# MPSCNNCrossChannelNormalization A normalization kernel applied across feature channels. ``` class MPSCNNCrossChannelNormalization ``` ## Overview The normalization kernel applies the kernel to a local region across nearby feature channels, but with no spatial extent (i.e., they have the shape `kernel size x 1 x 1`). The normalized output is given by the function:  Where the normalizing factor is:  Where `N` is the kernel size. The window `Q(k)` itself is defined as: ![Q(k) = [max(0, k-floor(N/2)), min(D-1, k+floor((N-1)/2)]](images/com.apple.metalperformanceshaders/media-2903527@2x.png) Where `k` is the feature channel index (running from 0 to `D-1`) and `D` is the number of feature channels, and the values of [`alpha`](/documentation/MetalPerformanceShaders/MPSCNNCrossChannelNormalization/alpha), [`beta`](/documentation/MetalPerformanceShaders/MPSCNNCrossChannelNormalization/beta), and [`delta`](/documentation/MetalPerformanceShaders/MPSCNNCrossChannelNormalization/delta) are set via properties. It is your responsibility to ensure that the combination of the values of the [`delta`](/documentation/MetalPerformanceShaders/MPSCNNCrossChannelNormalization/delta) and [`alpha`](/documentation/MetalPerformanceShaders/MPSCNNCrossChannelNormalization/alpha) properties does not result in a situation where the denominator becomes zero - in such situations the resulting pixel-value is undefined. > Note: > The encoding methods in the ``doc://com.apple.metalperformanceshaders/documentation/MetalPerformanceShaders/MPSUnaryImageKernel`` class can be used to encode an ``doc://com.apple.metalperformanceshaders/documentation/MetalPerformanceShaders/MPSCNNCrossChannelNormalization`` object to a object. ## Topics ### Initializers [`init(coder:device:)`](/documentation/MetalPerformanceShaders/MPSCNNCrossChannelNormalization/init(coder:device:)) Initializes a normalization kernel in a channel. [`init(device:kernelSize:)`](/documentation/MetalPerformanceShaders/MPSCNNCrossChannelNormalization/init(device:kernelSize:)) Initializes a normalization kernel in a channel. ### Instance Properties [`alpha`](/documentation/MetalPerformanceShaders/MPSCNNCrossChannelNormalization/alpha) The “alpha” variable of the kernel function. [`beta`](/documentation/MetalPerformanceShaders/MPSCNNCrossChannelNormalization/beta) The “beta” variable of the kernel function. [`delta`](/documentation/MetalPerformanceShaders/MPSCNNCrossChannelNormalization/delta) The “delta” variable of the kernel function. [`kernelSize`](/documentation/MetalPerformanceShaders/MPSCNNCrossChannelNormalization/kernelSize) The size of the square kernel window. --- Copyright © 2026 Apple Inc. All rights reserved. | [Terms of Use](https://www.apple.com/legal/internet-services/terms/site.html) | [Privacy Policy](https://www.apple.com/privacy/privacy-policy)