  With the introduction of anti-aliased convolutional neural networks (CNN),
there has been some resurgence in relooking the way pooling is done in CNNs.
The fundamental building block of the anti-aliased CNN has been the application
of Gaussian smoothing before the pooling operation to reduce the distortion due
to aliasing thereby making CNNs shift invariant. Wavelet based approaches have
also been proposed as a possibility of additional noise removal capability and
gave interesting results for even segmentation tasks. However, all the
approaches proposed completely remove the high frequency components under the
assumption that they are noise. However, by removing high frequency components,
the edges in the feature maps are also smoothed. In this work, an exhaustive
analysis of the edge preserving pooling options for classification,
segmentation and autoencoders are presented. Two novel pooling approaches are
presented such as Laplacian-Gaussian Concatenation with Attention (LGCA)
pooling and Wavelet based approximate-detailed coefficient concatenation with
attention (WADCA) pooling. The results suggest that the proposed pooling
approaches outperform the conventional pooling as well as blur pooling for
classification, segmentation and autoencoders.
