deletions | additions       diff --git a/section_Part_Detectors_Calculating_the__.tex b/section_Part_Detectors_Calculating_the__.tex  index dc58fbe..6ebeb85 100644  --- a/section_Part_Detectors_Calculating_the__.tex  +++ b/section_Part_Detectors_Calculating_the__.tex 
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spans $10^{\circ}$. For pedestrians there is no a-priori light/dark  scheme between foreground and background (due to clothes and scenes)  that justifies the use of the ``signed'' gradients with range $0^{\circ}-360^{\circ}$:  in other words, we use the contrast insensitive version \cite{dpm-pami}. \cite{Felzenszwalb_2010}.  To reduce aliasing, when an angle does not fall squarely in the middle  of a bin, its gradient magnitude is split linearly between the neighboring  bin centers. The outcome can be seen as a sparse image with 18 channels,  which is further processed by applying a spatial convolution,  to spread the votes to 4 neighboring pixels \cite{DBLP:conf/iccv/WangHY09}. \cite{Wang_2009}.  \item [{STEP 3.}] We then spatially aggregate the histograms into cells  made by $7\times7$ pixel regions, by defining the feature vector  at a cell to be the sum of its pixel-level histograms. 
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feature vector for the whole part image is obtained by concatenating  the vectors of all the blocks.  \end{description}  When the initial part image is rotated such that its orientation is not aligned with the image grid, the default approach is to normalize this situation by counter-rotating the entire image (or the bounding box of the part) before processing it as a canonical window. This can be computationally expensive during training, where image parts have all sorts of orientations, and during testing, even if we limit the number of detectable angles. Furthermore, dealing with changes in the scaling factor of the human figures and the foreshortening of limbs introduces additional computational burdens. In the following, we introduce a novel approximation method that manages to speed up the detection process.