Image convolution: Difference between revisions

One class of image digital filters is described by a rectangular matrix of real coefficients called [https://en.wikipedia.org/wiki/Kernel_(image_processing) '''kernel'''] convoluted in a sliding window of image pixels. Usually the kernel is square <math>K_{kl}</math>, where <i>k</i>, <i>l</i> are in the range -<i>R</i>,-<i>R</i>+1,..,<i>R</i>-1,<i>R</i>. <i>W</i>=2<i>R</i>+1 is the kernel width. The filter determines the new value of a monochromatic image pixel P_<i>ij</i> as a convolution of the image pixels in the window centered in <i>i</i>, <i>j</i> and the kernel values:

'''Color images''' are usually split into the channels which are filtered independently. A color model can be changed as well, i.e. filtration is performed not necessarily in RGB. Common kernels sizes are 3x3 and 5x5. The complexity of filtrating grows quadratically ([[O]](<i>n</i>²)) with the kernel width.