text:
\section{Conclusion}

In this work, we have proposed a novel, non-Euclidean approach for the estimation of 3D shapes from single monocular 2D images.
In particular, we generalized the established active shape model approach to Kendall's shape space combining concepts from geometric statistics and computational differential geometry.
The resulting geometric model provides efficient, yet highly consistent estimation of 3D shapes due to a natural encoding of constraints.

We have demonstrated the performance of our approach in experiments on the reconstruction of human poses as well as head skeletons of basking sharks.
The advantages of the proposed scheme are particularly apparent in qualitative comparison to previous approaches that rely on assumptions of linearity.
While former approaches attained lower reprojection errors, the corresponding 3D shapes show defects like non-physiological distortions indicating a need for further domain-specific regularization.
For example, the convex relaxation of the ASM proposed in~\cite{zhou20153d} developed strong  asymmetries although basis shapes are symmetric.
In contrast, our geometric method yielded highly physiological results even in challenging situations where the target shape differed greatly from the training distribution.

In future work, we plan to extend our approach to more advanced camera models to be able to account for strong perspective effects.
Furthermore, while we use the 2D Kendall shape space distance as reprojection error, weighted or $\ell^1$-like extensions could be employed to incorporate uncertainty in 2D landmark detection or to increase robustness against outliers, respectively.

\paragraph{Acknowledgments}
We are grateful for the funding by Deutsche Forschungsgemeinschaft (DFG) through Germany's Excellence Strategy -- The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID:~390685689) and by Bundesministerium f\"ur Bildung und Forschung (BMBF) through BIFOLD -- The Berlin Institute for the Foundations of Learning and Data (ref.~01IS18025A and ref.~01IS18037A).
The basking shark work was funded in part by an HFSP Program Grant (RGP0010-2020 to M.N.D.).
We also want to thank the British Museum of Natural History and Zoological Museum, University of Copenhagen for providing basking shark specimens, Pepijn Kamminga, James Maclaine, Allison Luger and Henrik Lauridsen for help acquiring CT data, and Alex Mustard (Underwater Photography) and Maura Mitchell (Manx Basking Shark Watch) for granting us permission to use their underwater images of basking sharks.

\clearpage
\bibliographystyle{splncs04}

\section{Experiments}
\label{sec:experiments}

We perform qualitative and quantitative evaluation of the proposed Kendall shape space (\emph{KSS}) approach in experiments concerning the estimation of human poses as well as head skeletons of basking sharks.
Throughout the experiments, we additionally provide results for the vanilla ASM approach as well as a recent convex relaxation thereof presented by Zhou et al.~\cite{zhou20153d}.
We will refer to the former and latter as \textit{ASM non-convex} and \textit{ASM convex}, respectively.

\subsection{Human Pose Estimation}

The design of this experiment closely follows the setup proposed in~\cite{zhou20153d} in order to provide comparability.
In particular, we employ the MoCap dataset\footnote{Carnegie Mellon University - Graphics Lab - motion capture library \url{http://mocap.cs.cmu.edu/}} for defining training and test shapes.
Sequences from subject 86 are used as training data and sequences from subjects 13, 14 and 15 are used as testing data.
All sequences are composed of a variety of poses, including running, climbing, jumping, and dancing, and can hence be used to define a comprehensive set of basis shapes.
While 41 landmarks are used to encode human poses in the MoCap database, we use a reduced representation comprising a subset of 15 landmarks mimicking the construction in~\cite{zhou20153d}.
To reduce the effects of rotation and translation as much as possible for the Euclidean approaches, we perform generalized Procrustes analysis of the data during pre-processing.

As this dataset features abundant training data, we apply a strategy to learn an appropriate set of a restricted number of basis shapes.
An immediate choice to determine such a set would be to perform barycentric subspace analysis~\cite{pennec2018barycentric}, thus finding an optimal subspace w.r.t.\ unexplained variance.
However, as this could introduce a positive bias for our approach when comparing to the Euclidean ones, we opt for the established k-means clustering~\cite{lloyd1982least}.
Specifically, we set the basis shapes as the arithmetic means of each determined cluster thereby providing a homogeneous sampling according to the Euclidean metric.

\subsubsection{Quantitative Testing}

\begin{figure}[t]
    \centering
    \includegraphics[width=\textwidth]{human_errors.png}
    \caption{Boxplots of shape estimation errors of human pose test shapes using the three approaches.}
    \label{fig:human_testing}
\end{figure}
\begin{table}[b]
    \parbox{\linewidth}{
    \centering
    \caption{Mean(variance) estimation errors for human pose test shapes.}
    \label{tab:human_errors}
    \begin{tabular}{|c|c|c|c|c|}
        \hline
         &\#Basis shapes & 32 & 64 & 128 \\
         \hline
         \rule{0pt}{0.25cm} \multirow{3}{*}{Subject 13}& ASM NC & 0.462(0.121) &0.548(0.142) & 0.571(0.104) \\
         & ASM Conv & 0.550(0.071) &0.513(0.100) & 0.461(0.059) \\
        & KSS & \textbf{0.295(0.031)} & \textbf{0.295(0.031)} &  \textbf{0.288(0.038)} \\
         \hline
         \rule{0pt}{0.25cm}\multirow{3}{*}{Subject 14} &ASM NC &0.475(0.129) &0.544(0.127) & 0.644(0.128) \\
         & ASM Conv & 0.583(0.066) &0.566(0.077) & 0.533(0.087) \\
         & KSS & \textbf{0.267(0.029)} &  \textbf{0.258(0.028)} &  \textbf{0.242(0.019)} \\
         \hline
         \rule{0pt}{0.25cm}\multirow{3}{*}{Subject 15} & ASM NC &0.358(0.136) &0.406(0.122) & 0.457(0.089) \\
         & ASM Conv &0.450(0.092) & 0.416(0.069) & 0.366(0.043) \\
         & KSS & \textbf{0.221(0.034)}  & \textbf{0.231(0.027)} & \textbf{0.221(0.021)}  \\
         \hline
    \end{tabular}
    }
\end{table}
Similar to the creation of basis shapes, 200 shapes were chosen for each of the test subjects by performing k-means clustering on the pose sequences.
The shapes were then projected along the $z$-direction to create the 2D landmarks.
We then estimated the 3D shapes from the 2D landmarks for all approaches with different numbers of basis shapes (32, 64, and 128) and computed for each reconstruction the estimation error as the Procrustes distance~(\ref{eq:dist}) between the true and estimated shapes.
Fig.~\ref{fig:human_testing} shows boxplots of estimation errors obtained for the derived test shapes for the ASM non-convex, ASM convex, and our approach (listed as KSS), respectively.
Table~\ref{tab:human_errors} gives an overview of the error distribution. Statistical Friedman tests were conducted for the different combinations of test subjects and number of basis shapes to examine the effect that the reconstruction methods had on estimation errors. Results showed that the methods lead to statistically significant differences in estimation errors ($p < 0.001$).
The Kendall shape space approach out-performs the other approaches by estimating the unknown 3D shapes with consistently lower errors for all sets of basis shapes and test subjects.
The accuracy of the approach is directly proportional to the number of basis shapes used.

\subsubsection{Qualitative Testing}

\begin{figure}[t]
    \centering
    \includegraphics[width=9cm]{figure_man_new.png}
    \caption{Comparison of the three approaches for 3D shape estimation applied to an image of a basket ball player. Top row: Fitting of the estimated shapes (green) to the landmarks (yellow). Bottom row: side views of the estimated shapes. Left: ASM non-convex approach. Middle: ASM convex approach. Right: KSS approach (ours).}
    \label{fig:man}
\end{figure}

Next, we investigate the performance of the approaches in estimating the 3D pose of people in real-world images with manually labelled landmarks.
Fig.~\ref{fig:man} shows the estimated 3D poses of a basket ball player from different viewpoints using all three approaches.
The ASM approaches perform very well in estimating a 3D shape that fits to the 2D landmarks, but the estimated shapes are implausible, which can be seen by viewing them from the side.
Moreover, they are vastly different from the basis shapes.
The proposed approach, although compromising an exact fit to the 2D landmarks, is able to estimate the 3D pose with greater plausibility.
This may be attributed to more consistent interpolation between the basis shapes adhering to the Kendall shape space constraints,
which lead to reduced distortion of the basis shapes.

A similar scenario is shown in Fig.~\ref{fig:ballet}.
Here, however, even though the KSS results in a plausible shape, it does not fit to the shape we would expect to obtain.
This is most likely attributed to the fact that the ballet pose cannot be estimated from the given basis shapes.

\subsection{Estimating Head Skeletons of Basking Sharks}
\begin{figure}[t]
    \centering
    \includegraphics[width=9cm]{figure_ballet_new}
    \caption{Comparison of the three approaches for 3D shape estimation applied to an image of a ballet dancer. Top row: Fitting of the estimated shapes (green) to the landmarks (yellow). Bottom row: side views of the estimated shapes. Left: ASM non-convex approach. Middle: ASM convex approach. Right: KSS approach (ours).}
    \label{fig:ballet}
\end{figure}
\begin{figure}[t]
    \centering
    \begin{subfigure}{\textwidth}
    \centering
    \includegraphics[width=8cm]{bs_scan.png}
    \caption{CT scan of a basking shark (BS3) in left lateral view.}
    \end{subfigure}
    \begin{subfigure}{\textwidth}
    \centering
    \includegraphics[width=\textwidth]{skeleton_creation_new.png}
    \caption{(left)~Segmented CT scan of the head skeleton of a basking shark (BS3, ventral view). (middle)~Piece-wise linear skeleton created by selecting end points of each region.(right)~Skeleton split into right and left halves.}
    \end{subfigure}
    \begin{subfigure}{\textwidth}
    \centering
    \includegraphics[width=8cm]{mirrored.png}
    \caption{Basking shark skeleton shapes created by mirroring optimized half skeletons. (top)~Top/dorsal-view showing the expansion of gill arches. (bottom)~Front/anterior-view showing varying degrees of openness of the mouth.}
    \end{subfigure}
    \caption{From CT scan to skeletal representation of shark head. (a)~Volume rendering of CT scan. (b)~Segmentation, skeletonization, and separation of left and right parts of the skeleton. (c)~Opening of skeleton to create open-mouth configurations of the head.}
    \label{fig:bs_skeleton_creation}
\end{figure}

In this section, we give the results for the application that motivated the new approach for shape estimation, that is, the estimation of the shape of the head skeletons of basking sharks in feeding position.
As specimens are hard to come by and the species is heavily protected under conservation laws in many countries, the ability to extract the 3D structure of the head region non-invasively, using real-world underwater images is a great contribution to the field of biology.
We use computed tomography~(CT) scans of the heads of three basking sharks (\textit{Cetorhinus maximus}) from two museum collections (BMNH: British Museum of Natural History; ZMUC: Zoological Museum, University of Copenhagen); sample and scan information are as follows: BS1: BMNH 1978.6.22.1, size: $512 \times 512 \times 1389$;
BS2: BMNH 2004.4.15.30, size: $512 \times 512 \times 1654$;
BS3: ZMUC (no accession number), size: $512 \times 512 \times 1862$.
BS1 and BS2 were scanned at the Royal Brompton Hospital, BS3 at the Aarhus University Hospital.
CT data were used to derive basis shapes and test the methods on real-world images of the species with manually labelled landmarks.
BS3 is shown in Fig.~\ref{fig:bs_skeleton_creation}a.

Basking sharks feed by holding their mouths agape and ballooning the pharynx (throat region), allowing water to flow out the gill slits on the sides of the head~\cite{sanderson2016fish,sims2008sieving,wegner2015elasmobranch}.
The pharynx is supported by jointed branchial arches, comprising rod-like skeletal elements linked together to form a mobile skeletal basket around the throat, which can expand and collapse.
The kinematics of the pharyngeal skeleton are key to the filtering mechanism, but cannot be visualized from outside the body.
From the CT scans of basking sharks, the relevant elements of the head skeleton (the jaw, hyoid and branchial arches, skull, and spine) are isolated using manual and automatic segmentation techniques.
These isolated elements are then used to create a piece-wise linear skeleton of the sharks' pharyngeal region by labelling the start and end points of each skeletal element (e.g.\ the rod-like ceratobranchial cartilages; Fig.~\ref{fig:bs_skeleton_creation}b) and connecting each point pair via a linear segment.
Due to preservation conditions (e.g.\ specimens fixed in non-physiological positions), sharks in the CT scans showed non-physiological deformations (e.g.\ the branchial basket collapsed asymmetrically under the shark's weight), structures needed correction before creating the set of basis shapes.
Due to the bilateral symmetry of basking sharks, their right and left halves are essentially identical: skeletons were split into right and left halves which could later be mirrored to create full skeletons.
A set of optimization problems which aim to conserve the lengths of segments were used to move the spine and the ventral plate (a portion of the branchial basket) of the half skeletons into an anatomically plausible position~\cite{wegner2015elasmobranch}.
The mouth of the skeleton was opened using the same method.
The corrected skeletons were then mirrored w.r.t.\ the sagittal plane.
Fig.~\ref{fig:bs_skeleton_creation}c visualizes this process.
The anatomical arrangements of the final skeletons were approved by experts in the field (M.~Dean \& F.~Mollen, personal communication).

\subsubsection{Analysis of reconstruction accuracy}

\begin{figure}[t]
    \centering
    \includegraphics[width=9cm]{errors_shark_new_all.png}
    \caption{Boxplots of shape estimation errors of basking shark test shapes for the three approaches using the basis shapes from BS3.}
    \label{fig:bs_testing}
\end{figure}
\begin{table}[b]
    \parbox{\linewidth}{
        \centering
        \caption{Mean(variance) estimation errors for basking shark test shapes for symmetric and asymmetric projections using (15/29) basis shapes from Basking Shark 3.}
        \label{tab:bs_errors}
        \begin{tabular}{|c|c|c|c|c|c|}
        \hline
        &\#Basis Shapes & 15 (sym) & 15 (asym) &29 (sym) & 29 (asym)\\ \hline
             \rule{0pt}{0.25cm} \multirow{3}{*}{BS1} & ASM NC & 0.231(0.002) & \textbf{0.146(3e-04)} & \textbf{0.306(0.020)} & \textbf{0.136(2e-04)}  \\
             & ASM Conv & 0.854(0.030) & 0.836(0.013) & 0.857(0.036) & 0.820(0.011) \\
             & KSS & \textbf{0.215(0.001)} & 0.151(3e-04) & 0.336(0.025) & 0.156(0.0003)\\ \hline
             \rule{0pt}{0.25cm} \multirow{3}{*}{BS2} & ASM NC & 0.286(0.001) & \textbf{0.145(1e-04)} & 0.281(0.014) & \textbf{0.137(9.7e-05)}\\
             & ASM Conv & 0.906(0.041) & 0.757 (0.021) & 0.755(0.041) & 0.747(0.013) \\
             & KSS & \textbf{0.236(0.001)} & 0.153(3e-04) & \textbf{0.256(0.012)} & 0.150(3.5e-04) \\
        \hline
        \end{tabular}
    }
\end{table}

Similar to human pose estimation, quantitative and qualitative analyses were performed for all approaches.
In the quantitative experiments, we used the head skeleton shapes (29 in total) of one of the basking sharks to estimate the shapes (28/29) of the other two.
Two types of projections, bilaterally symmetric and asymmetric, are used to estimate the 3D shape.
The former is the case when viewing the shark anteriorly (from the front) and the latter when viewing from the side (e.g.\ where one side of the throat is more visible than the other).
Both scenarios are equally important when extracting the 3D shape from images.
Fig.~\ref{fig:bs_testing} shows the errors in estimation using all the approaches and Table~\ref{tab:bs_errors} provides some error statistics. Again, statistically significant differences have been confirmed via Friedmann tests ($p < 0.001$) for each combination of subject and viewpoints.
Contrary to the human pose estimation, the ASM non-convex and our approach provide similar estimation errors for the basking shark experiment with the former being slightly superior for 5 out of the 8 cases.
These results indicate that the basking shark data might be located in a region of relatively low curvature in shape space that is well approximated by a hyper-plane.

\subsubsection{Qualitative validation on underwater imagery}

\begin{figure}[t]
    \centering
    \includegraphics[width=9cm]{figure_bs1_new}
    \caption{Comparison of the three approaches for 3D shape estimation applied to an under-water image\protect\footnotemark\ of a basking shark. Top row: Fitting of the estimated shapes (green) to the landmarks (yellow). Middle row: top views of the estimated shapes. Bottom row: side views. Left: ASM non-convex approach. Middle: ASM convex approach. Right: KSS approach (ours).}
    \label{fig:bs1}
\end{figure}
\footnotetext{Source: \url{https://www.amustard.com/library/albums/1/AMU_12_300611_0014.jpg}}
\begin{figure}[t]
    \centering
    \includegraphics[width=9cm]{figure_bs2_new}
    \caption{Comparison of the three approaches for 3D shape estimation applied to an under-water image\protect\footnotemark\ of a basking shark. Top row: Fitting of the estimated shapes (green) to the landmarks (yellow). Middle row: top views of the estimated shapes. Bottom row: side views. Left: ASM non-convex approach. Middle: ASM convex approach. Right: KSS approach (ours).}
    \label{fig:bs2}
\end{figure}
\footnotetext{Source: \url{https://www.manxbaskingsharkwatch.org/shark-files/biology-behaviour/feeding}}

We investigated the performances of the approaches in estimating the 3D structure of basking shark heads in underwater images with manually placed landmarks.
Shapes from all three sharks (86 in total) were used as basis shapes.
Figs.~\ref{fig:bs1} and \ref{fig:bs2} show the results obtained using the two ASM approaches and the novel KSS approach.
Similarly to the results for the estimation of real-world human poses, the shape estimations obtained from the two ASM approaches fit the 2D landmarks very well but fail to produce convincing results when looking from a different view.
This is particularly striking for the ASM convex approach but is also noticeable for the ASM non-convex method---the estimated shape of which is unnaturally elongated.
In contrast, applying the KSS approach results in 3D shapes that are very plausible and show a widely opened mouth.

\section{Introduction}

The reconstruction of a 3D shape from 2D images is an important problem of computer vision that has been the subject of research for decades ~\cite{tomasi1992shape,bregler2000recovering}.
It is a widespread challenge with sample applications including motion recognition and tracking, autonomous driving, as well as robot-assisted surgery and navigation.
Generally, estimating the 3D shape of an object from single monocular 2D images is an ill-posed problem in the sense of Hadamard.
To tackle this problem, several approaches have been proposed, the choice of which greatly depends on the type and amount of data, and the application.

One common approach is to use a series of 2D images~\cite{howe2004silhouette,cao20133d} or multiple cameras~\cite{larsen2007temporally,jiang20123d,mustafa2015general}.
This is used, for example, in photogrammetry.
In order to calculate the depth, corresponding points in 2D images need to be identified~\cite{plankers2001tracking,cao20133d,agudo2014good}.

Another approach is based on physical modeling of the object to be estimated~\cite{sanzari2016bayesian,akhter2015pose}.
Here, the object is described as a kinematic tree consisting of segments connected by joints.
Each joint contains some degrees of freedom (DOF), indicating the directions it is allowed to move.
The object is modeled by the DOF of all joints.
Length constraints can also be added, such as limb lengths constraints in a human pose.
This helps reduce the depth ambiguity by constraining the relative position of the joints.

In lieu of additional viewpoints or physical models, another line of work regularizes the estimation problem by employing prior knowledge learned from examples of the respective object class.
Some works in this category are based on the concept of shape spaces.
Here, the 3D shape of an object is estimated by interpolating through a set of pre-defined 3D shapes, called training shapes, that represent possible deformations of the object.
Given a 2D projection of the object, the aim is to find the ideal camera parameters and the shape coefficients describing the interpolation.
Most commonly, \emph{active shape model} (ASM) techniques are used~\cite{mori2006recovering,hejrati2012,ramakrishna2012,wang2014,zia2013,zhou20153d}.
ASM has been used intensively for the purpose of recognizing and locating non-rigid objects in the presence of noise and occlusion~\cite{heimann2009SSMreview,ambellan2019statistical}.
It aims at providing a robust approach, which accommodates shape variability by arguing that when the objects deform in ways characteristic to the class of objects they represent, the method should be able to recognize them.
Here, the \emph{shape} of a class of objects is described by a set of labeled \emph{landmark} points, each representing a particular part of the object or its boundary.
Given a set of pre-defined \emph{basis shapes} of an object, the assumption is that any shape of the object can be described by linearly interpolating between basis shapes.
The legitimacy of the model is determined by the set of training shapes, which needs to include the variability in the shape of the object.

Apart from these more classical approaches, recent years have mostly been devoted to the development of deep learning-based methods that exploit domain-specific data repositories with abundant samples (e.g., \textit{ShapeNet}, \textit{Human3.6M}).
In 2017, a kinematic skeleton fitting method using a \emph{convolutional neural network} (CNN) was proposed that regresses 2D and 3D joint positions jointly in real-time~\cite{mehta2017vnect}.
More recently, \emph{Procrustean regression networks} (PRN) were proposed~\cite{park2020procrustean}.
Using a novel loss function, they solve the problem of automatically determining the rotation.
Another recent deep learning-based method, \emph{KShapeNet}~\cite{friji2020kshapenet}, makes use of Kendall's shape space by modeling shape sequences first as trajectories on Kendall's non-linear shape space, which are then mapped to the linear tangent space.
The authors report~\cite{friji2020kshapenet} that the non-linear motion can be captured better using their approach than using previous geometric deep-learning methods.

In general, the training of deep neural network models requires a considerable amount of data.
While the generalization of learned models to new classes with few available examples has become a highly popular research topic (see e.g.~\cite{michalkiewicz2020few}), such base models are rarely available in many applications.
There is therefore a strong impetus to develop so-called shallow learning approaches that can be applied even if few-shot learning is not an option.

Our work contributes to this area by deriving a novel shape space-based approach.
We demonstrate the effectiveness of the proposed scheme in an application to the study of marine animal behavior.
In this application, we are faced with the retrieval of the 3D shape of a non-rigid (biological) object — the head skeleton of a basking shark — from single monocular 2D images.
Basking sharks (\textit{Cetorhinus maximus}) are massive animals and thought to be one of the most efficient filter-feeding fish in terms of the throughput of water filtered through their gill rakers~\cite{sanderson2016fish}.
Details about the underlying morphology of the basking shark filter apparatus and particularly how it is configured when the animal feeds have not been studied due to various challenges in acquiring real-world data.
In this study, we address this issue, using several computed-tomography (CT) scans to create skeletal representations of basking shark head structure.
From these, and known aspects of the biology (e.g.\ shark cranial anatomy, feeding  behaviors), we semi-automatically created plausible configurations of the skeleton which we use as training shapes to describe the shape space.
The ultimate goal is, given a photograph of a basking shark in feeding position, to estimate a plausible 3D shape of the skeletal representation from the training data and annotations of the skeletal joints in the form of 2D landmarks.
\begin{figure}[t]
    \centering
    \includegraphics[width=\textwidth]{methodology_final}
    \caption{Methodology diagram for the proposed method.}
    \label{fig:methodology}
\end{figure}

Since the number of training shapes is very limited in our application, deep learning-based methods cannot be applied.
When using only a single 2D image, photogrammetry-based methods also cannot be applied.
And for a physical modeling-based approach, information about the movement of the skeletal elements that is supported by the joints would be necessary.
This information is not available.
We therefore resort to shape space-based methods.
In particular, we develop a new \emph{Kendall shape space}~(KSS) approach for the reconstruction of 3D shape from 2D landmarks.
Our overall workflow is sketched in Fig.~\ref{fig:methodology}.
In order to evaluate our approach, we compare it qualitatively and quantitatively with state-of-the-art ASM approaches~\cite{zhou20153d} on both human poses and basking shark skeletons.
Due to the limited number of training shapes for the basking sharks, we are mainly interested in the performance of the approaches w.r.t.\ a small number of training shapes.

The results of our experiments suggest that our method is substantially more robust than previous shape space-based methods.
This is particularly true for real world data both of human beings and shark data.
It is also computationally very efficient and provides plausible interpolations without auxiliary regularization since the estimated shape will always lie on a subspace in Kendall's shape space spanned by the training data.

The source code of the proposed method together with the derived basking shark shapes have been made publicly available~\cite{Code}.

\section{Methods}\label{sec:methods}

In this work, we approach the problem of estimating the shape of 3D objects from single images.
To this end, we employ a landmark-based representation, viz.\ a set of ordered 3D points $(x_i)_{i=1,\ldots,k}$ that correspond to homologous points (e.g.\ joint centers in a skeleton) common to all subjects belonging to the object class under study.
By assuming the weak perspective camera model, the projection or forward map is given by the linear system
\begin{equation} \label{eq:projection}
    W = \Pi R X + t\mathbf{1}_k^T,
\end{equation}
where $X\in\mathbb{R}^{3 \times k}$ and $W\in\mathbb{R}^{2 \times k}$ denote the matrices of stacked landmarks and their 2D projections, respectively.
The rotation $R\in SO(3)$ and translation $t\in\mathbb{R}^2$ encode the camera coordinate system while the projection is carried out by the matrix
\[
\Pi = \left(
\begin{array}{ccc}
    \alpha & 0 & 0 \\
     0 & \alpha & 0
\end{array}
\right),
\]
where the scalar $\alpha$ depends only on the focal length and distance to the object.
The inverse problem of finding the 3D configuration corresponding to given projections is commonly formulated in terms of a least-squares problem.
However, the underdeterminedness renders such a problem ill-posed requiring inclusion of prior knowledge in order to obtain feasible solutions.
An established strategy based on the active shape model~\cite{cootes1995active} is to restrict the search space to linear combinations of basis shapes $B_1,\ldots,B_n \in \mathbb{R}^{3 \times k}$, i.e.
\begin{equation}
    \label{eq:linear_blend}
    \textstyle
    X = \sum_{j=1}^n c_j B_j,
\end{equation}
with weights $c_j$ satisfying the constraint $\sum_j c_j = 1$.
The quality of this approach, however, depends on the validity of the assumption that instances of the object class are well approximated by a hyper-planar manifold.
In general, the shape of an object is considered to be invariant under rotation, translation and scaling and, hence, takes values in a nonlinear space with quotient structure.
In particular, for landmark-based representations, this concept gives rise to the well-known Kendall shape space~\cite{kendall1984shape}.
The non-Euclidean nature of shape space not only violates the linearity assumption but furthermore prevents direct application of algebraic expressions such as Eq.~(\ref{eq:linear_blend}) due to the lack of a global vector space structure.
Nevertheless, the framework of (computational) differential geometry provides us with a rich toolset to generalize the ASM approach for use within the reconstruction problem.

\subsection{Geometric model}

Before we formulate a manifold version of the least-squares estimation, we first recall essential notions and properties from Kendall's shape space.
We refer the reader to the comprehensive work~\cite{kendall2009shape} for an in-depth introduction.

Let $X\in\mathbb{R}^{m\times k}$ be the matrix holding $k$ landmarks $x_i \in \mathbb{R}^{m}$ as columns.
We remove the effect of translations and scaling by subtracting the row-wise mean from each landmark and then dividing $X$ by its \emph{Frobenius norm} (denoted $\|\cdot\|$).
The set of all such configurations constitutes the \emph{pre-shape space}
\begin{equation*}
    \textstyle
    \mathcal{S}^k_m=\{X \in \mathbb{R}^{m \times k} \: : \sum_{i=1}^k x_i=0 \: , \, \| x\|=1 \}.
\end{equation*}
Now, the left action of $SO(m)$ on $\mathcal{S}^k_m$ given by $(R, X) \mapsto RX$ defines an equivalence relation given by $X \sim Y$ if and only if $Y = RX$ for some $R \in SO(m)$.
Kendall's shape space is defined as the quotient $\Sigma^k_m = \mathcal{S}^k_m /\mathord{\sim}$.
Now, denoting the canonical projection of $\sim$ by $\pi$ and the spherical distance by $d_\mathcal{S}(X,Y)= \text{arccos}\left< X,Y \right>$, the induced distance between any two shapes $\pi(X)$ and $\pi(Y)$ is given by
\begin{equation} \label{eq:dist}
    \textstyle
    d_{\Sigma}(X,Y):= \underset{R\in SO(m)}{\min} d_\mathcal{S}(X,RY) = \text{arccos}\sum_{i=1}^n \lambda_i,
\end{equation}
where $\lambda_1 \geq \lambda_2 \geq \dots \geq \lambda_{m-1} \geq |\lambda_m|$ are the pseudo-singular values of $YX^T$~\cite{nava2020geodesic}.
The points $X$ and $Y$ are said to be \emph{well-positioned} (denoted by $X \overset{w}{\sim} Y$), if and only if, $YX^T$ is symmetric and $d_\mathcal{S}(X,Y)=d_{\Sigma}(X,Y)$.
Note that for $m\geq3$, the shape space $\Sigma^k_m$ contains singularities making it a strata of manifolds with varying dimensions.

In order to generalize the ASM approach, we first note that Eq.~(\ref{eq:linear_blend}) effectively parametrizes the affine subspace spanned by the basis shapes.
A common approach to obtain equivalent notions in Riemannian manifolds is to define \emph{geodesic subspaces} that are spanned by generalized straight lines (geodesics) emanating from a reference point and with directions restricted to a linear subspace of the tangent space~\cite{fletcher2004principal}.
However, as geodesic subspaces rely on tangent vectors, they can only be defined within regular strata of the shape space.
Therefore, we opt for an alternative construction by Pennec~\cite{pennec2018barycentric} called \emph{barycentric subspaces}, which are defined as the locus of points that are weighted means of the basis shapes.
Specifically, let $b_1 = \pi(B_1),\ldots,b_n = \pi(B_n)\in\Sigma^k_m$ be a set of $n$ distinct basis shapes, then the \emph{Fr\'echet barycentric subspace} is given by
\begin{equation*}
    FBS_{(b_j)_j} = \left\{ \argmin_{p\in\Sigma^k_m} \sum_{j=1}^n c_j \, d^2_\Sigma(p,b_j) : \sum_{j=1}^n c_j \neq 0 \right\}.
\end{equation*}

With a notion of affine submanifold at hand, we next derive a reprojection error that is defined on Kendall's shape space.
Consistently to the 3D case, we will treat the 2D projections as points in shape space $\Sigma^k_2$ and employ the geodesic distance as objective for the reconstruction problem.
To this end, we re-formulate the projection (\ref{eq:projection}) as a map from 3D KSS to 2D KSS by
\begin{equation} \label{eq:projection_Kendall}
    p \in \Sigma^k_3 \mapsto \pi\circ\nu(R_{[1,2]}\pi^\dagger(p)) \in \Sigma^k_2,
\end{equation}
where $\nu$ performs normalization (i.e.\ projects onto the sphere) and the subscript~$[1,2]$ refers to the first two rows of $R \in SO(3)$.
To assure class invariance under $\sim$, we introduce the map $\pi^\dagger$, which yields a unique representative for a shape by well-positioning to a fixed reference pre-shape $X \in \mathcal{S}^k_3$, viz.
\begin{equation}
    \pi^\dagger : p \in \Sigma^k_m \mapsto P \in \mathcal{S}^k_m ~~ s.t. ~ \pi(P) = p, P \overset{w}{\sim} X.
\end{equation}
Note that due to the quotient structure, the re-formulation no longer depends on the scaling and translation camera parameters $\alpha$ and $t$ found in the original formulation (\ref{eq:projection}).

We are now in the position to obtain a geometry-aware counterpart of the estimation problem in terms of the projection (\ref{eq:projection_Kendall}) and the Fr\'echet barycentric subspace resulting in the following optimization problem
\begin{equation} \label{eq:3Dfrom2D}
    \min_{p, R} d_\Sigma^2\left(W,\nu(R_{[1,2]}\pi^\dagger(p))\right) ~~ s.t. ~ p \in FBS_{(b_j)_j}, R \in SO(3).
\end{equation}

\subsection{Algorithmic treatment}

In order to solve the reconstruction problem (\ref{eq:3Dfrom2D}), we employ an alternating optimization strategy taking advantage of the product structure of the search space, viz.\ $FBS_{(B_j)_j} \times SO(3)$.
Each outer iteration thus consists of two steps: First, rotation $R$ is minimized while considering the current shape estimate $p$ fixed.
To this end, we perform Riemannian optimization on the \textit{Stiefel} manifold $$V_2(\mathbb{R}^3) := \{X \in \mathbb{R}^{3 \times 2} : X^TX = I_2\} \cong SO(3)$$ utilizing the \texttt{Pymanopt}~\cite{boumal2014manopt} library.
Second, we fix the rotation $R$ and solve the resulting sub-problem w.r.t.\ shape $p$ parametrized by barycentric weights.
For Riemannian computations on Kendall's space space, we employ \texttt{Morphomatics}~\cite{Morphomatics}.
As both steps are guaranteed to weakly decrease the reconstruction objective, we obtain a simple, yet convergent optimization scheme.
In particular, both sub-problems are solved employing steepest descent strategies, where gradients are computed via automatic differentiation with \texttt{JAX}~\cite{frostig2018compiling}.

Due to the non-Euclidean structure of the shape space, there are no closed-form expressions for determining the (weighted) Fr\'echet mean of a given collection of sample points.
Here, we adopt an efficient, inductive estimator to derive a parameterization of the Fr\'echet barycentric subspace that exhibits only a linear computational cost in the number of basis shapes.
In particular, let $b_1,\ldots,b_n \in \Sigma^k_3$ and $w_1,\ldots,w_n \in \mathbb{R}$ such that $\sum_{j=1}^n w_j \neq 0$, then the parameterization $(w_j)_j \mapsto \mu_n \in \Sigma^k_3$ is given by the recursion
\begin{equation}
    \mu_1 = b_1 ~~~~~~~~~~ \mu_j = \gamma_{\mu_{j-1}}^{b_j}\left(\frac{w_j}{\sum_{l=1}^j w_l}\right),
\end{equation}
where $\gamma_{\mu_{j-1}}^{b_j}$ denotes the shortest geodesic from $\mu_{j-1}$ to $b_j$.
Note that under certain conditions (cf.~\cite{chakraborty2020manifoldnet}) the recursion can be shown to converge to the actual weighted Fr\'echet mean.
In any case, we expect the Fr\'echet barycentric subspace to be contained in the image of the above parameterization.


text:
<!DOCTYPE html>

    <meta charset="utf-8" />
    <meta name="viewport" content="width=device-width,initial-scale=1" />
    <title>Elix Toast</title>

    <link rel="stylesheet" href="demos.css" />

Click a button to toggle a toast from that location:

          <button alt="top left" onclick="toggleToast('top-left')"></button>
          <button alt="top" onclick="toggleToast('top')"></button>
          <button alt="top right" onclick="toggleToast('top-right')"></button>

          <button
            alt="bottom left"
            onclick="toggleToast('bottom-left')"
          ></button>
          <button alt="bottom" onclick="toggleToast('bottom')"></button>
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            alt="bottom right"
            onclick="toggleToast('bottom-right')"
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redpajama_set_name: RedPajamaGithub


This seems to be the season to celebrate one of the most dubious players of contemporary Indian politics. A recently published book hailed Narasimha Rao as a half-lion. Another admirer's account was launched with much fanfare last week. And there are gaga reviews of the books and their subject all around. Why this great interest in Rao now? Is it because 2016 marks the 25th year of Indian reforms? A brilliant series of news reports and interviews by journalist Shaji Vikraman in The Indian Express has conclusively established that the reforms would have happened with or without Rao. It was a historical inevitability. An earlier government, and another finance minister—Yashwant Sinha—had worked on the blueprint for many of Manmohan Singh's famous budget proposals of 1991, which unleashed the reforms. Or is it a conspiracy to airbrush a prime minister who practised mumbo-jumbo, had a personal tantrik—Chandraswamy—and had Subramanian Swamy for advisor? Either way, what is shocking is that the admirers tend to forget who Rao really was: the home minister of India responsible for the law and order in Delhi when the anti-Sikh riots broke out in early November 1984; an unelected prime minister who used the brute power of his office to get elected almost unopposed (prime opponent, Telugu Desam Party, didn't contest the bypolls to Nandyal in November 1991) six months after he was nominated to the PMO by the Gandhi family loyalists; the prime minister who retired for a siesta when Babri Masjid was being demolished by Hindutva goons; the man who was at the helm when the country went up in flames during the long-drawn post-Babri riots and subsequent Bombay blasts; and also, the prime minister who presided over one of the most corrupt cabinets in Indian history.
Much of our modern political malaise can be traced back to Rao. Sure, there was cronyism during the licence-permit raj days. But Rao institutionalised crony capitalism in a new and liberalised economy by handing over the levers of the economy to some of the most corrupt players while opening up various sectors to private capital. That was a crime against the future, against a new Indian dawn. There was a stock scam in the emerging share market, there was an oil scam in the newly privatised oilfields, there was a telecom scam in the high-tech sunrise sector and then, there were old economy scandals all over, from sugar to urea. His minority government became a majority one by buying Jharkhand Mukti Morcha MPs. But Rao should always be remembered for his culpability in letting the police stand by in Delhi when about 3,000 innocent men, women and children were killed, mostly burnt alive. Rajiv Gandhi and even Rahul Gandhi are constantly made to atone for Rao's sins. But nobody ever asked Rao what he did or did not do to let the Sikhs burn, to let the Babri Masjid and the people of India down, to let cronyism get into the DNA of a liberalised economy. Every reference to Rao would reek of the blood of those killed in 1984 and in 1992-93.


On May 19, 1999, Cuba met Puerto Rico in one of the most spectacular finals in the history of Centrobasket competitions. The event took place in Havana's Ciudad Deportiva coliseum, and the Cuban team won the tight game 67 to 63, in what was the country's last appearance as the home team in an international tournament.
At that time, no one would have imagined that 18 years later, the same opponent would be featured in Cuba's return to this level of basketball competition, in a game on November 26, when the two teams face off on the same court, in the second round of continental qualifying events for the World Cup.
Yoannis Zaldívar, is training on the Giraldo Córdova Cardín indoor court, in the city of Ciego de Ávila. Cuba will begin its participation as the visitor on the 23rd against Mexico - another strong rival in the C group which also includes the United States.
The group working in Ciego de Ávila began with all of the country's stars with the exception of those playing in the Argentine National Basketball League: Santiago de Cuba's pivot, Javier Justiz (2.10 meters), a key member of the team; and two promising young players, Yoanki Mensía (1.96) and Karel Guzmán (1.95), who will be arriving prior to the big game.
The roster includes Artemisa's Osmel Oliva (1.78); Orestes Torres (2.04) and Lisván Valdés (1.98) from Havana; and Villa Clara's Yoel Cubilla (2.04), who just completed his participation in El Savador's major league.
Another key player is Havana's Jasiel Rivero (2.04), who is in great condition, completing the 14 member national selection, along with teammate Abel Font (2.06); Pinar del Río's Eliecer Quintana (2.05); Yuniskel Molina (1.85) from Matanzas; Camagüey's Carlos César Villegas (1.99); plus William Granda (1.90) and Yasser Rodríguez (1.86), both from Ciego de Avila.
Zaldívar told the newspaper Invasor that Granda is still recovering from an injury that prevented him from training, and that Cubilla will compete although his ankle is bothering him.
This young team, inexperienced but talented - with players averaging 25 years of age and 1.97 meters in height - is facing a stiff challenge, and little chance of winning one of the three tickets to the next round. Two years ago, during the FIBA AmeriCup held in Mexico City, they lost all of their games with Canada, Puerto Rico, Venezuela, and Argentina. But they are back to try again.


The HuiNa 6-Channel 2.4G Dump Truck is a scale model of a real mining dump truck that works just like the real thing. The frame is made of hard metal reinforced alloy for durability, while the powerful 4WD double motors allows for traversing even the toughest terrain. The wheels are made of hard metal for durability with slip-resistent rubber tyres.


Take a trip to Maui and experience the most amazing vacation you've ever had! Dive into the pristine waters, walk on the sand and gaze at the amazing views that this island has! But first, make sure to book your stay in one of our Maui beachfront rentals! Browse through our collection below!
White sandy beaches, tropical breezes, and swaying palms… They're what Maui vacation dreams are made of. Thanks to Maui's year-round warm weather, miles of pristine beaches, and beachfront vacation rentals, your views of the ocean don't have to end when you enter one of our Maui beach view or Maui beachfront rentals.
Whether you're looking to be right on the beach or just close enough to enjoy the ocean view, our variety of beachfront and beach view rentals have plenty to offer. The first thing you will likely notice as soon as you step into your beachfront or beach view accommodations is the view spread out before you. Large windows and glass doors take advantage of Maui's inherent beauty as your natural décor. Indoor-outdoor living means you can fling wide your doors and utilize the extended space on the lanai to enjoy morning coffee or evening cocktails with a view.
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Diane from Voice Write Africa interviews popular book review blogger Mary Okeke, who is a Nigerian living in Barcelona, Spain. She speaks to us about Spain, her passion for books and will even teach us a few words in Igbo which is her native language... Please click here to read more.
Very interesting interview with Diane from Voice Write Africa.
This is good. Spread the message.
Awww thanks. Yeah I read somewhere you are a Nurse Professor. You give classes in Uni right? Not everyone can be a Nurse. It comes within.... you know the feeling of always wanting to help one another.


text:
ActiveRecord::Schema.define(version: 20150102235549) do

  create_table "people", force: :cascade do |t|
    t.string   "name"
    t.datetime "created_at", null: false
    t.datetime "updated_at", null: false
  end

end


text:
Thelma & Louise (1991)
R | 130 min | Adventure, Crime, Drama
Two best friends set out on an adventure, but it soon turns around to a terrifying escape from being hunted by the police, as these two girls escape for the crimes they committed.
Watch on Prime Video included with Prime
Michael Madsen
Christopher McDonald
Lena, the Waitress
Sonny Carl Davis
Shelly Desai
East Indian Motel Clerk
(as Shelly De Sai)
Carol Mansell
Stephen Polk
Surveillance Man
Callie Khouri
Won 1 Oscar.
Another 22 wins & 48 nominations.
8 December 2008 | Nazi_Fighter_David
| A rare moment in cinema of the total rejection of the rule of law and patriarchy
The road movie is traditionally a male genre, relying on the sense of freedom and independence that having one's own transport provides and which has usually been the privilege of men… What is innovatory about "Thelma & Louise" is the way it reequips the genre for women
Thelma (Geena Davis) is a housewife trapped in a meaningless marriage, Louise (Susan Sarandon) is a waitress in a not very significant relationship… They decide to give themselves a little space by taking off for a weekend… But when Louise shoots a man who is trying to rape Thelma, they are precipitated into a far more radical break with their past lives
The setting of action in the American southwest and the acts of outlawry the women are obliged to commit in order to keep on the run give the film some of the feel of a Western… What makes it nevertheless a women's film is that the relationship between the two principals is at the center of the story… The various men they encounter, both the ones they leave behind and those they meet on the road have less importance for Thelma and Louise than the two women do for each other
Predictably, the film met with hostility from some male viewers, on the grounds that the men were caricatured and that the film encouraged violence
Legends of the Fall
Meet Joe Black
Black Rain
The Mexican
G.I. Jane
Fatal Attraction
Won Best Original Screenplay in the same year that The Silence of the Lambs (1991) swept the major awards at the Oscars (including Best Adapted Screenplay), making it the only other film to win a major award that year.
Louise: You know, certain words and phrases just keep drifting through my mind. Things like, incarceration, cavity search, death by electrocution, life imprisonment, shit like that. You know what I'm sayin'? So do I want to come out alive? I don't know. I.....
Towards the end the windshield from the front shows the lines from the windshield wipers, but from the driver's seat looking out, the windshield is clear.
I Don't Want To Love You (But I Do)
Written by Paul Kennerly
Performed by Kelly Willis
Courtesy of MCA Records
Synopsis (WARNING: Spoilers)
Adventure | Crime | Drama
USA, UK, France
Derby Acres, California, USA
$16,500,000 (estimated)
Opening Weekend:
$6,101,297 (USA) (27 May 1991)
Gross:
$45,361,000 (USA)
12 July 2019 | BuzzSugar
Remember When Brad Pitt and Leonardo DiCaprio Were on Growing Pains? Because They Sure Do
'Queen & Slim' First Look, Motown Panel With Valerie Jarrett Highlight Essence Festival Events
08 July 2019 | MovieWeb
The Big Lebowski Spin-Off The Jesus Rolls Is Coming to Theaters in 2020
Movies at 25 in 2016
2016 National Film Registry
IMDb Movie Top 250's One Day Wonders
Cheesy Movie Chat-Up Line
Alternate Movie Endings

redpajama_set_name: RedPajamaCommonCrawl


With ten years in business, Catax are experts in Capital Allowances and Research and Development (R&D) tax relief so their clients get the optimum benefit. Catax try and ensure their average client benefit for Capital Allowances is £46,000 and £39,000 for R&D. They understand that tax law can be confusing and requires specialist knowledge, so they take great care to keep things simple for their clients. Catax break down the claims process for Their clients so all you need to do is discuss your specific situation, provide them with some details, and they take care of the rest. There are no complicated forms to fill out, no legal language to unpick and no tax law to get your head around. And you'll have a dedicated case manager to keep you updated at every stage. It could be the easiest money you'll ever make.
We were tasked by their agency, Peppermint Soda, to create a series of animations for their new website. The style of the animations was simple but clean and the animations were designed to make sure the process of working with Catax was clear throughout. We worked in Adobe aftereffects to bring the animations to life.


text:
Matt Overton had head shaved for more than Colts coach Chuck Pagano
Colts long snapper Matt Overton had been thinking about adding some meaning to a timely close shave long before coach Chuck Pagano was diagnosed with leukemia.
Overton learned weeks ago he would be visiting Indiana University Health's Simon Cancer Center on Tuesday and saw it as an opportunity to honor a couple of family members for October's breast cancer awareness month. He agreed to have his head shaved.
Overton's grandmother, Marilyn Overton, is a breast cancer survivor. Overton's great aunt, Marge McGinnis, was diagnosed with the disease last summer.
Then Pagano was admitted to the Simon Cancer Center last week.
"I kind of had it in the back of my mind I would do something," Overton said. "I wanted to pay my respects to the patients and kind of honor them, too. With the circumstances we face with coach Pagano, it's kind of my way to support him and his family as well.
"In light of what's going on right now, it kind of hit us hard as a team and an organization. There has been a lot of support. It was just an inspiring and encouraging day, to see all the patients there and the doctors. We know those people are in good hands, coach Pagano is in good hands. Just to see the joy on their faces of us coming in there and interacting with them and spending time with them, it really puts life in perspective."
It's what you would expect from a guy like Overton, a testament to perseverance. His journey to the NFL took six years, through the United Football League and Arena Football 2, before he landed with the Colts this season.
When teased that he didn't have much hair before, that he kept it pretty tight, Overton was playfully defensive.
"Not a lot, but it was still significant," he said. "It wasn't like I was cutting off six inches, but still …"
Overton's conversion to Mr. Clean included the shaver being handed to Colts rookie tight end Dwayne Allen. Talk about commitment.
"There were four guys who participated in the head shaving event, one of them being Dwayne, he's the one who finished it off," Overton said. "One of the leading doctors helped, and then there were two patients. The shears came from one of the patients who shaves his head every day, so it was cool to have him cut my hair.
"The shears were a little dull, I'm not going to lie, it kind of hurt sometimes."
But it could have been a lot worse.
"Dwayne tried to play a little trick on me and leave a little rat's tail back there, but I caught him," Overton said. "It was all in fun. I think the patients had a really good time with it."


These unfinished wood easels are ideal for holding place cards and table markers at weddings. Paint them in your wedding colors! Add them to the buffet to identify the entrées or use them to display photos of the happy couple. They're a simple way to give your special celebration a charming DIY touch. 4" x 5"


text:
Sergio Gomez signs up with Man U in £11M deal (photos)
Home - Sports - Sergio Gomez signs up with Man U in £11M deal (photos)
Premier League champions, Manchester City have confirmed the capture of Spanish left-back, Sergio Gomez from Belgian club Anderlecht.
Gomez started his career in Barcelona's La Masia Academy as an attacking midfielder before moving on to Borussia Dortmund.
City will pay an initial £11m ($13m) fee for the 21-year-old with the potential for the price to rise further in unspecified add-ons.
The Premier League champions signed Gomez after allowing Oleksandr Zinchenko to join Arsenal in a £32million ($38m) deal.
Gomez spent two seasons on loan with Spanish side Huesca before moving to Anderlecht, where he starred under former City captain Vincent Kompany, claiming 15 assists and being named the club's Player of the Year.
Gomez signed four-year contract at the Etihad Stadium.
"City are the best team in England and in Pep Guardiola I have a chance to learn and develop under the most outstanding manager in world football," Gomez said after his move was made official on Tuesday morning, August 16.
"To be able to be part of this club is a dream come true for me and something any young player would aspire to.
"The number of trophies City have won over the past few years has been incredible and the style of football the team plays under Pep is the most exciting in Europe. Playing for and being guided by Pep and his coaches is going to be very special."
"When [my brother] went on a school trip to London, I asked him to buy me the Manchester City shirt with the name and number of David Silva. At that time, I was wearing the number 21 too," he added.
"He was one of my favourite players in that position because when I was a kid I used to play in Silva's position. That's the story of the shirt and I have kept it well since."
24-year Man and 61-year Woman weds in US
4 Kids declared dead after eating noodles in South Africa
Miracle baby survives 24 hours after its mother buried her alive


Hand thrown on the potter's wheel, the latte tumbler is an everyday piece. Whether its topped up with water, coffee, tea, or a generous serving of wine - you will find yourself reaching for it. This tumbler is the larger of the two and is around 12oz in volume, about the size of a standard large barista-made coffee. The tumbler is double dipped in a smooth matte glaze, and finished with a raw clay base. Please note that sizing is approximate as all items are hand thrown.
All products are oven and dishwasher safe.
Designed and created on Waiheke Island, New Zealand.


The concept of landscape renovations may be new to most people but as many homeowners look to invest in their home it's becoming very popular. Creating your dream landscape can be costly for those who don't go about it the right way. This article is designed to help anyone looking to budget properly for a successful landscape experience that is enjoyable for years to come.
It was another interesting week in the building, architecture, and landscape industry. The end of June and heading into the 4th of July weekend, the industry often sees a bit of slow down as people take their Summer vacations but we are sending out thinstone and building veneer by the truckload (and LTL) on a daily basis. This week our team read some interesting articles that we wanted to share. Starting with the valuation of Houzz and mixing in several others we thought were interesting.
Our customer support and marketing team receive countless calls a day asking for information. While our team is very knowledgeable, even we seek out the best natural stone resources to share with our customers, colleagues, and network. Now we're sharing them in this article.


text:
Q: Make recursive function stack - safe with Free Monads Trampoline in Scala? I've specified trait for my model:
sealed trait TreeStructureModel{
  val parentId: Option[Long]
  val title: String
  val id: Long
}

Then I'm building a tree from the records from the DB:
trait SimpleTree[+TreeStructureModel]{
  val title: String
  val id: Long
}
trait Node[+TreeStructureModel] extends SimpleTree[TreeStructureModel]{
  val inner: List[SimpleTree[TreeStructureModel]]
}
trait Leaf[+TreeStructureModel] extends SimpleTree[TreeStructureModel]

case class NodeImp[T <: TreeStructureModel](title: String, inner: List[SimpleTree[T]], id: Long) extends Node[T]
case class LeafImp[T <: TreeStructureModel](title: String, id: Long) extends Leaf[T]

object SimpleTree{
  def apply[T <: TreeStructureModel](ls: List[T]): List[SimpleTree[T]] = {
    def build(ls: List[T], current: T): SimpleTree[T] = {
      val children = ls.filter{ v => v.parentId.isDefined && v.parentId.get == current.id}
      if(children.isEmpty){
        LeafImp(title = current.title, id = current.id)
      } else {
        val newLs = ls.filterNot{ v => v.parentId.isDefined && v.parentId.get == current.id}
        NodeImp(title = current.title, id = current.id, inner = children.map{ch => build(newLs, ch)})
    }
  }
    val roots = ls.filter{ v => v.parentId.isEmpty}
    val others = ls.filterNot{ v => v.parentId.isEmpty}
    roots.map(build(others, _))
  }
}

This code works fine but uses non-tail recursive calls. So, my concern is that it will fail on big list of records. I've found a great article on using Free monads Trampoline over a non-tail recursion.
This looks like a way to go but I can't rewrite my code to make it stack safe. In the example in the article there is only one recursive call in the function but in my function there can be a lot, to build a tree. Can somebody more experienced with Free monads help me with this? Is this even possible?

A: You can rewrite your function as tail-recursive, without scalaz. Occam's razor, you know ...
 def build(
   ls: List[T],
   kids: Map[Long, List[T]],
   result: Map[Long, SimpleTree[T]]
 ) = ls match {
   case Nil => result
   case head :: tail if result.contains(head.id) => build(tail, kids, result)
   case head :: tail =>
     kids(head.id).partition(result.contains(_.id)) match {
       case (Nil, Nil) =>
         build(tail, kids, result + (head.id->LeafImp(head.title, head.id)))
       case (done, Nil) =>
         build(
           tail,
           kids,
           result +
           (head.id->NodeImp(head.title, head.id, done.map(_.id).map(result)))
         )
       case (_, missing) =>
         build(missing ++ tail, kids, result)
     }
  }

  def apply(ls: List[T]) = {
    val (roots, others) = list.partition(_.parentId.isEmpty)
    val nodes = build(ls, others.groupBy(_.parentId.get), Map.empty)
    roots.map(_.id).map(nodes)
  }

A: Elaborating on my comment, making the build method return a Trampoline and using traverse in place of map:
import scalaz.Free.Trampoline
import scalaz.Trampoline
import scalaz.syntax.traverse._
import scalaz.std.list._

sealed trait TreeStructureModel{
  val parentId: Option[Long]
  val title: String
  val id: Long
}

trait SimpleTree[+TreeStructureModel]{
  val title: String
  val id: Long
}
trait Node[+TreeStructureModel] extends SimpleTree[TreeStructureModel]{
  val inner: List[SimpleTree[TreeStructureModel]]
}
trait Leaf[+TreeStructureModel] extends SimpleTree[TreeStructureModel]

case class NodeImp[T <: TreeStructureModel](title: String, inner: List[SimpleTree[T]], id: Long) extends Node[T]
case class LeafImp[T <: TreeStructureModel](title: String, id: Long) extends Leaf[T]

object SimpleTree{
  def apply[T <: TreeStructureModel](ls: List[T]): List[SimpleTree[T]] = {
    def build(ls: List[T], current: T): Trampoline[SimpleTree[T]] = {
      val children = ls.filter{ v => v.parentId.isDefined && v.parentId.get == current.id}
      if(children.isEmpty){
        Trampoline.done(LeafImp(title = current.title, id = current.id))
      } else {
        val newLs = ls.filterNot{ v => v.parentId.isDefined && v.parentId.get == current.id}
        children.traverse(build(newLs, _)).map(trees => NodeImp(title = current.title, id = current.id, inner = trees))
      }
    }
    val roots = ls.filter{ v => v.parentId.isEmpty}
    val others = ls.filterNot{ v => v.parentId.isEmpty}
    roots.map(build(others, _).run)
  }
}

Note that I did minimal necessary changes to your code to use Trampoline. I would further suggest to use a single call to partition instead of a pair of filter and filterNot.
It would still be a good exercise to make the method tail-recursive directly.

redpajama_set_name: RedPajamaStackExchange


text:
Il pavano è un'antica variante del veneto, parlata un tempo nel contado di Padova, da cui il nome.

Le odierne parlate venete centrali, influenzate dal veneziano, conservano ben poche tracce del pavano. Rivestì tuttavia un ruolo fondamentale per il fiorire di una cosiddetta letteratura pavana comprendente numerose opere a tema scherzoso, sia in versi che in prosa, composte tra il XIV e il XVII secolo. I primi autori a scrivere in pavano furono Nicolò de' Rossi (1308-1309) e Marsilio da Carrara, ma il massimo esponente di questa corrente è Angelo Beolco detto il Ruzante (XVI secolo), cui seguirono per tutto il Seicento una serie di suoi imitatori. Perfino Galileo Galilei scrisse, in tutto o in parte e sotto pseudonimo, un libello in pavano, il Dialogo de Cecco di Ronchitti da Bruzene in perpuosito de la Stella Nuova (1605).

Caratteristiche
Il tratto più tipico del pavano era l'utilizzo esteso della metafonesi, con la trasformazione di /e/ e /o/ mediante /i/,: péro "pera" al plurale diventa pìri; pómo "mela" al plurale diventa pùmi. Un fenomeno simile avviene nelle vocali aperte, che vengono dittongate: zucòlo "zucchino" al plurale è zucuòli.

I suffissi latini -atu e -ate vengono resi con -ò e -è: parentò "parentado", amistò "amicizia". Questo fenomeno fu ricordato - e biasimato - da Dante nel De vulgari eloquentia.

Va ricordata anche la prima persona plurale del presente indicativo in -ón o -óm (favelóm "parliamo"), in seguito sostituita dalla forma in -émo di origine veneziana (favelémo).

Note

Bibliografia
Antichi testi di letteratura pavana, pubblicati da Emilio Lovarini, Bologna, Romagnoli Dall'Acqua, 1894.

Emilio Lovarini, Studi sul Ruzzante e la letteratura pavana, a cura di Gianfranco Folena, Padova, Antenore, 1965.
Ivano Paccagnella, Vocabolario del pavano (XIV-XVII secolo), Padova, Esedra, 2012.

Collegamenti esterni

Pavano
Cultura a Padova

redpajama_set_name: RedPajamaWikipedia


EZChildTrack is a childcare management platform that helps centralize and streamline operations for afterschool programs, summer camps, daycare services, preschool programs, and more. Program directors, site coordinators, and staff members can get real-time access to data and reduce time spent on repetitive tasks. The parent portal allows parents to register and enroll their children in programs online, make payments, view statements, and manage childcare information.
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We have been using EZ Child Track for 3 years now. The product is constantly, but subtly, evolving to meet the needs of our business. Our families are comfortable with the program and like being able to set up auto-pay or just go online to pay when needed. We connected an email address to the Contact Us and parents enjoy this feature. We also use many of the reports that can be generated to help inform us about delinquent accounts and enrollment. We are very pleased with EZ Child Track. It meets the needs of our Preschool and Afterschool programs.
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We deployed EZChildTrack in our business within an accelerated timeframe to address an urgent need for "transformational" change. The software is exceptionally configurable and straight forward; the Thomas Kelly team was equally exceptional in their support of our implementation. Thomas Kelly has also been very open to our feedback for future enhancements and development and has already delivered new releases incorporating our suggestions.
Westfield Washington Schools (WWS) will soon be starting our third year with EZ ChildTrack, and we are overall very pleased. WWS Student Support Programs uses EZ ChildTrack extensively throughout the entire year to manage the business side of our programs and also offer the convenience of the online parent portal for parents to enroll, make payments, and manage their account. During the school year, the online website is used for our early childcare programs and our before and after school programs. In the summer, WWS Student Support Programs continues to use EZ ChildTrack with our extensive summer camp program. The company is very responsive to their customer needs by providing frequent enhancements that add value to the software. Both their tech support group and ticket items we submit through the business management side are very responsive in addressing questions and resolved issues in a timely manner. EZ ChildTrack continues to meet our needs as we continue to grow, and our parents appreciate the ease of this program.
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text:
spotlight 2018: main menu
With contributions from
The Reflection Group
Table of Contents 2018
Exploring new policy pathways
Redefining policies for sustainable development
Box – The world needs to revamp international tax cooperation
Alternative national reports throw light on inequalities
Box – Claim of 'leave no one behind' must include indigenous peoples
Box – How to leave no one behind in statistics?
1 – The increasing concentration of wealth and economic power as an obstacle to sustainable development – and what to do about it
Box – De-financialization requires global economic governance reform
2 – Policies that strengthen the nexus between food, health, ecology, livelihoods and identities
Box – The food-health-environment nexus
3 – Vector of hope, source of fear
Box – Half of humanity is NOT online
Box – Data sovereignty
Box – Machines (algorithms) are already deciding our future
4 – Care systems and SDGs: reclaiming policies for life sustainability
Box – The National Care System in Uruguay
5 – Quest for sustainable peace and development under militarized security approaches
SDG 1: Mobilize the financial means for social protection systems for all
SDG 2: Approaching SDG 2 through the Right to Food and Nutrition
SDG 3: The need to strengthen public funding for the WHO
SDG 4: The quest for public funding for education and SDG 4
SDG 5: Women, macroeconomic policies and the SDGs
SDG 6: (Re)municipalization of water
SDG 7: Power for the people? The chimera of pro-poor energy solutions
SDG 8: What policies are needed to achieve Goal 8?
SDG 9: Alternatives to PPPs – growing instances of de-privatization
SDG 10: Invoking extraterritorial human rights obligations to confront extreme inequalities between countries
SDG 11: To ensure sustainable waste services, we must value waste workers and make sure they are in decent jobs
SDG 12: Curbing the consumption of ultra-processed foods and beverages critical to achieving SDG 12
SDG 13: Climate Justice – How climate change battles are increasingly being fought, and won, in court
SDG 14: Sustainable fishery or Blue Economy?
SDG 15: The 30-year search for biodiversity gold: history repeats itself?
SDG 16: Policies to address the gender dimension of Illicit Financial Flows
SDG 17: Trading away the SDGs?
Book traversal links for Exploring new policy pathways
Exploring new policy pathways ›
Download this chapter in pdf format here.
Este capítulo en español.
By the Global Coalition for Social Protection Floors
The international commitment is explicit and ambitious: "Implement nationally appropriate social protection systems and measures for all, including floors, and by 2030 achieve substantial coverage of the poor and the vulnerable" (SDG target 1.3). Social protection systems include contributory and non-contributory schemes for children, people in active age and older persons, as for example child grants, health insurance or pension programmes. Social protection floors provide at least a basic level of income security and access to health services for all residents in all main contingencies along the life cycle, as defined in the ILO Social Protection Floors Recommendation 2012 (no. 202). 1
There is no doubt that social protection is a key instrument to end poverty and to give people access to opportunities for a self-determined life in dignity. National social protection systems can also contribute to achieving other SDGs, including food security, good health, decent work, gender equality, reduced inequality and cohesive communities.
The social protection target is ambitious as there is an extremely wide gap between the commitment and the current situation. The ILO World Social Protection Report 2017-2019 shows that only 29 percent of the world's population is covered by adequate social protection. 2 And yet many more countries than those who already have complete social protection systems could afford at least to complete their Social Protection Floors (SPFs). The forthcoming 2018 update 3 of the SPF Index that the Global Coalition for Social Protection Floors has published in 2016, finds that
32 countries would require no more than 1 percent of Gross Domestic Product (GDP);
39 countries would require between 1 and 2 percent of GDP to complete their SPFs in the short run. 4
In medium term, a number of countries should be able to close most of their social protection gaps, including:
45 countries with SPFs gaps of between 2 and 4 percent of GDP and
9 further countries with gaps of between 4 and 6 percent GDP.
In the longer term
12 further countries might be able to close most of their gaps between 6 and 10 percent of GDP.
However, even for countries that have the political will to close the gap and the organizational capacity to implement the required policies, a major challenge is to mobilize and maintain the necessary resources to cover the cost in a sustainable way, year in and year out, through good times and bad. Social protection spending is not a short-term effort but needs to be planned and guaranteed for the indefinite future.
Large differences in the funding of social protection
The ILO found large regional differences in the funding of social protection, ranging from about 15 percent of GDP in Europe to 4.5 percent in Africa on average. That funding is almost exclusively mobilized through taxation, social security contributions and other public revenues. Very little official development assistance (ODA) is used to support social protection in developing countries. Total ODA for social protection disbursed in the years 2010-2015 varied between US$ 1.9 billion and US$ 2.6 billion or only about 2 percent of total ODA. 5
In many countries, contributory pensions, employer paid insurance for workers injured on the job and other social insurance systems provide social protection to some of the population, albeit usually not for all people and in particular not for people living in poverty in the informal economy, who are generally not in a position to pay the mandatory contributions. It is thus necessary to allocate government expenditures to social protection systems to protect people from poverty, for which countries need to build strong and fair national tax systems, increase efficiency in tax collection and administration, and end tax evasion and fraud. In some cases, budget expenditures can be reallocated from less essential uses to social protection. In some countries it will be necessary to raise taxes or other fiscal revenues, which should be done in a progressive manner, for instance through taxing personal and corporate income, as well as property and wealth.
Financing mechanisms for social protection
The choice of financing mechanisms should take account the administrative demands of their implementation and their impact on investments and economic performance. But it is essential also to consider the net fiscal impact and incidence of the combination of financing choices and transfer payments on poverty and on inequality. 6 A well-designed mix of financing mechanisms and social protection transfer programmes can reduce both poverty and inequality as decades of experience in Europe and other parts of the world show.
Striving for universal social protection, some countries have used and improved the fiscal resources earned from extractive industries. A case in point is Bolivia, where the sharing of revenues of gas exports changed from 18 percent to the government and 82 percent to the producers to a revenue 50-50 split, which led to the pledge of additional funds to core social services, including a universal old age pension, and a cash transfer for children in public primary schools to compensate for the cost of books, uniforms and transportation. 7
Political will as well as long term fiscal planning is needed to maintain social protection expenditures in the face of economic volatility (and increase them as conditions warrant). For commodity-dependent developing countries, some governments build up a reserve fund during boom times to draw down during bad times. It requires government discipline during boom times when there may be strong political pressure to expand government expenditure in unsustainable ways and in which the government administration might assume that the next crisis will fall on a successor government. The success of such a strategy requires good fiscal monitoring, including by civil society organizations.
Even if at first sight social protection seems to be a purely domestic public task, there is without doubt also an international responsibility to support developing countries in this regard, as backed by the extraterritorial state obligations agreed upon in the International Covenant on Economic, Social and Cultural Rights (ICESCR, Art. 2.1). One element of this responsibility is to help individual countries to collect taxes owed that presently escape their fiscal systems. Internationally coordinated efforts are required to effectively reduce tax evasion. Technical assistance is also beneficial to help countries design systems that prevent opportunities for legal, but unethical, tax avoidance schemes, and so not offer competing tax incentives to foreign investors that erode the national tax base in other countries and constitute a fiscal 'race to the bottom'.
There is a human rights obligation to protect ongoing social protection spending in times of economic distress. Austerity measures typically taken after crises occur must not cut into social protection spending that protects people from the most disastrous fall-out of these crises. The Committee on Economic, Social and Cultural Rights in General Comment 19 (2008) has noted that states have a minimum core obligation to provide some form of social protection, which is not subject to availability of resources. The positive economic effects of social protection as investments in social and economic development must also be recognized, for instance, in terms of supporting skill development and employability, as well as sustaining aggregate demand. During the international financial crisis of 2008, for instance, we observed the stabilizing effect of social protection in some countries, preventing worse impacts on people and economies and enabling faster recoveries.
One reason social protection is threatened in crisis periods is that priority is given to continuing to pay government creditors. It is high time to re-calibrate the risk-sharing between involved parties. The obligation to protect people from intolerable hardship should take precedence over the obligation to honour debt payments when government revenues contract. However, we do not need to wait for sovereign bankruptcy and measures of last resort to protect spending for basic social protection. Proposals to design loans and bonds that automatically postpone or cancel debt servicing during periods of economic stress, called "State-contingent debt", have many supporters but need to be put into practice. Moreover, the practice of lending conditionalities requiring States to scale back their social protection systems must be immediately reconsidered.
International ODA for social protection has to increase. Public funds will be usefully spent to contribute to national efforts to design, implement and finance systems of social protection. A reliable international funding mechanism for social protection could have added value, especially as a bridging mechanism for least developed low-income countries that might not yet have sufficient fiscal capacity. In this regards a Global Fund for Social Protection has been proposed that would aim at creating a solidarity-based financing mechanism for social protection floors. 8 The Fund would be governed by a board consisting of representatives from different constituencies, including the UN, ILO, donor countries, recipient countries and civil society. ODA resources could be complemented by innovative sources of development finance, such as a financial transactions tax (FTT), carbon taxes, and/or a decision by the International Monetary Fund (IMF) to issue new Special Drawing Rights (SDRs) for unrestricted use.
Mobilizing adequate public resources to cover the cost of social protection floors and social protection in a wider sense is a challenging terrain on the international as well as the national level. And yet, the challenge can be met because the requisite techniques and mechanisms of public finance exist. They will have to be implemented to guarantee that nobody is left behind.
The Global Coalition for Social Protection Floors is a network of around 100 NGOs and unions promoting the right of all people residing in a country to social security, regardless of documentation. It promotes social protection floors as key instruments to achieve the overarching social goal of the global development agenda (www.socialprotectionfloorscoalition.org).
1. The objective of universal, human rights-based, social protection is embedded in numerous international laws and agreements, including the Universal Declaration of Human Rights, the International Covenant on Economic, Social and Cultural Rights as well as the ILO Convention 102 on Social Security, and the ILO Social Protection Floors Recommendation No. 202.
2. ILO (2017).
3. Bierbaum et al. (2018).
4. These estimates assume that all transfers are perfectly targeted on the people living below the poverty line.
5. UN (2017).
6. Inchauste/Lustig, ed. (2017).
7. Ortiz/Cummins/Karunanethy (2017), p. 13.
8. De Schutter/Sepúlveda (2012), Cichon (2015) and Global Coalition for Social Protection Floors (2015).
Bierbaum, Mira/Schildberg, Cäcilie/Cichon, Michael (2018): Social Protection Floor Index – Update and Country Studies. Berlin: Friedrich-Ebert-Stfitung.
www.socialprotectionfloorscoalition.org/wp-content/uploads/2018/01/2017-Social-Protection-Index.pdf
Cichon, Michael (2015): A Global Fund for Social Protection Floors: Eight Good Reasons Why It Can Easily be Done. Geneva: UNRISD.
www.unrisd.org/road-to-addis-cichon
De Schutter, Olivier/Sepúlveda, Magdalena (2012): A Global Fund for Social Protection (GFSP), Executive Summary. Geneva: United Nations.
www.ohchr.org/Documents/Issues/Food/20121009_GFSP_execsummary_en.pdf
Global Coalition for Social Protection Floors (2015): A Global Fund for Social Protection. A proposal for the Conference on Financing for Development Addis Ababa. Geneva.
www.socialprotectionfloorscoalition.org/wp-content/uploads/2015/05/FfD_GFSP14April2015final.pdf
Herman, Barry (2018): Sustainably financing social protection floors, Brot für die Welt, Berlin
https://www.brot-fuer-die-welt.de/themen/fachpublikationen/armut-sozialpolitik/
ILO (2017): World Social Protection Report 2017-2019. Universal social protection to achieve the Sustainable Development Goals. Geneva.
www.ilo.org/global/publications/books/WCMS_604882/lang – en/index.htm
Inchauste, Gabriela/Lustig, Nora (Ed.) (2017): The Distributional Impact of Taxes and Transfers. Washington, D.C.: World Bank.
https://openknowledge.worldbank.org/bitstream/handle/10986/27980/9781464810916.pdf
Ortiz, Isabel/Cummins,Matthew/Karunanethy, Kalaivani (2017): Fiscal Space for Social Protection and the SDGs: Options to expand social investments in 187 countries. Geneva/New York: ILO, UNICEF and UN Women.
www.social-protection.org/gimi/RessourcePDF.action?ressource.ressourceId=51537
UN (2018): Financing for Development: Progress and Prospects 2018. Report of the Inter-agency Task Force on Financing for Development. New York.
https://developmentfinance.un.org/iatf2018
Book traversal links for SDG 1: Mobilize the financial means for social protection systems for all
‹ 5 – Quest for sustainable peace and development under militarized security approaches
SDG 2: Approaching SDG 2 through the Right to Food and Nutrition ›
Arab NGO Network for Development
P.O.Box: 5792/14
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www.annd.org
Center for Economic and Social Rights
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91B0FBB4-04A9-D5D7-16F0F3976AA697ED
C9A22247-E776-B892-2D807E7555171534
Diamond Jackson '21 to Study Education Policy at Harvard
by Libby Militello '22
Connections and Careers
Diamond Jackson '21 Photo: Nancy L. Ford
At last Saturday's Commencement, Diamond Jackson's '21 four busy years at Hamilton came to an end. She served as the chair of the C. Christine Johnson Voices of Color Lecture Series, co-president of the Black & Latinx Student Union, supervisor at the Academic Center for Excellence (ACE), HEOP summer residential assistant, and as a student researcher, completing Emerson, Kirkland, and Levitt Center projects.
Jackson's wide breadth of experience will be put to use this fall at the Harvard Graduate School of Education, where she'll study education policy. Jackson cites her Hamilton experiences and guidance from Lecturer in Sociology Meredith Madden as key factors in her decision to pursue a path in education policy.
"After taking Education and Sociology courses like Issues in Education, Urban Education, and Poverty & Inequality with Professor Madden, who also supervised me on each of my research projects, I became really aware of how different parts of my identity had shaped my experiences with education and continued to do so," Jackson said.
In her multiple undergraduate research projects, Jackson focused on the mental health of Black students and the narratives of low-income Black women who are athletes at Predominantly White Institutions (PWIs). At Harvard, she plans to continue her focus on how policy shapes student experiences at colleges and universities.
Jackson explained that her experience as a first-generation student influenced her path to graduate school.
"For many first-generation students — particularly those who haven't been educated in predominantly white and wealthy schools prior to Hamilton — it can be hard to know just what resources exist at Hamilton waiting to be utilized," she said. "For me, talking to my peers and professors about my interests and goals has been crucial to my success at Hamilton. My support team continues to share opportunities with me to ensure a successful future."
Diamond Jackson '21
Hometown: Bronx, N.Y.
High School: Manhattan Hunter Science High School
Class of 2021 Outcomes ?
Jackson said that Harvard's Education Policy & Analysis program allows for a great deal of intellectual freedom, something that reminds her of Hamilton's open curriculum. She is looking forward to take advantage of the program's flexibility to gain a clearer picture of what her future away from College Hill holds.
"I am passionate about continuing with research, and getting into some policy work as well, though I'm not quite sure what that looks like just yet. But that's a part of what's so exciting about this," Jackson explained. "Although I already know I'm zealous about research, I'm looking forward to learning more about other opportunities involving education policy."
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She got her start in television production and advertising and parlayed that into a career that now encompasses public relations, advertising, marketing, production and media coordination.
She has extensive certifications in copywriting, editing, photography and graphic design and utilizing those skills has won 25 national awards for her work.
One of her proudest accomplishments includes a documentary video on the life of American folk artist Walter Anderson that was featured in the Smithsonian Museum of American Art in Washington, D.C.
Gretchen has a passion for people and believes that effective advertising and marketing services can be both affordable and effective.
From small budget start-ups to billion-dollar businesses, Gretchen will work with you to create a campaign, program or plan that will meet your budget and exceed your expectations.
Gretchen serves her community on various boards, committees and councils including the Orlando Sports Foundation and the West Orange Chamber of Commerce.
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His 30+ years of industry experience lend a certain no-nonsense professionalism to the agency that helps bring projects in on time and on budget.
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As the technical director at GGMA you'll often find him working with clients on their video and television projects in our dedicated HD editing suite.
He's also the main audio engineer at Green Grass and can help you record radio ads, voice-overs, books on tape, special event audio tracks and he's also our expert on live event audio.
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It was with great pleasure that I heard of your recent promotion to (Designation Title) through an update yesterday on LinkedIn.
You are inheriting a great team, and I'm sure that your ability to lead by example in motivating others will make them even more effective and productive. You have done a fine job there for many years, and you deserve the recognition and responsibility of the position.
Congratulations and good luck in your new position – onward and upward!


Holiday casual looks are relative like I always say but even while looking casual, you need to nail it.
The holidays are still in full swing, except you are working like me, I'm sure you are having fun. Although with the fuel situation still ongoing, it's been a bit of a downer. My people are still turning up though! Almost all the concerts were sold out and Lagos is bubbling as usual, albeit a little low-key.
So, Christmas colors again, because it is over doesn't mean we should not look the part eh? Prior to this outfit, I stayed away from the cliche white and red holiday outfits. I would rather go full red but I already did a little white and red with my shoes in this post. I got this oversize t-shirt as a gift from babe, thank God he gets my style kinda, decided to match the colors with the inscription on the skirt so I stole my mum's pleated red skirt.
Pleats trended a lot this year. I have always been into pleats right from University days ( I attended an Anglican school so pleated midi skirts were totally cool then) so it was quite easy for me to reactivate my love for them. I wear a few to church too but this red one my mum never wore, was perfect for the shirt.
Last month, I got this pair of oh-so-gorgeous Arata slip-on wedge sneakers from the Tsubo team and it was basically love on first sight. If you follow me on Instagram, my insta stories were proof of that. Created in 1997, Tsubo is a Japanese brand with products blends comfort and performance features of athletic profiles with the style and character of casual footwear. I really like the color as it is one I don't have (or would have never bought myself). It is a light weight foam mid sole that provides ample cushioning, makes me feel like I'm walking on air. I've been itching to try the sneaker on midi skirt again like I did here and this did it. The color of the sneakers broke the red & white monotone, it was perfect for an holiday look.
A black Baker hat on my head, my clutch purse as a waste purse and a ripped denim choker for that street style appeal. I really love how it came out.
No need to tell you about my new year resolutions (I don't have any) since I already shared the things I'm dropping in 2017. I am excited about the new year, always feels like a clean slate and another chance to get it right. All I want us to do is enter 2018 with God and an optimistic mind and watch God come through for us.
How are your holidays going? Do you like the sneakers and skirt trend? Would you rock this look? Please drop your comments.


text:
South University, Richmond's Master in Science of Physician Assistant program receives ARC-PA extension for 10 more years
March 31, 2021 12:57 ET | Source: South University
Richmond, VA, March 31, 2021 (GLOBE NEWSWIRE) -- March 31, 2021 For Immediate Release: South University,...
South University, West Palm Beach Welcomes Inaugural Master of Science in Physician Assistant class
Royal Palm, West Palm Beach, March 02, 2021 (GLOBE NEWSWIRE) -- For Immediate Release – West Palm Beach FL South University is proud to announce the launch of a new Master of Science in Physician...