Specifically, in the maxout network:
http://proceedings.mlr.press/v28/goodfellow13.pdf
answers:
https://www.quora.com/What-is-a-cross-channel-pooling-in-convolutional-neural-networks
If it is a convolution module outputing 50 feature maps, then the cross channel pooling will output 5 feature map, where each point in the feature map is the max of the points at the same position in the 10 underlying feature maps.