good understanding of government policy. In other words, we're very good at pointing the finger at other people, less good at pointing it at ourselves.
Bobby Duffy's Perils of Perception research sheds light on this phenomenon. He found that when challenged about immigration statistics, many respondents simply rejected the official figures if they didn't fit their world view.
Those familiar with cognitive science will not be surprised.
If policy experts are to help the public understand current affairs and encourage an informed public debate, we need to recognise the power of perception.
Cognitive gaps cannot be addressed by simply presenting facts. We need to frame the issues.
We need to reconsider the premise of our communications: the notion of the rational citizen who ingests complex arguments and formulates political opinions accordingly.
Tellingly, this is not just true of the general public. We found that the closer respondents were to the heart of politics, the more they reported that emotion played a role in shaping their political views.
What may seem at first to be a surprising admission of emotional honesty by political and policy professionals, may simply be evidence of heightened self-awareness. The public are almost certainly as prone to emotion as those who work in politics or policy.
In communicating policy, think tanks need to recognise the limits of the traditional approach – i.e. presenting facts and statistics, hoping they will speak for themselves.
In highlighting these limits, we are not making the case for bleeding-heart communications. We are simply making a pragmatic case for the need for the human to find a place in policy communications.
There is no other way to counter the populist monopoly on feeling.
The need to engage is about more than a sense of moral duty. It should also be about a sense of self-preservation for those who seek to influence policy.
Last year, we explored questions around trust in think tanks. Only a quarter of people interested in politics reported trusting what think tanks have to say, and four-in-ten believed think tanks had the interests of the elite at heart. In other words, the state of play isn't great.
This year we explored the question of accountability over policy influence. We recognise that not all think tanks see themselves as influencers of policy. But when it comes to public trust, it is perception that counts.
While eight-in-ten Brits think organisations who influence government need to be accountable, only four-in-ten think accountability is a reality. A 39-point gap. Among those interested in politics, the gap rises to 48 points.
A different story emerges for those who work in politics and policy. They are both less likely to place importance on accountability, and they are much more likely to say that political influencers are already being held accountable.
This gap in perception should be food for thought for those involved in influencing policy, whose business it is to engage with policy makers. The public outcry against the Institute for Economic Affairs, and the recurrent "Who funds you?" requests, shows think tanks increasingly under scrutiny.
Society does not write a blank cheque. Organisations need to earn the right to do what they do: they need a metaphorical licence to operate. Especially when it comes to influencing power.
Examples abound in the corporate world where companies and industries did not maintain their licence to operate. Uber quite literally lost their licence to operate in London, forcing it to make changes to its practices to be reapproved. The sugar industry has been fighting a perception war for some years now, and lost a significant battle with the introduction of a sugar tax. And fracking as an industry has never had it easy.
Today we see plastics, e-cigarettes, and social media companies facing challenges to their operating models. It is not clear whether policy influencers are at crisis point yet, but the warnings lights are starting to flash.
There is no single unanimously trusted source of policy ideas across any of the groups we tested. That much is clear.
Among the UK public, think tanks come some way below local community organisations and academia as trusted sources of policy ideas. And think tanks are neck-and-neck with the trade unions, NGOs and charities, and online movements.
Perhaps most worrying for think tanks is that people who work in politics or policy are only marginally more likely to trust them to come up with ideas to improve the country than the civil service. The business of ideas is close to being trumped by the very organisation it is intended to support.
The lack of trust in institutions to come up with ideas to improve the country has left the field wide open.
And in that space "people like me" dominate. In every segment, this populist feeling is mimicked.
Among insiders – those that work in politics and policy – the story is no different.
No-one is seen as coming up with ideas for a better Britain.
Our findings on how people like to receive political or policy ideas opens an interesting twist on what engagement could come to mean.
This year's research explored the formats which people engage with most, in the context of political or policy ideas. Out of the twenty formats tested – which included PDF reports, events, mainstream news, social media and infographics – the top five were perhaps unsurprising.
Mainstream news retained a place at the top table, though there was a marked difference between online and print – the latter on a downward trend, the former more stable. Documentaries were also a popular format. Most notable, however, was the prominence of peer conversation and social media. And the clear preference for social media among younger audiences foreshadowed what policy communication may look like in 5-10 years time.
The question is this: in a world where people prefer talking things through with people they trust, is there an opportunity for a rethink of what engagement means?
Rather than playing a paternalistic role of bestowing knowledge on the public, could think tanks could have more of a role as convenors? Generating ideas, framing the debate, and then orchestrating an informed public dialogue. The public wants policy experts to speak out and engage. But they need to speak in terms which will resonate with humans – public and policy makers alike – with all their foibles.
Yes, policy experts will win the intellectual argument all day long, based on their vast bank of facts and statistics. But if their facts challenge an individual's pre-existing frames – be they policy maker or public – the facts will be dismissed almost every time.
This tension lies at the heart of the frustration which is driving populism – a gut-feel that the facts and statistics are not reflecting people's own lived experience.
If Watford is anything to go by, the human experience needs to have a voice.
What role is there for think tanks?
How can think tanks tap into the human?
What are the risks for think tanks?
We've presented the full findings to communicators and researchers at policy organisations like IPPR, Centre for Policy Studies, RUSI, and the Institute for Government. Get in touch with Tim Moots if you'd like to arrange a complimentary presentation of the full results.
We would like to thank the many individuals who have supported us – including challenging our thinking – over the past few years. Special mentions to Andrew Marshall, Benedict McAleenan, Clara Widdison, David Wastell, Emily Duncan, Enrique Mendizabal, Helen Dempster, Joe Miller, John Schwartz, Joseph Barnsley, Katy Murray, Laura McDonald, and Madeleine Burns. Credits to Katie and Andy for the design of this site, Vitaliy for build, and Tim for keeping us all in line.


I have to thank the Stuff You Missed in History Podcast for reminding me about this one, They recently rebroadcast a show about Albert J. Tirrell's murder trial – the first time in America the Sleepwalking Defense was used. You can listen to that podcast here if you want more details about the case than I'm going to go into.
Let me take a step back for a second. Tirrell was accused of the violent murder of his mistress on October 27, 1845. He was seen with her earlier in the day, and bought a ticket out of town that evening. When the case came to trial, his defense was that he didn't kill her, but if he did he was sleepwalking and not responsible for the crime. The case against him was very circumstantial. Remember crime scene investigations, finger printing and lots of other investigative tools we take for granted now just didn't exist. Had they, the government likely would have gotten finger prints off the bloody knife left near the body. Anyway, the jury acquitted. They said that the sleepwalking defense played no part in their decision to find him not guilty. But, the sleepwalking defense was born.
How could this defense possibly work?
Sleepwalking is an altered state of unconsciousness where parts of the brain remain asleep but the person can still act. Sleepwalkers can get violent because the part of the brain that regulates conduct is still sleeping. Crazy weird but true.
Individuals with Lewey Body Dementia don't get the "I'm sleeping" cut off signal from the brain. I've watched my Dad, who was diagnosed with the disease in 2012, fall asleep in the car while we waited for my Mom to pick the ham up from the Honeybaked Ham store, unwrap an "imaginary" sandwich and eat it. See, before my Mom went into the store she asked him if she should bring him a ham sandwich. He said, "yes." He fell asleep in the car while we waited for her to get through the pre-Easter line. And his brain translated this conversation into "eating" that sandwich (including biting into it, chewing and swallowing) while he was asleep. Weirder still, he was "full" when he woke up and she offered him the actual sandwich. This sort of sleep disorder is a hallmark of Lewey Body Dementia.
In 2005, the Delaware Court stated "that sombolisim can be recognized as a defense to most criminal acts" in State v. Cabrera, 891 A.2d 1066. Many crimes require the accused intend the criminal conduct. If you pass out and are unconscious when you stumble into someone, you're generally not guilty of assault. "Generally" because if you are "unconscious" because of something you did like drink too much then the defense doesn't apply. If the crime requires "intent" like a murder or sexual offense, then there's an argument that the defendant wasn't "conscious" and couldn't have intended the conduct. Some states treat sleepwalking like insanity, in other words, the person didn't know or understand they were doing wrong. Others treat sleepwalking as a form of unconsciousness. Still other courts don't think the medical community has accepted the phenomenon to the point where the Court can except it as evidence.
But, as science progresses this seemingly crazy defense might actually get more traction. Until then, I thought I should note that in the vast majority of the cases I read on this defense, the defendant was still convicted.


Dark Souls: Black Iron Tarkus.
For "can't" you did pretty darn well, imho.
@captain: Surprisingly enough only 4~5 hours. I thought it would take longer because I can't "make" knight armor at all.
Cool! Take you long to do?


In case you missed it, Washington incoming freshman Nigel Williams-Goss finished his high school career with a standout performance in the Jordan Brand Classic. He led the West team to a 102-98 victory.
Late in the game, Williams-Goss made a steal and converted the turnover into a layup despite being fouled. He converted the ensuing free throw and his three-point-play gave the West a 99-96 lead with 28.5 seconds left.
Paul Biancardi, who is the director of recruiting at ESPN.com, says the Huskies are receiving a dynamic leader.
Solid showing by Washington seniors Abdul Gaddy and Aziz N'Diaye last week at the Portsmouth Invitational Tournament. They were two of 64 players invited to the tournament.
Gaddy received a bit of bad luck from the start. Oregon forward Arsalan Kazemi was originally assigned to his team, but decided not to attend. Gaddy's squad was absent of big-time stars. Still he put up respectable stats in three games.
Gaddy started every game and averaged 10.7 points, 6.3 assists, 4.3 rebounds, 2.0 steals, 3.0 turnovers and 31.3 minutes. His team went 0-3.
Meanwhile N'Diaye did his thing, which was provide a defensive presence in the middle and rebound. He also started every game and averaged 6.3 points, 8.0 rebounds, 2.3 blocks and 21.3 minutes. His team finished 2-1.
N'Diaye's team included Washington State senior Brock Motum who started one game. He averaged 8.6 points. 8.0 rebounds and 3.0 assists.
Other Pac-12 players at the tournament included Oregon's E.J. Singler and Tony Woods, Arizona's Mark Lyons and UCLA's Larry Drew II. Former UW player Elston Turner also competed.
No Pac-12 player was chosen to the 12-man all-tournament team. BYU's Brandon Davies was selected the tournament MVP.
— Sometimes a tweet won't do. Oregon State junior Eric Moreland felt the need to call a press conference today to announce he's staying in school. He was the sixth-leading scorer on a team that tied for last in the Pac-12 last season. He averaged 9.4 points, 10.6 rebounds and 2.5 blocks.
— Arizona freshman Grant Jerrett is considering turning pro.
— If Colorado junior Andre Roberson leaves school, then the Buffaloes will go from Pac-12 title contender to middle of the pack.
— New UCLA coach Steve Alford poached assistant David Grace away from Oregon State, which makes life hard on Beavers coach Craig Robinson who has a hole to fill on his staff before the big recruiting season begins in July.


At ITT Technical Institute-Austin, 92.0% percent of first-time undergrads receive financial aid, 52.0% receive grants and/or scholarships (an average of $3,182), and 84% receive loans ($8,521 on average). On-campus room and board costs about $7,119.
Taking into account total living expenses and financial aid, the average net cost of attending ITT Technical Institute-Austin is $22,430 per year.
Ask your friends about ITT Technical Institute-Austin!
Click Here for a map view of ITT Technical Institute-Austin & see nearby schools, housing availability, location restaurants, and more...!
Local newspaper: The Austin Chronicle .


Raidlight EazyFlask Pocket Soft Flask 600ml - Blue - trail running bottle.
Hands free hydration. Stop fumbling with your bottles and focus on your run. The RaidLight EazyFlask with straw makes staying hydrated easier and more convenient. With 600ml (20oz) of capacity you can carry 1200ml of fluid in your front bottle pockets for all your trail runs. The wide mouth top allows for easy refilling and rinsing.


text:
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Sudan's main pro-democracy faction agrees to participate in UN talks
Widespread condemnation after government websites in Ukraine are shut down by 'massive' cyber hack
NATO-Russia Council meets for a "not an easy discussion"
More drone strikes in Tigray even as government calls for dialogue
Europe mourns the death of European Parliament president, David Sassoli
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Turkish Foreign Minister assures Armenian NGOs border will be open sooner or later
Five representatives of Armenian NGOs currently visiting Turkey as guests of the Turkish think-tank TEPAV yesterday met the Turkish Foreign Minister Ahmit Davitogluy in Ankara. According to Hurriyet Daily News the Minister assured the visiting Armenians that Turkey's eastern frontier with Armenia will eventually reopen for cross-border traffic.
"The Turkish foreign minister is sure the border will open sooner or later, so we can come back to Turkey and visit historical sites," Arthur Ghazaryan of the Union of Manufacturers' and Businessmen of Armenia told the Hürriyet Daily News on Monday following a meeting with Turkish Foreign Minister Ahmet Davutoğlu in Ankara. A five-member Armenian group, including business and nongovernmental leaders, met with Davutoğlu and Foreign Ministry Undersecretary Feridun Sinirlioğlu to discuss the Turkish-Armenian normalization process and the currently stalled talks on the matter, participants told the Daily News.
"We asked the minister when the process will restart," said Mikayel Hovhannisyan of the Eurasia Partnership Foundation. "Unfortunately I did not receive any exact date but I received assurance that the Turkish side will implement necessary steps to that end."
The group told the foreign minister that Armenian society and even the international community were expecting Turkey to move on.
"We said the ball is in Turkey's court. Armenia is waiting for Turkey to play ball," said Ghazaryan. "Turkish-Armenian relations are like a train starting to move," said the Institute for Civil Society and Regional Development's Aghavni Karakhanian, another Armenian attending the meeting. "There is no reverse we can only go forward. We cannot stop the moving train."
The Armenians said they were impressed by the open and frank discussions at the ministry. Richard Giragosian of the Regional Studies Center said he was first impressed by the "amount of time" the ministry gave them and the fact the foreign minister was "very forthcoming." "I was impressed by the quality of Davutoğlu and his open and frank exchange with us."
The 1915 events were also discussed during the meeting. The visiting group said there was much more awareness in Turkey now compared to a couple of years ago. Giragosian said he told Davutoğlu the mental border was open between the two neighboring countries despite the sealed border – something the foreign minister agreed on, he added.
source: Hurriyet Daily News
photo: Turkish Armenian border; photo courtesy of Hurriyet Daily News
Borrell tells the European Parliament that the situation in Afghanistan was critical, but the EU will remain engaged
Borrell underlined that the European Union will make every effort to support the peace process and to remain a committed partner to the Afghan people. "Of course, we will have to take into account the evolving situation, but disengagement is not an option. We are clear on that: there is no alternative to a negotiated political settlement, through inclusive peace talks.
Nagorno-Karabakh becomes Russia's latest protectorate in the South Caucasus
Azerbaijan, Turkey, and Russia all gained something as a result of the second Karabakh war, while Armenia and Nagorno-Karabakh lost almost everything, says Benyamin Poghosyan in this op-ed
Benyamin Poghosyan
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redpajama_set_name: RedPajamaCommonCrawl


text:
Fact check: In 2016, Trump didn't tweet about replacing Scalia on Supreme Court
Camille Caldera
The claim: In 2016, President Trump tweeted that Obama 'should wait until he leaves office' to pick a Supreme Court justice
Despite calls from Democrats to delay the process until after the election, President Donald Trump has said he will announce a nominee to the Supreme Court on Saturday.
Some who appear to oppose that have shared a tweet on Facebook and Instagram that attempts to levy the president's own words against him.
The tweet claims to be from April 2016, the midst of a battle between President Barack Obama and Senate Republicans over confirming nominee Judge Merrick Garland to the high court in the months leading up to the presidential election.
"Obama should wait until he leaves office to pick another Justice! If he doesn't, he should be fired," the tweet reads.
The only issue? It isn't real.
Users who posted the tweet did not respond to requests from USA TODAY for comment.
Fact check:No guarantee Obama would've replaced Ginsburg with a progressive justice
No record of tweet in archive of tweets from Trump
Searches for the text of the tweet reveal there is no record of it in the Trump Twitter Archive. It also does not appear under a search of tweets on the day it purports to have been sent — April 3, 2016.
In fact, beyond a tweet about his death, Trump never took to Twitter to address the contentious fight to replace Justice Antonin Scalia.
The only tweet that comes up under the search "Garland," for example, is about Judy Garland, not Merrick Garland.
However, Trump did address the fight to fill Scalia's vacancy on Good Morning America in March 2016.
"I think they should wait until the next president and let the next president pick," he said at the time, according to Politico.
Fact check:False claim suggesting Trump nominated Biden to the Supreme Court started out as satire
Our rating: False
Based on our research, the claim that President Donald Trump tweeted that Barack Obama "should wait until he leaves office to pick another Justice" is FALSE. Trump never tweeted that.
Our fact-check sources:
Trump Twitter Archive, Searches for: "Obama should wait until he leaves office to pick another Justice! If he doesn't, he should be fired," 04/03/2016, "Supreme Court," and "Merrick Garland."
Donald J. Trump, Feb. 13, 2016, tweet
USA TODAY, Sept. 22, President Donald Trump to announce Supreme Court nominee to fill Ruth Bader Ginsburg's seat on Saturday
Politico, March 16, 2016, Trump: Senate should block Obama's Supreme Court nominee
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This fact check is available at IFCN's 2020 US Elections FactChat #Chatbot on WhatsApp. Click here, for more.


text:
Cannabinoids and multiple sclerosis
Roger G Pertwee
There is a growing amount of evidence to suggest that cannabis and individual cannabinoids may be effective in suppressing certain symptoms of multiple sclerosis and spinal cord injury, including spasticity and pain. Anecdotal evidence is to be found in newspaper reports and also in responses to questionnaires. Clinical evidence comes from trials, albeit with rather small numbers of patients. These trials have shown that cannabis, Delta(9)-tetrahydrocannabinol, and nabilone can produce objective and/or subjective relief from spasticity, pain, tremor, and nocturia in patients with multiple sclerosis (8 trials) or spinal cord injury (1 trial), The clinical evidence is supported by results from experiments with animal models of multiple sclerosis. Some of these experiments', performed with mice with chronic relapsing experimental allergic encephalomyelitis (CREAE), have provided strong evidence that cannabinoid-induced reductions in tremor and spasticity are mediated by cannabinoid receptors, both CB1 and CB2. Endocannabinoid concentrations are elevated in the brains and spinal cords of CREAE mice with spasticity, and in line with this observation, spasticity exhibited by CREAE mice can be ameliorated by inhibitors of endocannabinoid membrane transport or enzymic hydrolysis. Research is now needed to establish whether increased endocannabinoid production occurs in multiple sclerosis. Future research should also be directed at obtaining more conclusive evidence about the efficacy of cannabis or individual cannabinoids against the signs and symptoms of these disorders, at devising better modes of administration for cannabinoids and at exploring strategies that maximize separation between the sought-after therapeutic effects and the unwanted effects of these drugs, (C) 2002 Elsevier Science Inc. All rights reserved.
Pharmacology & Therapeutics
tetrahydrocannabinol
nabilone
experimental autoimmune encephalomyelitis
inverse agonist
CB2 receptors
control spasticity
adenylate-cyclase
urinary-incontincence
rat-brain
Pertwee, R. G. (2002). Cannabinoids and multiple sclerosis. Pharmacology & Therapeutics, 95(2), 165-174. https://doi.org/10.1016/S0163-7258(02)00255-3
Cannabinoids and multiple sclerosis. / Pertwee, Roger G.
In: Pharmacology & Therapeutics, Vol. 95, No. 2, 08.2002, p. 165-174.
Pertwee, RG 2002, 'Cannabinoids and multiple sclerosis', Pharmacology & Therapeutics, vol. 95, no. 2, pp. 165-174. https://doi.org/10.1016/S0163-7258(02)00255-3
Pertwee RG. Cannabinoids and multiple sclerosis. Pharmacology & Therapeutics. 2002 Aug;95(2):165-174. https://doi.org/10.1016/S0163-7258(02)00255-3
Pertwee, Roger G. / Cannabinoids and multiple sclerosis. In: Pharmacology & Therapeutics. 2002 ; Vol. 95, No. 2. pp. 165-174.
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The war in Syria has been going on for 7 years. Endless tragic news reports made people numb and indifferent. Just before Christmas, the conflict escalated in the city of Aleppo. Most NGO's were leaving the region, except for the Red Cross. New funds were needed. Urgently. Everyone knows the song "Let It Snow" from Dean Martin as one of the happiest Christmas songs of all time. They associate it with happiness, good times, snow and most of all celebrating Christmas together with their family. If there is one thing that the people in Aleppo weren't doing on the 24th of December, it was celebrating Christmas with their loved ones while eating a nice, fried turkey. By showing people horrible news footage on a very happy Christmas song, the Red Cross started a conversation and opened people's eyes. Donations went up by 270%.