Martin Coath edited section_Methods_The_abbreviation_textsc__.tex  about 8 years ago

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\section{Methods}  The abbreviation \textsc{skv} when applied to auditory signals was derived from \textbf{SK}ewness over \textbf{V}ariable time, reflecting the measure of asymmetry, the \textit{Skewness} or \textit{third normalized moment}, and the technique of varying the time window over which this value was calculated. For image processing the \textbf{V} will stand for \textbf{V}ariable spatial frequency which also relates to the size of the window used.  The simplest form of the algorithm was used for all the results in this paper. For results derived from monochrome images each pixel is defined by three values $i,j,k$ where $i$ and $j$ are the row and column positions of the pixel respectively, and $k$ is the value of the pixel on the greyscale gray-scale  from 0 (black) to 1 (white). Images are processed on a pixel-by-pixel basis and the \textsc{skv} value of each pixels is calculated thus: \begin{enumerate}  \item assemble the vector $\vec{k}_{j}$ of values for a horizontal window of $n$ contiguous pixels $k_{[i,j; i,j+1; i,j+n-1]}$  \item repeat with $\vec{k}_{i}$, a vector of values for a vertical window of $n$ pixels $k_{[i,j; i+1,j; i+n-1,j]}$  \item both vectors are normalized, so they can be treated as distributions, and the Skewness $\gamma$ of each distribution distribution, \textit{i.e.} the asymmetry in the gray-scale values in both direction,  is calculated, $\gamma_j$ and $\gamma_i$ \item the \textsc{skv} value of the pixel is the larger of the two values $\max(\gamma_j, \gamma_i)$  \end{enumerate}