Re:Show HN: C++ Implementation of the Paper Median Filter in...
by DoctorOetker on Sunday October 20, 2019 @02:46PM
(#21306169)
before trying to find out if it can be similarily optimized in deep learning, one would have to define a differentiable equivalent of histograms / means.
One approach would be to define the histogram as
H(x) = sum_i_0,N ( A * exp(-((x-x_i)/B)^2)) with B a spread parameter, and A a normalization constant so that a single sample integrates to a unit area under the gaussian. The mean M would then be the value such that integrating from minus infinity to M equals N/2 (half the samples below, and half above, with sample position blurred along the histogram)
Perhaps a different convolution function can be chosen for easier integration? A/(x+B)^2, is symmetric and perhaps more easily integrated.
One approach would be to define the histogram as
H(x) = sum_i_0,N ( A * exp(-((x-x_i)/B)^2)) with B a spread parameter, and A a normalization constant so that a single sample integrates to a unit area under the gaussian. The mean M would then be the value such that integrating from minus infinity to M equals N/2 (half the samples below, and half above, with sample position blurred along the histogram)
Perhaps a different convolution function can be chosen for easier integration? A/(x+B)^2, is symmetric and perhaps more easily integrated.