text:
No Evidence That Testosterone Reduces Cognitive Empathy
No Evidence That Testosterone Reduces…
It's long been known that autism is far more prevalent in males than in females. What hasn't been understood is why. "Of course, the primary suspect when we have something that is sharply differentiated by sex is testosterone," says Gideon Nave, an assistant professor of marketing in Penn's Wharton School. Yet a new study led by Nave implores scientists to keep looking.
In two randomize control studies of testosterone administration which were the largest of their kind and include nearly 650 men, Nave and colleagues found no evidence of a link with cognitive empathy, the capacity to read the emotions of others, a trait that is characteristically impaired in people with autism. They report their findings in the journal Proceedings of the Royal Society B: Biological Sciences.
Test of reading emotions
"Several earlier studies have suggest a connection between testosterone and reduce cognitive empathy; but samples were very small, and it's very difficult to determine a direct link," says Amos Nadler of Western University; also the first author of the study. "Our results unequivocally show that there is not a linear causal relation between testosterone exposure and cognitive empathy."
Prior to this work, the strongest evidence for a link between testosterone exposure reduce cognitive empathy; hence came in 2011 in a study that find administering testosterone to healthy women reduce their performance on a test of reading emotions. The results suggest the testosterone impair their performance. Moreover, the work point to the ratio of the length of the participant's second finger to their fourth finger; hence known as the 2-D:4-D ratio, as a proxy for sensitivity to testosterone.
Some believe that the ratio declines with increase in utero exposure to testosterone though evidence for that connection is mix. That study's authors contend that their findings support the idea that prenatal testosterone exposure create a more masculinize brain that less readily infer the emotional state of others. The study was use as support for the "extreme male brain" hypothesis of autism; which contends that autism is an exaggeration of "male" tendencies toward a cognitive style characterize by systemizing over empathizing.
Testosterone administration affect
Participants were then show a photo of an actor's eyes; also ask to select the emotional state that best describe their expression. All participants also had their 2-D:4-D ratio measured. While the testosterone gel did increase participants' levels of the hormone; so the researchers find no evidence that testosterone administration affect performance on tests of cognitive empathy. They also find no relationship between participants' performance on the tests and their 2-D:4-D ratio.
"The results are plain," says Nave. "However, it's important to note that the absence of evidence is not evidence of absence. We found that there is no evidence to support this effect of testosterone; but that doesn't rule out any possible effects. From what we know, though, it seems that if testosterone does have an influence; so the effect is complex, not linear. Reality is typically not that simple."
And the new study includes more participants than the earlier one by almost two orders of magnitude; augmenting the researchers' confidence in the results. The extreme male brain theory of autism has receive a lot of attention but, Nave notes, "if you look at the literature carefully; there is still not really strong support for it. "For now, They think we have to embrace our ignorance on this."
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text:
\section*{Abstract}
In complex plasmas, the behavior of freely floating micrometer sized particles is studied. The particles can be directly visualized and recorded by digital video cameras. To analyze the dynamics of single particles, reliable algorithms are required to accurately determine their positions to sub-pixel accuracy from the recorded images. Typically, straightforward algorithms are used for this task.
Here, we combine the algorithms with common techniques for image processing. We study several algorithms and pre- and post-processing methods, and we investigate the impact of the choice of threshold parameters, including an automatic threshold detection.
The results quantitatively show that each algorithm and method has its own advantage, often depending on the problem at hand. This knowledge is applicable not only to complex plasmas, but useful for any kind of comparable image-based particle tracking, e.g.\ in the field of colloids or granular matter.

\section*{Introduction}
Particle detection in digital images is a crucial first step in the analysis of many-particle systems in the case that individual particles can be detected by direct optical measurements. Efforts to optimize particle detection can be found in a wide range of fields: in biophysics, single particle tracking is used to study the motion of
particles (e.g.\ proteins, molecules or viruses) involved in cell membrane and intracellular activities \citep{Saxton:1997,Sbalzarini:2005,Chenouard:2014}.
Particle detection and tracking from optical measurements is utilized in granular matter research \citep{Tsai:2004,Harrington:2014}, and in colloidal physics, where the dynamics of systems of nano- to micrometer sized particles can be investigated by analyzing single particle motion from direct video microscopy \citep{Crocker:1996,Leocmach:2013}.

Complex plasmas \citep{Fortov:2005,Morfill:2009,Ivlev:2012} consist of micrometer sized particles injected into a low-temperature plasma composed of electrons, ions and neutral gas. These particles are large enough to be visible to digital cameras with an appropriate optics, and provide an excellent opportunity to study fundamental dynamics on the kinetic level of individual particles.
In contrast to colloids, where particles are embedded in a viscous medium and therefore over-damped, complex plasmas are virtually undamped, and the time scale of dynamical processes is short and therefore easily accessible. The particles are typically illuminated with a sheet of laser light, and the reflected light can be observed with digital cameras. Since the particle distances are large (with a magnitude of several hundreds of micrometers), individual particles can be observed directly as mostly disjunct small groups of illuminated pixels on the camera sensor.

From those ``blobs'' of pixels, particle positions can be determined to sub-pixel accuracy -- a necessity for the study of dynamics of single particles -- with an adequately chosen algorithm.

By detecting individual particles, and tracing them through consecutive images (this is possible if the particle displacement between two images is small enough to allow for a unique assignment), velocities can be obtained. This method is called Particle Tracking Velocimetry (PTV), and has the advantage of more precise velocity measurements \citep{Pereira2006} in contrast to Particle Image Velocimetry (PIV)\citep{Williams2016}, where only spatially averaged velocity vectors are obtained, especially in particle clouds too dense for single particle detection.

Complex plasmas are three-dimensional systems, and currently the interest in 3D optical particle diagnostics is growing \citep{Jambor:2016,Melzer:2016}. To triangulate the real position of a particle in 3D space, additional requirements are imposed on particle detection algorithms. Hence, we are also looking for algorithms for the detection of particles which are nearby each other on the image plane due to their overlapping motion in different layers. These algorithms can also be useful for particle tracking in systems with a high packing density.

With the methods presented in this paper we show that the commonly acquired accuracy can be exceeded without unnecessary increasing the complexity of the procedure. This is accomplished by combining simple image pre- and post-processing procedures with an improved version of the commonly used algorithm for blob detection, and to some extent by applying automatic threshold detection.

Usually, straightforward algorithms are used for blob detection \citep{Crocker:1996, Feng:2007, Ivanov:2007}, which is justified by the simple search feature and the typically low image noise. We show that this algorithm can be improved by generalizing it to blobs being not necessarily simply connected sets of pixels. Other more complex blob detection algorithms, such as SimpleBlobDetector \citep[SimpleBlobDetector]{opencv_library} or MSER \citep{Matas:2002}, did not turn out to be satisfactory in our case.

Though some of the techniques are well-known, a combination of them as well as an investigation of their individual influence on the accuracy of particle detection was not performed elsewhere to such an extent, especially for the typical particle shapes obtained in complex plasma experiments (for example, \citet{Feng:2007} is mostly involved in examining one particular core algorithm without pre- and post-processing, while \citet{Ivanov:2007} investigated some methods for pre- and post-processing, but does not combine the methods in the result).

Here, we not only investigate pre-processing, particle detection and post-processing in combination, but also take into account particle sizes and several kinds of image noise in our results. Additionally, we introduce Otsu binarization as an automated procedure. We also show that the choice of methods strongly depends on the image features (e.g. noise).

The paper is organized as follows: After a description of the general approach in \secref{section:General Approach}, \secref{section: Simulated Images} shows how the artificial images are generated to test the quality of the algorithms. In sections \ref{section:Preprocessing (Image Processing)}, \ref{section:Moment Method (Blob Detection)} and \ref{section:Fitting Postprocessing} the different steps of image processing and particle detection are presented in more detail, followed by some examples in \secref{section:Examples}. Finally, the conclusion summarizes the paper in \secref{section:Conclusion}.

\section{General Approach}\label{section:General Approach}

The process of obtaining particle coordinates from experimental data (images) can be divided into the following necessary steps:

\begin{description}
\item [Image acquisition] Get the image from real world.
\item [Image processing] Prepare/enhance the image (e.g.\ by filtering).
\item [Blob detection] Identify particle positions.
\item [Postprocessing] Enhance found positions of particles (e.g.\ fitting).
\end{description}

Each step is an own field of research. In the following, they are explained in the depth necessary for this work.

\subsection{Image Acquisition}
Image acquisition is part of the experiment, and is only mentioned here for completeness, since the details of the experimental procedures go beyond the scope of this paper. To get good images, we need a proper illumination of the particles, a matched optical system, and an appropriate camera with an applicable storage system.

In this step, image noise is introduced. The sources are manifold, e.g.\ thermal behavior of the camera chip, noise of the involved electronics, defect pixels or radiation influencing the complete system. The noise causes uncertainties, which can be abstracted as additive white Gaussian noise and salt and pepper noise, superimposed on the pixels.

In the following, we assume a camera giving $8$ Bit gray scale images.

\subsection{Image Processing}
Preparing the image is a task extremely dependent on the blob detection algorithm to be chosen for the next step, e.g.\ an algorithm using edge detection will not work well if the edges of the blob are destroyed by applying a smoothing filter. In that case, a sharpening filter would be preferable.

One particle can be seen approximately as a point source of light, and the point spread function describes what we can expect to see on the image sensor. The point spread function defines how an ideal point source will be mapped by a system of optical components. In the case of point-like particles, the Airy disc \citep{Airy:1835} gives a good approximation of this mapping.

Optical side lobes of the point spread function can be reduced by a Hanning amplitude filter (a convolution with the Hann function) \citep{Kumar:2013}. The Hann function, visualized in \figref{fig:example shapes}, with the parameter $N$ for a point $r$ is given by:
\begin{align*}
\hspace{-7mm}w(r) = \left\{ \begin{array}{ll}
    \frac{1}{2} - \frac{1}{2} \cos{\left( \frac{ 2 \pi \left(r-\frac{N-1}{2}\right)}{N-1} \right)} & \mbox{\hspace{-2mm}if } \abs{r} \leq \frac{N-1}{2} \\
    0 & \mbox{\hspace{-2mm}else.} \\ \end{array}\right.
\end{align*}

The parameter $N$ influences the width of the window. The Hanning amplitude filter is in principal a low-pass filter. This kind of filter passes signals with a spatial frequency less than the (user chosen) cutoff frequency, and can therefore reduce high-frequency image noise, e.g.\ Gaussian white noise.

This filter can easily be implemented by using template matching from the library opencv \citep{opencv_library}.

\begin{figure}
  \includegraphics[width=0.49\textwidth]{figure_1}
  \caption{From left to right:
    (a) Image of a particle of size $\sigma_{x,y} =1$. In (b) high noise is added (Gaussian noise with $\operatorname{SNR}\, =5$, and salt and pepper noise with a probability of $0.5 \mbox{ \%}$), (c) the noisy image is then filtered by a Hanning amplitude filter with $N=5$, (d) and finally the filtered image is clustered by Otsu's method.
  }\label{fig:example of hann filtered image}
\end{figure}

In \figref{fig:example of hann filtered image}, an example shows the effect of a Hanning amplitude filter.

Of course it is in general a good idea to use combined low-pass and high-pass filtering. High-pass filtering does the opposite to a low-pass filter: pass spatial frequencies below a cutoff and thus reduce image noise such as large-scale intensity gradients. But a high-pass filter can mask the behavior of a low-pass filter -- e.g.\ the blurring of a low-pass filter would be reduced by a high-pass filter. Since we want to investigate the effect of specific filters, we do not want this masking. Usually, we do not observe low frequency noise in our images, and therefore omit high-pass filtering in this paper.

In general it should be mentioned, that \citet{Crocker:1996} and \citet{Ivanov:2007} use a simple but effective filter, which behaves similar to a high-pass filter. They subtract a background calculated by a convolution with a boxcar kernel (moving average) from the image after low-pass filtering by a convolution with a Gaussian kernel.

\subsection{Blob Detection}\label{section:Blob Detection}
In the complex plasma community, a typical approach for blob detection is the moment method \citep{Feng:2007, Ivanov:2007}, which is a simplified version of the approach by \citet{Crocker:1996} \footnote{You can find many implementations in the internet, e. g.: \href{http://www.physics.emory.edu/faculty/weeks/idl/}{www.physics.emory.edu/faculty/weeks/idl}}:

\begin{enumerate}
\item Find connected pixels brighter than a threshold (a particle).
\item Calculate center of every particle (position of a particle).
\end{enumerate}

In the literature \citep{Feng:2007, Ivanov:2007}, connected pixels are assumed to be a set, which is simply connected. More general, we now define a set of pixels $P_i$ belonging to a particle as:
\begin{alignat*}{2}
P_i \subset &\left\{ p: I(p)>I_{threshold} \right\}\\
\end{alignat*}
\begin{alignat*}{2}
  \mbox{with: }& \left(\left|P_i\right| = 1\right) \lor \\
  & \quad \left( \forall  p_j \in P_i: \right.\\
  & \qquad \left. \exists p_k \in P_i \setminus \left\{p_j\right\}:d(p_j, p_k)<r \right)\\
  & \forall  p_j \in P_i: \\
  & \quad \forall p_k \in \left\{ p: I(p)>I_{threshold} \right\} \setminus P_i:\\
  & \qquad d(p_j, p_k) \geq r\\
  &\left|P_i\right| \geq m_p\\
& x_d\left(P_i\right) \geq m_x \\
& y_d\left(P_i\right) \geq m_y \\
&\frac{\left|P_i\right|}{ x_d\left(P_i\right) \times y_d\left(P_i\right) } \geq m_d\\
& \frac{1}{\left|P_i\right|} \sum_{p \in P_i}^{}{I(p)} \geq m_{bd}\\
\end{alignat*}
\begin{alignat*}{2}
\mbox{with: }& x_d(P_i) := \max\left\{x\left(p_j\right)-x\left(p_k\right): \right.\\
& \qquad \qquad \qquad \qquad \left. p_j, p_k \in P_i\right\}\\
& y_d(P_i) := \max\left\{y\left(p_j\right)-y\left(p_k\right): \right.\\
& \qquad \qquad \qquad \qquad \left. p_j, p_k \in P_i\right\}\\
\end{alignat*}

Here, $P_i$ is a set of pixels and represents the particle with the number $i$, $I(p)$ is the intensity of the pixel $p$, $I_{threshold}$ is the intensity of the threshold, $\left|P_i\right|$ denotes the cardinal number of $P_i$, $d(p_j,p_k)$ is the distance of the two pixels $p_j$ and $p_k$, $r$ is a search radius, $m_p$ is the minimum number of pixels a particle needs to be composed of, $x(p)$ is the $x$ coordinate of $p$, $y(p)$ is the $y$ coordinate of $p$, $m_x$ is the minimum length in $x$ direction in pixel, $m_y$ is the minimum length in $y$ direction in pixel, $m_d$ is the minimum density of a particle (density being the total number of pixels weighted by the area of the smallest rectangle envelope of $P_i$), $m_{bd}$ is the minimum brightness density. The brightness density is defined as the sum of all intensity values of the pixels in $P_i$, weighted by the total number of pixels in the set $P_i$.

The parameter $r$ allows to identify sets of pixels as a particle $P_{i}$ even if those pixels are not directly connected. For example, setting $r = 1$ leads to a simply connected set as used in the mentioned literature, while setting $r = 1.5 > \sqrt{1^2+1^2}$ (assuming quadratic pixels with side length $1$) allows pixels in $P_{i}$ to be connected only by a corner.
For larger values of $r$, the pixels in the set $P_{i}$ do not need to be simply connected at all. This can be used for compensation of pepper noise or intensity jitter.
In addition, to be recognized as separate particles, the shortest distance between the particle contours of two neighboring particles must be $\ge r$.

The center $\left(x_c(P_i), y_c(P_i)\right)$ can be calculated using the pixel positions and --- as often done in the mentioned literature --- the brightness of them:
\begin{alignat*}{2}
x_c(P_i) = \frac{\sum_{p \in P_i}^{}{x(p) \left(I(p) - I_{base}\right)}}{\sum_{p \in P_i}^{}{\left(I(p) - I_{base}\right)}}\\
y_c(P_i) = \frac{\sum_{p \in P_i}^{}{y(p) \left(I(p) - I_{base}\right)}}{\sum_{p \in P_i}^{}{\left(I(p) - I_{base}\right)}}
\end{alignat*}
Here, $I_{base}$ gives an offset. In \citet{Feng:2007} this offset is discussed and it is recommended to use $I_{base} = I_{threshold}$ to reduce the error.

Other blob detection algorithms (\citet[SimpleBlobDetector and MSER]{opencv_library}) were tested, but proved to be unreliable and could only detect some of our largest particles. Since those algorithms increase the complexity and computation time without reaching the quality of our proposed blob detection method for the small particle images prevalent in complex plasmas, they were not investigated further.

\subsection{Postprocessing}
\begin{figure}
  \includegraphics[width=0.49\textwidth]{figure_2}
  \caption{Shown are: the Hann function with $N=5$ in pink ({\color{french_rose}$\blacksquare$}) , and the generalized Gaussian point spread function with $p=1$ in blue ({\color{royalblue}$\blacksquare$}) ,  $p=3$  in green ({\color{mint_green}$\blacksquare$})  and  $p=2$ in yellow ({\color{peach}$\blacksquare$}) . The latter is identical to the normal distribution. The width is $\sigma=1$ for all cases. With different parameters $p$, the generalized Gaussian is able to mimic different particle shapes, which can e.g.\ result from defocused images.}\label{fig:example shapes}
\end{figure}
Since the blob detection is not an exact deconvolution, we are bound to have errors. To overcome this, we can fit a function to the approximate particle coordinates obtained from the blob detection. We now use the concept of a particle as an approximate point source of light, and the subsequent description of $P_i$ as a point spread function similar to the Airy disc \citep{Airy:1835}. The latter can be approximated by a Gaussian or a generalized Gaussian point spread function \citep{Claxton:2008} (see \eqref{eq:generalized Gaussian point spread function} in \secref{section:Fitting Postprocessing}), visualized in \figref{fig:example shapes}.

In our procedure, we choose a generalized Gaussian point spread function and fit it to the approximate coordinates from the blob detection.

\section{Simulated Images}\label{section: Simulated Images}
To test our implementation we need well-defined, artificial images of particles. Here, the use of artificial images with well-defined particle positions is crucial to be able to calculate the deviation of tracked position to real position and thus to quantify the quality of our algorithms. The images are modelled after real-world experimental images of complex plasmas recorded by optical cameras.

The particles are represented by a bivariate normal distribution with a correlation of $0$:
\begin{align*}
\frac{1}{2 \pi \sigma_x \sigma_y}
\exp{\left( \frac{-1}{2}
 \left(\frac{(x-\mu_x)^2}{\sigma_x^2}+
 \frac{(y-\mu_y)^2}{\sigma_y^2}\right)
\right)}
\end{align*}

Since $(2 \pi \sigma_x \sigma_y)^{-1}$ is just a constant factor, it can be ignored. Furthermore, the image is scaled to values between $0$ and $1$.

In a real-life camera image, the brightness of a pixel is the integration over time and space. Therefore, we integrate the intensity values over one pixel:
\begin{align*}
&\int_{x_1}^{x_2}{
 \int_{y_1}^{y_2}{}}\\
& \exp{\left( \frac{-1}{2}
  \left(\frac{(x-\mu_x)^2}{\sigma_x^2}+
   \frac{(y-\mu_y)^2}{\sigma_y^2}\right)
  \right)}
 {dy}
{dx}
\end{align*}
\begin{align*}
        = &\left(\int_{x_1}^{x_2}{
        \exp{\left(\frac{-(x-\mu_x)^2}{2\sigma_x^2}\right)}
        dx}\right)\\
        &\times\left(\int_{y_1}^{y_2}{
        \exp{\left(\frac{-(y-\mu_y)^2}{2\sigma_y^2}\right)}
        dy}\right)
\end{align*}
\begin{align*}
        = &\frac{\pi \sigma_x \sigma_y}{2}
        \left(\erf{\left(\frac{x_1-\mu_x}{\sqrt{2} \sigma_x}\right)}-
          \erf{\left(\frac{x_2-\mu_x}{\sqrt{2} \sigma_x}\right)}
        \right)\\
        &\times \left(\erf{\left(\frac{y_1-\mu_y}{\sqrt{2} \sigma_y}\right)}-
          \erf{\left(\frac{y_2-\mu_y}{\sqrt{2} \sigma_y}\right)}
        \right)
\end{align*}

Again, the constant factor $(\pi \sigma_x \sigma_y)/2$ can be ignored, because the image is rescaled in the end. This procedure is repeated for each pixel.

\begin{figure}
  \includegraphics[width=0.49\textwidth]{figure_3}
  \caption{Simulated particles with $\sigma_x = 1 = \sigma_y$ without image noise. For better visibility the image is shown in inverted colors. The coordinates $(3, 4)$ of the left particle are centered in a pixel, the coordinates $(19.5, 3.5)$ of the right particle are exactly centered between two pixels, and the coordinates $(11.25, 3.8)$ of the middle one are chosen arbitrarily.}\label{fig:example particle sigma=1}
\end{figure}

Examples for artificial particle images are given in \figref{fig:example particle sigma=1}. The figure also illustrates the impact of the given sub-pixel location of the particle center on the intensity distribution.

To be able to describe the strength of the noise by one single parameter, we create an additive white Gaussian noise (AWGN) with a mean of $0$ and a standard deviation of $1$.
We can scale the noise to the image by a signal to noise ratio $\operatorname{SNR}\,$ with $B$ a matrix representing the noise free image, $B_{noise}$ a matrix representing the noise and $B_{noisy}$ a matrix representing the image with noise:
\begin{align*}
B_{noisy} = \max{\left\{0, \min{\left\{1,B + \frac{1}{\operatorname{SNR}\,} B_{noise}\right\}}\right\}}
\end{align*}

With this widely-used, simple noise model (e.g.\ it is often used in information theory \cite{Shannon:1948, Proakis:2001}), we can create a noise which behaves roughly similar to the thermal noise of camera sensors. In \citet[pages 43--44]{Pitas:2000}, this approach of cutting values is used to generate additive Laplacian noise\footnote{Because of a simple pseudo random number generator it was necessary to use a Laplacian instead of a Gaussian distribution in \citep[pages 43--44]{Pitas:2000}.}.

Our simple $\operatorname{SNR}\,$ is consistent with the well-known Rose criterion (\citet[page 97]{Rose:2013}), which states that a $\operatorname{SNR}\,$ of at least $5$ is necessary for a reliable detection. Due to this fact, \figref{fig:noise with snr} does not show bars for $\operatorname{SNR}\, = 5$.

By setting pixel intensities to $0$ or $1$ with a given probability, we can add salt and pepper noise. This kind of noise simulates defective pixels usually present on typical camera sensors. Pixels can appear dark (``pepper'') or bright (``salt''), regardless of the exposure, e.g.\ due to errors in the pixel electronics.
Bright pixels are easy to detect by taking dark-frame images (e.g.\ an image taken with covered lens), dark pixels can be detected with more effort by taking gray images. If a list of defective pixels is available, some cameras are able to correct these listed pixels by averaging the surrounding ones.

Though the occurence of excessive salt and pepper noise in an experimental setup should normally lead to an exchange of hardware, there are situations in which this is not an option. Good examples are experimental instruments in remote locations not accessible to technicians, e.g. satellites or sealed experimental devices on a space station, such as complex plasma microgravity research facilities (PK-3 Plus \citep{Thomas:2008}, PK-4 \citep{Pustylnik:2016}). Here, cameras are exposed to higher levels of radiation, and pixel deterioration, causing salt and pepper noise, becomes an issue. To still obtain good scientific results over an extended period of time, one needs to handle such noise sources adequately during data analysis as long as it is feasible.

\section[Preprocessing (Image Processing)]{Preprocessing\\(Image Processing)}\label{section:Preprocessing (Image Processing)}
Image preprocessing is not restricted to the use of general filters preserving the brightness distribution of particles, but can be extended to procedures for e.g.\ threshold detection, especially with regard to the requirements of the moment methods.

In the first step, the moment method needs a separation of the pixels belonging to particles, and pixels composing the background. Since our images represent particles illuminated with a laser, we can assume to have a bi-modal histogram.

This can be clustered for example by Otsu's method \citep{Otsu:1979}. This method separates the histogram of the image in $2$ classes -- below and above the threshold -- with the goal to minimize the variances of both classes. This leads to a maximal interclass variance. The image is then binarized according to the classes --- pixels of one class are usually shown as white, and those belonging to the other class as black.

There are other thresholding techniques available (for an overview see e.g.\ \citet{Sezgin:2004}). We use Otsu's method since it is in the top ten ranking of \citet{Sezgin:2004}, one of the most referenced (therefore well-known), and implemented e.g.\ in opencv \citep{opencv_library}.

Furthermore, a quick visual check of our example images with the tool ImageJ \citep{Schneider:2012} shows, that most available other techniques lead to erroneous  binarizations, with background pixels becoming falsely detected as signals and set to white.

We analyzed one of the more promising methods further: the intermodes thresholding of \citet{Prewitt:1966} (e.g.\ implemented in ImageJ \citep{Schneider:2012}) shows a detection rate similar to that of Otsu's method. It smoothes the histogram by running averages of size 3 until there are exactly two local maxima. The threshold is then the arithmetic mean of those. But only in the example of particle separation (\autoref{subsection:Particle Separation}) the intermodes thresholding performs superior to Otsu's method, because the intermodes thresholding chooses a higher threshold than Otsu's method. The higher threshold is chosen in all our examples, and the reason for this is simple and shows also the drawback of intermodes thresholding: dominant peaks in the histogram --- such as the peak at 1 in our perfectly ``illuminated'' artificial images --- are detected as one maximum and shift the average towards the maximum brightness value. Nonetheless, the performance of such a simple approach is excellent.

In \figref{fig:example of hann filtered image}, an image is shown representing the clustering by Otsu's method. For all further steps of calculating the particle center only the threshold value detected by Otsu's method is used, not the binarized image itself.
This means that in the first step of the moment method the threshold is used to identify ``white'' pixels belonging to a particle, while in the second step the position is calculated with the brightness values of the original image.

\begin{figure}
  \includegraphics[width=0.49\textwidth]{figure_4}
  \caption{Comparison of different strengths of additive white Gaussian noise: yellow ({\color{peach}$\blacksquare$})  bars for $\operatorname{SNR}\, = 10$, blue ({\color{royalblue}$\blacksquare$})  for $\operatorname{SNR}\, = 100$ and green ({\color{mint_green}$\blacksquare$})  for $\operatorname{SNR}\, = 1000$. Missing bars imply that not all particles where correctly detected (for $SNR=5$, this was the case for all algorithms). The ordinate shows the root mean square error of the distance between detected and real positions. There was no salt and pepper noise. The statistics/simulation was done with images containing $10000$ particles with $\sigma_{\{x, y\}} = 1$.}\label{fig:noise with snr}
\end{figure}

Different algorithms are compared with respect to different signal to noise ratios in \figref{fig:noise with snr}:

\begin{description}
\item [alg01\label{alg01}] moment method (\autoref{section:Blob Detection})
\item [alg02\label{alg02}] \nameref{alg01} with $I_{base} = I_{threshold}$
\item [alg03\label{alg03}] \nameref{alg02} preprocessed by a Hanning filter ($N = 5$)
\item [alg04\label{alg04}] \nameref{alg03} with the threshold automatically detected by Otsu's method
\item [alg05\label{alg05}] \nameref{alg04} with gamma adjustment with $\gamma=3$
\item [alg06\label{alg06}] \nameref{alg01} preprocessed by a Hanning filter ($N = 5$) and fitted by a generalized Gaussian (\autoref{section:Fitting Postprocessing})
\item [alg07\label{alg07}] \nameref{alg06} with the threshold automatically detected by Otsu's method
\end{description}

\begin{figure}
  \includegraphics[width=0.49\textwidth]{figure_5}
  \caption{Example images of $2$ particles for different signal to noise ratios, which were used in \figref{fig:noise with snr}. For better visibility, the upper parts of the images are shown in inverted colors.}\label{fig:noise with snr example images}
\end{figure}

Examples of single noisy particle images are shown in \figref{fig:noise with snr example images}. For a $\operatorname{SNR}\,$ of $5$, not all of the $10000$ particles could be detected by any of the algorithms.
While particles in the example images \figref{fig:noise with snr example images} are easy to identify for human eyes, the algorithms are more sensitive to the noise.

Comparing \nameref{alg01} and \nameref{alg03} in \figref{fig:noise with snr}, we can see that the Hanning filter used in \nameref{alg03} leads to a better detection rate in the case of high noise.

\citet{Feng:2007} recommend using $I_{base} = I_{threshold}$ in the moment method to reduce uncertainties in the found particle positions. \nameref{alg02} uses this method, and \figref{fig:noise with snr} shows that indeed the error can be reduced in comparison with the pure moment method in \nameref{alg01}.
\begin{figure}
  \includegraphics[width=0.49\textwidth]{figure_6}
  \caption{Comparison of different particle sizes: pink ({\color{french_rose}$\blacksquare$})  bars for $\sigma_{\{x, y\}} = 0.1$, yellow ({\color{peach}$\blacksquare$})  for $\sigma_{\{x, y\}} = 0.5$, blue ({\color{royalblue}$\blacksquare$})  for $\sigma_{\{x, y\}} = 1$ and green ({\color{mint_green}$\blacksquare$})  for $\sigma_{\{x, y\}} = 2$. Missing bars imply that not all particles where correctly detected. The ordinate shows the root mean square error of the distance between detected and real positions. There was a low Gaussian noise with a $\operatorname{SNR}\, = 100$, and no salt and pepper noise. The statistics/simulation was done with images containing $10000$ particles.}\label{fig:compare algorithm to particle size}
\end{figure}
\begin{figure}
  \includegraphics[width=0.49\textwidth]{figure_7}
  \caption{Example images of the different particle sizes used in \figref{fig:compare algorithm to particle size}.}\label{fig: compare algorithm to particle size example images}
\end{figure}
\begin{figure}
  \includegraphics[width=0.49\textwidth]{figure_8}
  \caption{Comparison of different particle sizes: pink ({\color{french_rose}$\blacksquare$})  points for $\sigma_{\{x, y\}} = 0.1$, yellow ({\color{peach}$\blacksquare$})  for $\sigma_{\{x, y\}} = 0.5$ and blue ({\color{royalblue}$\blacksquare$})  for $\sigma_{\{x, y\}} = 1$. For $\sigma_{\{x, y\}} = 2$, the same visual result was obtained as for $\sigma_{\{x, y\}} = 1$. There was a low Gaussian noise added, with a $\operatorname{SNR}\, = 100$, and no salt and pepper noise. The statistic/simulation was done with images containing $10000$ particles. The abscissa shows the sub-pixel coordinate of the real positions, whereas the ordinate shows the respective absolute error of the positions calculated with \nameref{alg06}.}\label{fig:compare algorithm to particle size positions}
\end{figure}
However, this is not true for small particles ($\sigma_{\{x, y\}} \in \{0.1, 0.5\}$), as shown in \figref{fig:compare algorithm to particle size}. While \citet{Feng:2007} explain, why an inappropriately chosen threshold leads to pixel locking, here we see that another reason for pixel locking can be missing information, such as particles consisting of not enough pixels, as seen in \figref{fig: compare algorithm to particle size example images}. This is not an error of the algorithm, but of the measurement itself.
\figref{fig:compare algorithm to particle size positions} illustrates the influence of the particle size on \nameref{alg06}.
For particle sizes $\sigma_{\{x, y\}} \in \{0.1, 0.5\}$, the positions calculated by \nameref{alg06} are not statistically fluctuating around the real position. Instead, there is a systematic deviation depending on the real position -- a similar behavior can be observed for all presented algorithms.
For example, a particle with $\sigma_{\{x, y\}} = 0.1$ consists of more than one pixel only, if the absolute value of the chosen sub-pixel coordinate is greater than $0.25$ (cf. \figref{fig: compare algorithm to particle size example images}).
Therefore, for a coordinate with an absolute value of the chosen sub-pixel coordinate of less than $0.25$, any algorithm can find just that one pixel, and consequently only detect the exact coordinate of it, which yields $0$ as the sub-pixel coordinate.

The clustering by Otsu's method used in \nameref{alg04} and \nameref{alg07} performs well. Only for very small particles, in the example given by \figref{fig:compare algorithm to particle size} and visualized in \figref{fig: compare algorithm to particle size example images}, a stable detection is not possible. Increasing gamma (\nameref{alg05}) does slightly improve the accuracy of \nameref{alg04}, but not all particles can be detected any more. Comparing \nameref{alg02} and \nameref{alg04} shows that Otsu's method does not choose the best threshold. But as an automatic procedure processing all available pixel values, it can reduce human errors in the process of choosing the threshold.

\section[Moment Method (Blob Detection)]{Moment Method\\(Blob Detection)}\label{section:Moment Method (Blob Detection)}

\begin{figure}
  \includegraphics[width=0.49\textwidth]{figure_9}
  \caption{Comparison of different strength of pepper noise: pink ({\color{french_rose}$\blacksquare$})  bars for a probability of pepper noise of $1 \mbox{ \%}$, yellow ({\color{peach}$\blacksquare$})  for $5 \mbox{ \%}$, blue ({\color{royalblue}$\blacksquare$})  for $10 \mbox{ \%}$ and green ({\color{mint_green}$\blacksquare$})  for $20 \mbox{ \%}$. Missing bars imply that not all particles where correctly detected. The ordinate shows the root mean square error of the distance between detected and real positions. The Gaussian noise was added with a $\operatorname{SNR}\, = 100$. The statistics/simulation was done with images containing $10000$ particles with $\sigma_{\{x, y\}} = 1$.
The right image shows a single particle separated by pepper noise with a probability of $20 \mbox{ \%}$.}\label{fig:pepper noise}
\end{figure}

In \figref{fig:pepper noise}, different algorithms are compared with respect to different probabilities of pepper noise:

\begin{description}
\item [alg08\label{alg08}] \nameref{alg01} with a search radius $r=1$ (moment method with particles being only single connected sets, similar to \citep{Feng:2007, Ivanov:2007})
\item [alg09\label{alg09}] \nameref{alg01} with a search radius $r > 1$
\item [alg10\label{alg10}] \nameref{alg01} preprocessed by a Hanning filter ($N = 5$)
\end{description}

We can see that for high pepper noise \nameref{alg08} is not able to detect all particles correctly --- it finds too many, because some particles are split in two by the pepper noise.

Using \nameref{alg09}, the generalized moment method described in \secref{section:Blob Detection}, we are able to detect all particles correctly. The same holds for the Hanning filter in \nameref{alg10}. The quality of the latter is comparable to the generalized moment method. The only draw-back is the larger computing time of \nameref{alg10} (see \figref{fig:used processor time for noise with snr}, comparison of used processor times of \nameref{alg02} and \nameref{alg03}).

\section{Fitting (Postprocessing)}\label{section:Fitting Postprocessing}
Given approximate coordinates from the blob detection of the last \secref{section:Moment Method (Blob Detection)}, we can try to enhance them by fitting a generalized Gaussian point spread function, which is visualized in \figref{fig:example shapes} and given as:
\begin{align}
\frac{p^{1-\frac{1}{p}}}{2 \sigma \Gamma{\left( \frac{1}{p} \right)}} \times \exp{\left( \frac{-\sqrt{x^2+y^2}^p}{p \sigma^p} \right)} \label{eq:generalized Gaussian point spread function}
\end{align}

The fit is performed locally to every single particle. Therefore, we split the given image in non-overlapping squares with an approximated particle coordinate located in the center of the square. Every square is chosen with a maximal side length under the given restrictions.

Initially, the distance $d$ of two particles $i$ and $j$ is defined as:
\begin{align*}
&d\left(\left(\begin{array}{cc}x_i\\y_i\\\end{array}\right),\left(\begin{array}{cc}x_j\\y_j\\\end{array}\right)\right) := \\
&\qquad \max{\left\{|x_i-x_j|, |y_i-y_j|\right\}}
\end{align*}

Then, for a given particle coordinate $p_0 := (x_0, y_0)^T$ the closest particle $p_1 := (x_1, y_1)^T$ is found as:
\begin{align*}
&\forall i:
d\left(\left(\begin{array}{cc}x_i\\y_i\\\end{array}\right),p_0\right) \geq
d\left(p_1,p_0\right)\\
\end{align*}

With $\delta := \frac{1}{2} d((x_1, y_1)^T,(x_0, y_0)^T)$ and $\floor{.}$, $\ceil{.}$ the floor and ceiling functions\footnote{In practice, this should not be a mapping to integers $\ensuremath{\mathbb{Z}}$, but to image coordinates --- a subset of non-negative integers $N_0$.}
we get the vertices of the square as:
\begin{align*}
\left\{ \ceil{x_0 - \delta}, \floor{x_0 + \delta}, \ceil{y_0 - \delta}, \floor{y_1 + \delta} \right\}
\end{align*}

Now we generate separate problems for every square or particle. Let the given image be a matrix $I = \left(I_{i,j}\right)$. Here, we use the original image and not the prefiltered one.

An artificial image can be created with \eqref{eq:generalized Gaussian point spread function} as $A(x,\sigma,p) = \left(A_{i,j}(x,\sigma,p)\right)$ with the particle coordinate $x \in \ensuremath{\mathbb{R}}^2$ and $\sigma$, $p$ the parameters for the generalized Gaussian point spread function. With $b$ the averaged brightness of the background, this results in the optimization problem:
\begin{align*}
\min_{x,\sigma,p,b}{\sum_{i,j}^{}{\left(I_{i,j} - A_{i,j}(x,\sigma,p) - b\right)^2}}
\end{align*}

For solving this optimization problem we use the algorithm L-BFGS-B \citep{Byrd:1995, Zhu:1997, Morales:2011}, implemented in the python module/library SciPy \citep{Jones:2001}.

The gradient of the objective function is calculated numerically by a symmetric difference quotient if possible (e.g.\ on the boundary of the feasible solutions we cannot calculate a symmetric difference quotient).

\begin{figure}
  \includegraphics[width=0.49\textwidth]{figure_10}
  \caption{Comparison of used processor time of the simulations of \figref{fig:noise with snr}: pink ({\color{french_rose}$\blacksquare$})  bars for $\operatorname{SNR}\, = 5$, yellow ({\color{peach}$\blacksquare$})  for $\operatorname{SNR}\, = 10$, blue ({\color{royalblue}$\blacksquare$})  for $\operatorname{SNR}\, = 100$ and green ({\color{mint_green}$\blacksquare$})  for $\operatorname{SNR}\, = 1000$. The ordinate shows the measured processor time in seconds on an Intel Xeon processor E5-2643v3. The statistics/simulation was done with images containing $10000$ particles with $\sigma_{\{x, y\}} = 1$.}\label{fig:used processor time for noise with snr}
\end{figure}

In \figref{fig:noise with snr}, different algorithms were compared with respect to different signal to noise ratios, including those with fitting. Additionally, in \figref{fig:used processor time for noise with snr} the processor time used for the simulation is given. It is obvious that a small improvement by fitting a generalized Gaussian (\nameref{alg06} and \nameref{alg07}) leads to a large calculation time (\figref{fig:used processor time for noise with snr} shows a factor of $60$ to $144$).

The improved detection rate by Hanning filtering (e.g.\ \nameref{alg03}), and the automatically chosen threshold by Otsu's method (e.g.\ \nameref{alg04}) each lead to a larger error, as demonstrated in \figref{fig:noise with snr} and \figref{fig:compare algorithm to particle size}. This can be corrected by fitting (e.g.\ \nameref{alg06} and \nameref{alg07}).

Instead of successively fitting every individual particle in one image, one can try to fit all particles in one image simultaneously.
This assumption leads to a high dimensional optimization problem. In our implementation with the algorithm L-BFGS-B, this problem could not always be solved successfully. If it was successful, the result was sometimes slightly better than fitting every individual particle,  but at the cost of a considerably increased computing time: it was about $100$ times higher for $100$ particles, and about $700$ times higher for $1000$ particles.

\section{Examples}\label{section:Examples}
\subsection{Velocity}\label{subsection:Velocity}
In this section we will regard the velocity in images; this is the velocity of a particle in the image plane -- e. g. a 2D mapping of a real 3D motion.

Let us assume a sequence of images with a temporal distance of $dt = 10 \mbox{ ms}$ between $2$ consecutive images (equivalent to a frame rate of $100$ images per seconds), with particles modeled as a Gaussian with $\sigma = 1 \mbox{ pixel}$ and a $\operatorname{SNR}\, = 100$.

In our simulations  (see \figref{fig:noise with snr} and \figref{fig:compare algorithm to particle size}), the presented algorithms \nameref{alg06} and \nameref{alg07} yield a root mean square error of about $0.014 \mbox{ pixels}$ (or better). Assuming a distribution around $0$, the root mean square is the standard deviation.

When calculating a particle velocity from $2$ consecutive particle positions, each subject to the same uncertainties, error propagation leads to an error of $(2 \times 0.014)/dt$~$[\mbox{px}/\mbox{s}]$ in the velocity.

As an example, for a $4$ megapixel camera ($2048$x$2048$~$\mbox{px}^{2}$) with a field of view of $4 \mbox{ cm}$ by $4 \mbox{ cm}$ this leads to an uncertainty in the velocity of $0.056 \mbox{ mm}/\mbox{s}$.

In the following table a few examples are given with the resolution in $\mbox{mm}/\mbox{px}$, $dt$ in ms and the velocity in $\mbox{mm}/\mbox{s}$:
\begin{center}
\begin{tabular}{|c|c|c|c|c|}\hline
\multirow{2}{*}{$\operatorname{SNR}\,$} & pixel & \multirow{2}{*}{resolution} & \multirow{2}{*}{$dt$} & velocity \\
& error &  & &  error \\\hline\hline
$100$ & $0.014$ & $0.020$ & $10$ & $0.056$\\\hline
$100$ & $0.014$ & $0.020$ & $2$ & $0.28$\\\hline
$100$ & $0.014$ & $0.005$ & $12.5$ & $0.012$\\\hline
\end{tabular}
\end{center}
We neglect here that changing the resolution also changes the size of a particle on the image sensor. Otherwise, the error for the resolution of $0.005\mbox{ mm}/\mbox{px}$ would be reduced dramatically.

With the last example representing a $4$ megapixel camera ($2048$x$2048$~$\mbox{px}^{2}$) at 80 frames per seconds with a field of view of $11 \mbox{ mm}$ by $11 \mbox{ mm}$ we would be able to measure the velocity of particles ($\varnothing = 9.19 \mbox{ $\mu$m}$, $\rho = 1.51 \mbox{ g/cm}^3$) at room temperature, which would be about $0.08 \mbox{ mm/s}$. Experiments with a crystalline 2D complex plasma, and a comparable spatial camera resolution, were analyzed with the presented \nameref{alg01} by \citet{Knapek:2007}, yielding reasonable kinetic energies of the particles.

Knowing the uncertainties, especially for particle velocity calculation, should not be underestimated: Gaussian noise can easily mask a Maxwellian velocity distribution, but it is not possible to separate the two distributions (see e.g.\ \citet[chapter 7]{Knapek:2011}; here, as well as in other publications \citep{Knapek:2007,Knapek2:2007}, the applicability of our algorithm to real-world data is demonstrated in more detail). Therefore, it is of high importance to know the limit of resolvable particle motion (depending on particle size, $\operatorname{SNR}\,$ and the algorithms) for a specific experiment before interpreting the results.

\subsection{Particle Separation}\label{subsection:Particle Separation}
\begin{figure}
  \includegraphics[width=0.49\textwidth]{figure_11}
  \caption{Different particle distances: In the first row, the minimal particle distances are given in pixel. In the second row, example images are given. In the last row, these example images are prefiltered by Otsu's method as described in \nameref{alg04}.}\label{fig:different particle distance}
\end{figure}
Here, we assume two particles which are nearby each other on the image plane (see \figref{fig:different particle distance}), e.g.\ due to their overlapping motion in different layers. Further, we assume both particles have the same size on the image, e.g.\ an uniform illumination, a good enough depth of field and same particle size and texture.

We neglect the Gaussian beam profile of the laser in the simulation. This profile might give additional information about the depth of a particle: the pixel intensity values would reflect the (ambiguous) position of the particle within the spatial extent of the laser beam, and could be used for a relative depth evaluation between particles, but we do not use this kind of information in the presented algorithms.

Now we can use all algorithms introduced in \autoref{section:Preprocessing (Image Processing)}. Since we want to separate both particles, we do not want to detect particle pictures like \figref{fig:pepper noise} (right) as one particle. Also, we cannot use a too large Hanning amplitude filter, because it would wash-out distinctive edges of nearby particles.
Therefore, we have to demand a good $\operatorname{SNR}\,$ to avoid the necessity of preprocessing. This is usually available in typical images of complex plasmas obtained with a laser filter which suppresses background illumination (e.g.\ from the plasma glow).

We now introduce additional algorithms similar to \nameref{alg03} and \nameref{alg06}:

\begin{description}
\item [alg11\label{alg11}] \nameref{alg02} with a large threshold of $190$ and a search radius $r=1$
\item [alg12\label{alg12}] \nameref{alg11} with fitting a generalized Gaussian (\autoref{section:Fitting Postprocessing})
\end{description}

\begin{figure}
  \includegraphics[width=0.49\textwidth]{figure_12}
  \caption{Comparison of different particle distances: yellow ({\color{peach}$\blacksquare$})  for minimal particle distance of $4$ pixel, blue ({\color{royalblue}$\blacksquare$})  for minimal particle distance of $5$ pixel and green ({\color{mint_green}$\blacksquare$})  for minimal particle distance of $10$ pixel. Missing bars imply that not all particles where correctly detected (for a distance of $3$ pixel, this was the case for all algorithms). The ordinate shows the root mean square error of the distance between detected and real positions. The statistics/simulation was done with images containing $10000$ particles with $\sigma_{\{x, y\}} = 1$ and $\operatorname{SNR}\, = 100$.}\label{fig:particle distance}
\end{figure}

In \figref{fig:particle distance}, different particle distances, as visualized in \figref{fig:different particle distance}, are compared. Here, for all presented algorithms a search radius of $r=1$ was used. Particles with distances of $3$ pixels or less could not be separated. The moment method (\nameref{alg11}) described in \autoref{section:Blob Detection} with a large threshold of $130$ is able to separate particles with $\sigma_{\{x, y\}} = 1$ with a distance of only $4$ pixels. Choosing the threshold automatically
(for minimal particle distances of $3$, $4$, $5$ and $10$ pixels, the threshold was $78$, $71$, $73$ and $73$, respectively)
with \nameref{alg04} separates these particles down to a distance of $5$ pixels. In both cases, postprocessing the images by fitting (\nameref{alg12} and \nameref{alg07}) reduced the uncertainties.

The possibility to separate close-by particles can prove helpful in 3D diagnostics, e.g.\ for the analysis of data taken with a stereoscopic setup (several cameras viewing the same volume from different angles). Particles located close to each other on the image plane are typical features for this kind of diagnostics, and algorithms are needed to reliably detect particles in each of the camera views as the basis for a subsequent triangulation\citep{Alpers:2015}.

\section{Conclusion}\label{section:Conclusion}
In this paper we presented a comparison of several methods and algorithms for particle tracking from images. The methods and algorithms were tested on artificial images simulating data as they are obtained in complex plasma experiments, including realistic image noise (additive white Gaussian noise, salt and pepper noise). To increase the statistical significance, images with a large number of particles ($10000$) were analyzed. The proposed procedure for particle tracking consists of three major steps: image processing, blob detection and postprocessing.

In \autoref{section:Preprocessing (Image Processing)}, we show that using a Hanning filter to remove Gaussian noise during image processing results in a better detection rate in the presence of high noise, whereas the accuracy of the found positions is slightly reduced (\figref{fig:noise with snr}).

For images consisting of features (the particles) and a background (noise), the choice of a good threshold is important during image processing. With Otsu's method (used in \nameref{alg04}, \nameref{alg07}), we introduce this concept of automatic thresholding for particle detection in complex plasma for the first time (\autoref{section:Preprocessing (Image Processing)}). Other automatic thresholding techniques were tested, but did not prove to be suitable. The clustering by Otsu's method performs very well (\figref{fig:noise with snr}), yielding almost the same results as the manually chosen threshold for all but the smallest particle sizes (\figref{fig:compare algorithm to particle size}).
On the one hand, choosing the right threshold value is not an easy task, and an automatic method can dramatically reduce human errors. On the other hand, an automatism prohibits using expert knowledge of the user in special circumstances, e.g.\ for the task of particle separation (\autoref{subsection:Particle Separation}).

In \autoref{section:Blob Detection} we introduce an improved algorithm for blob detection: we generalized the set used for the moment method to a not necessarily simply connected set, and show that we can considerably improve particle detection in the presence of certain kinds of noise (e.g.\ salt and pepper noise, \figref{fig:pepper noise}) with this generalization.

We present a postprocessing method in \autoref{section:Fitting Postprocessing} to further enhance the accuracy of the detected particle positions by fitting a generalized Gaussian function to the intensity profiles of the particles. This is in particular interesting if prefiltering is necessary due to noisy images. Then, the postprocessing can reduce errors introduced by the prefilter (\figref{fig:compare algorithm to particle size}, \figref{fig:noise with snr}). Also, it can increase the sub-pixel resolution of particle positions. This is especially interesting for applications where small particle velocities, e.g.\ thermal velocities, are calculated from the positions (\autoref{subsection:Velocity}).

Another application is shown in \autoref{subsection:Particle Separation}: Particles which are close-by each other on the image plane can be separated by either manual or automatic threshold detection, and position accuracy was improved by the above postprocessing method. This kind of situation typically appears in the individual camera images of a stereoscopic imaging system.

In summary, image processing with a Hanning filter (\nameref{alg03}), and a subsequent blob detection with the moment method detects in the most cases all particles in our simulations, but needs a manually chosen threshold. Automatic threshold detection (\nameref{alg04}) results in a slightly reduced accuracy and a reduced detection rate, but has the advantage of the automatism. In both cases, postprocessing the acquired positions by fitting (\nameref{alg06} and \nameref{alg07}) reduced uncertainties in the particle coordinates at the cost of a large calculation time (\figref{fig:used processor time for noise with snr} shows a factor of $60$ to $144$), but for specific experiments with the requirement of a good sub-pixel resolution this can be very useful and worth the effort.

\section{Acknowledgments}
The authors are funded by DLR/BMWi under grant FKZ 50WM1441, and by STMWi (Bayerisches Staatsministerium f{\"u}r Wirtschaft und Medien, Energie und Technologie).

\bibliographystyle{plainnat}

redpajama_set_name: RedPajamaArXiv


text:
Q: Are you using your VPS' bandwidth when using it as VPN? I setup my VPS from a different country as an OpenVPN Access Server. I am now connecting to it from my PC using OpenVPN client. If I download 1GB of data to my PC while connected to the VPN, is my VPS also effectively transferring 1GB of bandwidth to my PC? To illustrate further, is this what's actually happening?
Website <---1GB Bandwidth---> VPS (used as VPN) <---1GB Bandwidth---> My PC

A: Yes, that's correct.  The VPN system (regardless of whether it's run on a VPS, or on a dedicated hardware system (like a VPN concentrator) basically works like this:
1) you establish a secured VPN "tunnel" to that server (or router).  All traffic that you configure (and the simplest case is to tunnel everything) will go from your machine to the VPN server.
2) the VPN server then has a connection to either a corporate network, or to "the internet".
So your drawing is correct.  To measure bandwidth, let's take a contrived example where all you do is send a 100kB request to the server (while connected to the VPN), and then the server responds with 1MB of data.  So in your picture above you've sent 100kB of data from "right to left" and you've sent 1MB of data from "left to right".
DEPENDING on how exactly your VPS provider bills for bandwidth, you could be billed/accounted for 100k, or 1MB, or 1.1MB.  (I don't actually know whether it's most common for VPS providers to bill bi-directionally or only for one direction, but I'd assume it's bidirectionally...)

redpajama_set_name: RedPajamaStackExchange


Thanks so much for writing this up. It's the most honest look at what I could be in for. Only lost 65 myself but my MD sent me to a surgeon who recommends this procedure as my best option. You should have a before/after up here or something!
Thanks, man, happy to be of help. Definitely wait until you get to a stable place before you have the procedure. It's gnarly, but worth it. I'm working on a recap now that I'm about 90% recovered, should be up over the weekend. If you have any questions, fire away!


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History of Bonaventure, Québec, Canada
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Are you from Bonaventure? Do you have ancestors from there? Tell us YOUR story!
Saint-Bonaventure is a municipality in the Drummond Regional County Municipality of southwestern Quebec.
Officially created on January 1 of the year one thousand eight hundred and sixty-seven in the territory of the canton of Upton, the municipality of Saint-Bonaventure is detached from the municipality of Saint-Guillaume...
Located geographically at the limits of the Seigneurie de Guire of royalist allegiance and French, in the British canton of Upton registered in 1792, the village is officially designated "Parish of Saint-Bonaventure" by a Catholic bishopric in 1856...
Like so many other villages around the world, Saint Bonaventure developed near water. The "Rivière-aux-Vaches", coming from Saint-Majorique, crosses the municipality and continues its course towards Saint-Pie-de-Guire and Saint-François-du-Lac. This river is truly responsible for the development of the first community of settlers...
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There is MUCH more to discover about Bonaventure, Québec, Canada. Read on!
1760 - The first permanent European settlement of Bonaventure was in 1760 by Acadian refugees who had successfully avoided the expulsion of Acadians that had begun in 1755.
1791 - Bonaventure parish opened
www.prdh-igd.com/en/Carte/2301
1855 - Église de Saint-Bonaventure established at Saint-Bonaventure
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1890 - St Bonaventure
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The Pocket Atlas and Gazetteer of the Dominion of Canada John George Bartholomew John Murdoch Harper January 1, 1890 London : J. Walker
1895 - Saint Bonaventure
Saint Bonaventure, a post village in Drummond co., Quebec, 30 miles from St. Hyacinthe.
Lippincott's Gazetteer of the World: A Complete Pronouncing Gazetteer Or Geographical Dictionary of the World Containing Notices of Over One Hundred and Twenty-five Thousand Places ... Joseph Thomas January 1, 1895 J.B. Lippincott
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Isn't it true that not all customers are good customers? We all know who our best customers are, they show up on time, they pay their bills and they communicate openly and honestly about what is going on.
I coach clients to identify their best customers in as much detail as possible. For example what do they drive where do they go out to eat, what credit cards do they carry in their wallets, where do they live, where do they send their kids to schools, what kind of vacations do they take, what level of education have they attained. This is just a small list of details you should know about your perfect customers.
When you have enough of these details you will learn to do what is needed to attract them. Once you have it you can develop your message and articulate your unique selling proposition. Or what can you define in your message that is different than anyone else and will attract clients to your company?
I typically suggest that you rate your clients ABCD. The worst classification of customers is "D's" or Duds. They are clients that don't pay, want everything for free, don't invest in themselves, make up stories, and are afraid to learn new things. This "D" customer is someone you may feel obligated to accept because they are a referral from a respected colleague, or because you feel you need the business.
The next category of clients is the "C" clients. They look good and seem like they will be a B or an A, but they disappoint you. I call "C's", "Can be better" customers. With "C's" we must work with them or position them to become at least a "B". They typically have the ability to become a "B" or an "A" but need to given strong reasons to improve.
"B" clients are good customers who do a lot of business with you and refer you from time to time. By working closely with a B customer, over time you can build trust through partnering to get the best solutions for all parties. Over time, a good "B" customer can become an "A" and there should be a lot of focus to make it happen.
"A" customers are a pleasure to work with and provide repeat business over a long period of time. They become raving fans and are willing to refer you to everyone they know. They are getting so much value out of the relationship they are willing to tell everyone they know. They are committed to helping you grow your business.
In conclusion, get rid of the Dud "D's", get the "B's" and "C's" to improve and do whatever you can to WOW your "A's" and this simple strategy will grow your business profitably while working with the people you choose, and create a more successful future.


No matter how well I feel I have prepared for the semester I always feel like I stumble through the first week of classes. Hence our theme for this blog post "falling" into the semester. Falling doesn't always have to be bad however. You can fall down stairs (see left) or off a cliff (see Wily Coyote) but you can also fall into a ball pool. And who doesn't love that. For that reason, the beginning of this semester, although stumbly, is a really exciting time because there a lot of new projects, but all of them are immensely exciting and hold great promise for the work we do in the DML and at the BGC in general.
The first is our foray into much more complicated museum interactives in the Confluences focus gallery. After some amazing work by students in the tutorial last spring designing prototypes for interactives that would go into the gallery, we decided to for the first time work with an outside developer to realize much more detailed and highly functional interactives than we could manage in-house. We began work with the developer Mediacombo this past Friday and we are looking forward to not only developing high quality gallery experiences, but also finding a way to bring the developers' knowledge into the classroom.
Our second big project is the development of an archive of digital student work. As work in the DML has increased we have had more and more projects coming through that we would like to archive and catalog as a record of the lab's role in the BGC's institutional life. In addition we want to give professors the opportunity and platform to show how their pedagogical practice has evolved and the student work that has resulted from those courses. We are looking to start the archive with work from Prof. Whelan's ongoing oral history project of designers and craftspeople, and with video and web projects from Prof. Jaffee's courses on the material culture of 19th and 20th century New York City. At this point we are looking at Omeka as the platform of choice and myself, and the DML workstudies and interns will be working with faculty, our art director Laura Grey and our digital content developer Vanessa Rossi to develop the archive and web sites.
One final project of note is the BGC's involvement in the development of a new digital edition of Franz Boas's 1897 monograph The Social Organization and the Secret Societies of the Kwakiutl Indians. This project, which is funded in its first year by a NEH Digital Start-up Grant, is an ambitious project to bring together thousands of texts, media, and objects to reassemble this important work in a way that was not possible when it was originally published. The project includes collaborators from institutions across North America and Europe and the DML will play an important role in hosting platforms for early stage collaboration and collection of materials through tools such as Wikidot wikis and Omeka, and may include an expansion into new tools such as ContentDM. This type of long-term project will be a challenge considering the scale of the work in relation to our previous endeavors, but is exactly the type of challenge that will help the DML to better serve the growing digital needs of the BGC community.
That's not even all that's going on. We will be preparing for a 2013 repeat of Prof. Jaffee's NEH-funded summer institute on material culture, which will have an increasingly developed digital practice aspect. In Prof. Gaskell's course Tangible Things we will be experimenting with telepresence and the study of distant objects in the classroom through video technology. Students in my own course, Media and Materiality, will be building a collection and timeline of media objects, using the Met's Heilbrunn Timeline of Art History as a model. There will also be beginning work done on focus gallery projects by Dean Peter Miller, AMNH post-doc Nicola Sharratt, associate curator Ann Tartsinis, and my own project on Interface Design.


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CENTAR Bar by Milan Dinevski, Erina Filipovska; North Macedonia
September 26, 2019|BigSEE Interior Design Award 2019 - Winner, Hospitality, Interior, North Macedonia|
Beer lovers in Skopje have recently got a new space where they can enjoy the taste of unfiltered craft beer in a pleasant atmosphere and a creative interior. The new beerhouse "Center bar" is located in the center of Skopje, on the same site where many years ago fast-food was offered. Unlike the past of the site, the beerhouse with its elegant industrial interior, designed by the architects Erina Filipovska and Milan Dinevski (City Creative Network) presents a completely different experience for the daily and evening exits in Skopje.
The bar is on two levels and is arranged simply, both exterior and interior. Without many applicative elements on the façade of the building in which it is located, without going out of the frame of its plasticity and accidentally or deliberately in the rhythm of the same, with a simple font and in Cyrillic alphabet, the name of the beerhouse is written with luminous letters. The big openings of the glass façade reveals part of the interior story, luring this way beer and good design lovers to enter and enjoy the interior of the space. "The motive for opening this beerhouse is the promotion of the first unfiltered craft beer in Macedonia as an exclusivity of this space. That is, the advertising approach for promotion of beer by creating a contemporary space, in relation to the contemporary way of consuming beer, through an architecturally shaped ambience at the best location.", say Dinevski and Filipovska.
With their ideas and design approach, they create a space with "easy" comfort at a glance and elegant and fine details, with simplicity in the cleanliness of the materials (concrete, wood, metal). The interior is a dynamic fusion of concrete with natural, achieved through a mix of bare and raw concrete and brick walls, structural elements with metal details, woodwork, greenery and furniture in pastel colors. Some of the installations are left entirely visible, carrying the theme of industrial space. In the whole picture, the interior essentially contains a moderate dose of retro style, but the way the space is shaped allows the space and the style to stay up-to-date even when the "fashion" of the retro trend passes.
A feeling of pleasantness is present on both levels, on the ground floor and in the gallery of the second level which offers greater intimacy. Right next to the entrance, in the double heighted space is located a comfortable island bar which dominates the first level. As a dominant, the bar is shifted from the center of the space, so it doesn't hinder the movement towards the stairs for the upper level, and at the same time has a close connection with the kitchen. Warmed with an unexpectedly rustic copper shell, complemented by a large tank for draft beer as a central design element, the bar receives an interesting backdrop on the side where it is in contact with the kitchen.
The barrier between the main space and the kitchen is a semi-transparent surface with irregular geometry, with which the cooking part is creatively closed. The stronger lighting in the area where the kitchen makes the illusion as it is in an open space, projects interesting silhouettes, which give a fun, street-like urban ambience. Other specific of this area is the beer-to-go shop positioned on the façade, in close contact with the sidewalk of the street, which fulfill the idea of division of the space by function.
The location, as the architects point out, is one more reason why the space has been re-shaped in this manner. "In the past, in absence of mobile phones, the main meeting location in Skopje was Record/Forum. With the shutdown of McDonald's, which was at the same space as the beerhouse, the logic of this location as a central spot in the city was shut down as well. Since the content makes the central spaces in the cities, there has been a desperate need for animation of this site. With the opportunity to work on this facility, we got the responsibility, the parameter we set ourselves, to make this location the main meeting place in Skopje again!", says the architects Dinevski and Filipovska.
As a balance between the micro-cement flooring on the first level and the concrete fine-ribbed ceiling, wooden covering of the stairs and the gallery floor appears. The black steel fence adds a "photoshop" contrast effect, like contour of the stairs and the gallery itself. The simple lined fence does not disrupt the views from the story to the bar and back and indirectly connects with the cables from the electrical installations left visible, especially with the lightening objects. The variety and dynamics of the first level are not repeated in the gallery space, which is organized as multi-zone and type of seating with furniture in pastel tones that additionally emphasizes the intimacy and pleasantness of the ambience.
The choice of materials and the determination to relieve the walls and the structural elements of finishing, especially in the areas along the façade window, putting an accent to the seating area beside it, allows a slight blending of the interior with the exterior – the street. The exposure of the raw surfaces, as well as the fictitious penetration of the city asphalt in the space, is unobtrusively calmed with the extraordinary elegance of the décor that retains the purpose of the space – enjoying the act of drinking beer.
"Center Bar" is a new place in the center of Skopje, which seems will remain faithful to its purposes – beer, food and socialization. With a mature awareness of the environment in which it is located, without attempt to escape the city and create an illusion of space outside the city, becomes another segment that should be part of the urban metabolism.
Description by Biljana Temelkovska originally published on www.design.mk
Milan Dinevski is an architect and curator based in Ljubljana, Slovenia.
Currently, he is the project manager of the Future Architecture Platform at the Museum of Architecture and Design MAO in Ljubljana. The Future Architecture Platform is the first pan–European platform of architecture museums, festivals and producers that promotes ideas by emerging creative practitioners for the future of cities and architecture to the wider public. He curated the exhibition Living with Water – Southern Fringe of Ljubljana dealing with urban development scenarios that explore the synergetic relationships between humankind and the natural environment.
Together with PhD Damjan Kokalevski, he is co-founder of City Creative Network (CCN), a citizen initiative and research center based in Skopje. CCN develops design concepts and editorial work with cross-disciplinary teams of students, architects, artists and other professionals worldwide.
Among others, he collaborated with BevkPerovic Architects from Ljubljana, Archipelagos design studio from New York and was part of the collective KUD C3 Ljubljana.
He started his education at the Faculty of Architecture in Skopje and is a holder of MArch degree from the Faculty of Architecture in Ljubljana. His work is focused on various initiatives, projects and research that connect urban planning, education, activism and city authorities.
Erina Filipovska is an architect, designer and maker born in 1982. Read more about her experiences here.
Authors: Milan Dinevski, Erina Filipovska
Photos: Andrijana Tilić
Location: Skopje, North Macedonia
Text provided by the authors of the project.


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Walnut Hills History >>Harriet Beecher Stowe
Tag Archives: Harriet Beecher Stowe
Ida Mae Rhodes
Ida Mae Rhodes was born in 1899 and lived until 2000 – 101 years. She went to the University of Cincinnati; most records show her graduating in 1919. Yet the university bulletin for 1919-1920 shows her as a junior, and in 1920 she became the president of the first African American sorority on the campus.[…]
Jennie Davis Porter
Jennie Davis Porter was born in 1876, the daughter of a school teacher and a former slave said to be Cincinnati's first African American undertaker. She attended the city's integrated schools, and graduated from Hughes High School in 1893. In 1897 she began to teach at Fredrick Douglass school, at the time the only African[…]
The most famous of the large and illustrious Beecher clan to arrive in Walnut Hills in 1832, Harriet was just 21 years old and at first lived in the shadow of her older sister Catherine. The sisters worked together in Catherine's Western Female Institute, and joined a literary circle known as the Semi-Colon Club. Both[…]
Catherine Beecher
Catherine Beecher moved to Cincinnati with her father and her adult siblings in 1832; the family settled in Walnut Hills. Catherine, 32, had already made a name for herself with her opposition to President Andrew Jackson's Indian Removal policy. Catherine recognized that women, denied the right to vote, had no direct influence on legislative behavior.[…]


Preparing for court starts the moment you instruct us as we deal with every case on the basis that court proceedings may be required if we cannot settle the claim for you on amicable terms with the defendant.
Once proceedings are issued at the court, a timetable (officially called 'court directions') is set by the court for the progression of a case towards a final hearing.
We will need to maintain regular contact with you as we complete the necessary court directions required to put together a file of all of the documents and evidence requested by the court and/or the defendant in preparation for the court hearing.
How can I prepare for the hearing?
Do I need to bring any documents with me to court?
What if I am ill and cannot attend the hearing?
What happens if my barrister is ill?
What happens if the judge is ill?
How should I behave at court?
Can I claim expenses for attending my hearing?
Although the court does not issue a dress code for the occasion, we would highly advise conservative smart clothing is worn rather than casual wear.
Dressing smartly and appropriately for attendance before a judge shows your intentions to court and respect for the judge who will hear your case. We all know that first impressions last, so you should endeavour to create a good one. We would recommend that you avoid wearing sports clothing, training shoes, etc… and wear smarter business type attire such as a suit; generally a shirt and tie or blouse, with pants and smart shoes with accompanying blazer.
2. How can I prepare for the hearing?
Approaching the date of your final hearing, it is advisable for you to read over your paperwork from the claim. This includes your witness statement, medical reports and other documents that have been collated during the course of your claim.
It is especially important that the night before the hearing, you refresh your memory with the key documents that form the essential arguments in your case. Your representative from here at the firm will go through the main issues with you. You will also have the opportunity to speak with any barrister who may represent you at court beforehand.
We suggest that you arrive at court early; at least 45 minutes before the hearing is listed to begin. You will therefore need to plan your journey and know where you are going, and leave with plenty of time to arrive on time. If you are driving, you should ensure that you know where to park as courts are commonly located in the city centres and do not have public parking facilities close by.
3. Do I need to bring any documents with me to court?
You do not have to worry about bringing any documents with you. A copy of all of the evidence that you have provided to us previously, including a copy of your statement will be brought by your representative from this firm and/or your barrister.
4. What happens if I am late for my hearing?
Whilst the court has the power to vary the time and the date of the hearing, they will not accept your lateness or failure to attend. The most serious of consequences can be the judge striking out your case entirely.
That is not to say there cannot be exceptions, but it would have be a serious and unavoidable reason such as a medical emergency.
If you are late or you know you will be late for your hearing, then when it is safe to do so, please contact your representative ASAP to let them know of your situation so that we can make the appropriate actions, contacts and awareness.
5. What if I am ill and cannot attend the hearing?
As already stated above, it would have to be a medical emergency for your hearing to be adjourned for this reason.
If you have been ill weeks prior to your court hearing date, it is your responsibility to let us know in advance so that we can make the appropriate decisions and actions to reschedule the hearing if necessary. We will need to apply to the court and obtain evidence of your illness as necessary.
If you have any questions or worries, then please contact your solicitor for more information.
6. What happens if my barrister is ill?
Your attendance at court is still required.
When the barrister is ill, they will inform their clerk, who will send someone to court to notify the judge and everyone present. Based on this, the judge will usually agree to adjourn the hearing for another time or an alternative barrister will be appointed to deal with your case.
7. What happens if the judge is ill?
There should be replacement judges available to ensure that your hearing goes ahead.
The most likely reason for the hearing to be adjourned by the court's own motion is when the court has been overbooked and there is no judge or courtroom available.
8. How should I behave at court?
At court you should behave by being courteous and respectful. You should not chew gum, eat, listen to music using earphones, read anything other than material that is related to the case, take photos, film or use a mobile phone for calls or otherwise.
Being angry or argumentative as you give evidence does not help your situation or improve your chances of winning your case. Staying calm, collected and sticking to the facts and being truthful will help you, particularly when questioned by the defendant's barrister or the judge.
When talking, you should speak loudly and clearly. You should only speak when you have permission to do so. Do not talk over other people, especially the judge. You should also refer to the judge as "Your Honour".
Find out more about What Happens At Court.
9. Can I claim expenses for attending my hearing?
If you incur any travel costs and loss of earnings in attending your hearing, please ensure you bring along a copy of your receipts, or letter from your employer or other proof of this with you. You need to make your barrister aware of these expenses by passing the proof onto them. The barrister can then ask the judge at the end of your case when you have been successful to include these losses in your claim. If you do not make your barrister aware of these losses, then you will lose out as they cannot be claimed once the your hearing has been concluded.


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Riefa Board or green roof growing medium as it is sometimes called, can be used in conjunction with many types of vegetation, including sedum, wildflower, chamomile and herbs.
A living roof not only looks great but has many other benefits including energy conservation, extending the life of a roof and other economical and ecological benefits.
View full technical data sheet here. Riefa Green Roof growing medium is IGV GmbH approved and accredited.
There is no minimum order and the green roof growing medium boards are delivered via Pallex network throughout the UK.
Riefa can also supply your sedum plants so you can complete your green roof system.


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The Global Scope of the World Video Game Hall of Fame
Posted April 1, 2016 by Jon-Paul Dyson
Vice President for Exhibits and Director of the International Center for the History of Electronic Games
Genius knows no boundaries.
That's the inescapable conclusion I reach when I look at the 2016 finalists for The Strong's World Video Game Hall of Fame. The nominated games are equally distributed across three continents (Asia, Europe, and North America) and reflect how the video game industry has developed around the world and how the most successful video games often tap into universal themes.
A group of three Minnesota college students created the oldest game in the group, The Oregon Trail, in 1971 on a mainframe school computer, and its popularity spread to other areas and other gaming platforms. While the game featured a unique American setting, its journey theme greatly influenced the development of educational games around the world. Countless other games have replicated it. John Madden Football (1990) is another game with a predominantly American theme, but it too has been hugely influential, showcasing the model of annual releases that video game franchises have adopted for other popular sports, such as soccer and basketball.
Just because a game has an American setting doesn't mean it owes its primary genesis to an American developer. Grand Theft Auto III (2001), for example, is set in a fictional East Coast American city, but the creators of its innovative, open-world game play were based in Great Britain. The original name of GTA III's developer, DMA Design, was taken from the way in which "Direct Memory Access" was abbreviated in a manual for the Commodore Amiga microcomputer. In Great Britain, home computers, as opposed to consoles, drove the development of the early electronic game market, and Elite (1984) is another highly influential open-world game that emerged from this British personal computer boom. Tomb Raider (1996) appeared on computers as well, although it and its many follow-up titles also achieved an enduring place on consoles and the wider public consciousness with the release of a major motion picture starring Angelina Jolie as Lara Croft.
Game developers on continental Europe also have a long track record of innovative game design, and they are represented among the nominees by one of the oldest games in the group and by the newest. Minecraft (2009), although only seven years old, has become a global phenomenon that tens of millions of people play. By contrast, Nürburgring (1975) is probably unfamiliar to many people, but it's a well-deserving pioneer. It is the first racing game to use a first-person perspective. It directly inspired the development of Atari's more well-known Night Driver (1976), which popularized racing games that put players in the driver's seats. Although long underappreciated, Nürburgring exerted enormous influence.
When it comes to influence, Japan deserves pride of place as a center for important game development. Space Invaders (1978) represents the first original Japanese video game to achieve worldwide impact as it sparked a global craze for arcade games. Also, when interest in arcade games flagged, Street Fighter II (1991) reinvigorated enthusiasm for coin-ops (and especially for fighting games) by giving players the chance to show off their skills in one-on-one combat with other players.
Legendary Nintendo developer Shigeru Miyamoto's The Legend of Zelda (1986) launched not only a series of fantasy video games of enduringly high-quality, but it also paved the way for many other fantasy video games on consoles such as Final Fantasy (1987) and its many sequels. Two other Japanese nominees, Sonic the Hedgehog (1991) and Pokemon Red and Green (originally released as Pocket Monsters Aka and Midori in 1996) likewise introduced enduringly popular franchises with worldwide followings.
The international appeal of these games proves that thoughtful, creative game design has universal appeal. This explains why the last two titles among the 2016 nominees, Sid Meier's Civilization (1991) and The Sims (2000), have earned such passionate followings, for they revolutionized simulations on a grand historical scale and in the familiar environment of domestic life.
Reviewing the international makeup of this year's finalists makes clear how global the games industry is and reminds video game fans of a basic truth: Games have worldwide appeal because play is universal—everyone plays. As the technological tools and the business infrastructure necessary to support game creation spread around the world, geniuses emerged everywhere to create games worthy of enshrinement in The Strong's World Video Game Hall of Fame.
Given this year's sample, I fully expect that in future years, nominated games will come from many additional countries—for great game design can cross any boundary.
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While telecommunications occupy the top positions, it's financial institutions that dominate the list of most powerful local brands.
South Africa's top 10 brands are MTN, Vodacom, Sasol, Standard Bank, Woolworths, FNB, Absa, Nedbank, Investec and Mediclinic.
South Africa's top brands, which contribute not only to the country's economy, but to the image they portray when doing business internationally, were unveiled on Thursday.
Brand South Africa and Brand Africa Finance hosted the breakfast announcement, which took place in Houghton, Johannesburg.
Brand Finance calculates the values of the brands in its league tables using the 'Royalty Relief approach'. This approach involves estimating the likely future sales that are attributable to a brand and calculating a royalty rate that would be charged for the use of the brand- which is what the owner would have to pay for the use of the brand — assuming it was not already owned.
The report revealed that the total value of the Top 50 brands increased 3% from R373 billion in 2015 to R384 billion this year.
MTN remains the most valuable brand despite losing 32% of its brand value due to some of its reputational challenges.
Woolworths – which stands at number five -holds the strongest brand position with an increase of 21% in brand value.
Telecommunication – Telkom has seen the greatest increase in brand value following the integration of Business Connexion and improved performance on the retail side with good ratings on Value for Money and Customer Satisfaction according to the South African Customer Satisfaction Index (SAcsi).
The increase in brand value sees Telkom move from 23rd position last year to 17th in 2016.
Interestingly, many of the top 10 brands from 2015 have retained their positions in 2016 except for Woolworths which has moved to fifth place, and Absa which has moved to seventh.
Brands seeing a significant increase in value include Investec (27%) and WesBank (27%).
Two new brands have entered the Top 50. Country Road, now owned by Woolworths – which enters at 31st place with a value of R4.64 billion and Growthpoint enters at 50 with a value of R1.47 billion.
SABMiller holds the most valuable portfolio amounting to R29.67 billion with four of its brands standing amongst the country's top 50: Castle, Carling Black Label, Hansa Pilsner and SABMiller.
SABMiller is followed by Firstrand with three brands (FNB, WesBank and RMB) valued at R23.12 billion.
Brand South Africa's CEO Dr Kingsley Makhubela congratulated the Top 50 corporate brands saying, South African commercial brands are a key component of a strong nation brand and how this is experienced by both domestic and international audiences.
"Commercial brands are key messengers in positioning the country competitively. At the same time, we express our appreciation to all other corporate brands in the country for your contribution to the growth and development of South Africa," said Makhubela.
Chairman of Brand Finance Africa, Thebe Ikalafeng said the story of the Top 50 corporate brands is a good story for the South Africa Nation Brand as well as the continental story.
Newly appointed Director of Brand Finance Africa, Jeremy Sampson, said the more competitive the market, the more important it is to have a strong brand, leverage it to its full potential and measured and monitor at all times.
"Brands are increasingly the major assets of companies, yet does anyone have an idea of their true value? Marketing is no longer a 'nice to have' it can be the difference between success and failure," added Sampson.