deletions | additions       diff --git a/subsection_Approximation_of_probability_distribution__.tex b/subsection_Approximation_of_probability_distribution__.tex  index 5bb6d52..8be0b34 100644  --- a/subsection_Approximation_of_probability_distribution__.tex  +++ b/subsection_Approximation_of_probability_distribution__.tex 
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\[P((x,y),T) = \sum_{(x',y')\in T}K((x,y),(x',y'))\]  where $K$ is a gaussian kernel. in practice we take a discrete gaussian kernel filter for $K$.  Whereas the simple histogram method places a spike function (i.e. $K = \delta_{(x,y)}$) \delta_{((x,y), .)}$)  at the bin corresponding to $(x,y)$ and update only a single bin, Parzen windowing places a kernel at the bin of $(x,y)$ and updates all bins falling under the kernel with the corresponding kernel value. As a result using a gaussian filter, the estimated distributions are more smooth and less sparse.