NAME

MPSCNNLocalContrastNormalizationGradient

SYNOPSIS

#import <MPSCNNNormalization.h>

Inherits MPSCNNGradientKernel.

Detailed Description

This depends on Metal.framework Specifies the local contrast normalization gradient filter. The local contrast normalization is quite similar to spatial normalization (see MPSCNNSpatialNormalization) in that it applies the filter over local regions which extend spatially, but are in separate feature channels (i.e., they have shape 1 x kernelWidth x kernelHeight), but instead of dividing by the local 'energy' of the feature, the denominator uses the local variance of the feature - effectively the mean value of the feature is subtracted from the signal. For each feature channel, the function computes the variance VAR(i,j) and mean M(i,j) of X(i,j) inside each rectangle around the spatial point (i,j).

Then the result is computed for each element of X as follows:

Y(i,j) = pm + ps * ( X(i,j) - p0 * M(i,j)) / (delta + alpha * VAR(i,j))^beta,

where kw and kh are the kernelWidth and the kernelHeight and pm, ps and p0 are parameters that can be used to offset and scale the result in various ways. For example setting pm=0, ps=1, p0=1, delta=0, alpha=1.0 and beta=0.5 scales input data so that the result has unit variance and zero mean, provided that input variance is positive. It is the end-users responsibility to ensure that the combination of the parameters delta and alpha does not result in a situation where the denominator becomes zero - in such situations the resulting pixel-value is undefined. A good way to guard against tiny variances is to regulate the expression with a small value for delta, for example delta = 1/1024 = 0.0009765625.

T(i,j) = (delta + alpha * VAR(i,j)) N = kw * kh

OutputGradient: dZ/dX(i,j) = ps * T(i,j)^(-beta) * ( dZ/dY(i,j) - (sum_{l,k in L(i),K(j)} dZ/dY(l,k) * (((p0/N) + (2*alpha*beta/N)*(X(k,l)-1)*(X(i,j)-M(i,j)*p0)/T(i,j)))) ) N is the kernel size. The window L(i) and K(j) itself is defined as: L(i) = [i-floor((kw-1)/2), i+floor(kw/2] K(j) = [j-floor((kh-1)/2), j+floor(kh/2]

For correct gradient computation all parameters must be the same as the original normalization filter.

Method Documentation

Property Documentation

Author

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