atrous

Atrous, from the French phrase à trous meaning “with holes,” is a term used in signal processing and computer vision to describe the dilation of a filter by inserting gaps between its coefficients. This creates a spaced or holey kernel, which expands the filter’s receptive field without increasing the number of parameters or reducing the resolution of the data.

In wavelet analysis, the à trous algorithm refers to a redundant, undecimated wavelet transform that uses dilated filters with increasingly larger gaps. At each scale, the filter taps are spaced farther apart, and no subsampling is performed, so the representation remains aligned with the original signal. This yields a multi-scale, shift-invariant decomposition that preserves spatial resolution.

In convolutional neural networks, atrous (dilated) convolution uses a dilation rate to insert zeros between kernel elements. For example, a 3×3 kernel with rate 2 effectively covers a 5×5 area while keeping only nine learnable parameters. This enlarges the receptive field and enables the network to capture broader context without pooling or downsampling, which is particularly useful in semantic segmentation and other dense prediction tasks. The approach can introduce gridding artifacts if the dilation is not carefully configured across layers.

Overall, atrous describes a simple yet powerful idea: analyze or process data at larger scales by introducing holes in the filter structure. Its use spans traditional signal processing and modern deep learning, where it supports multi-scale context without sacrificing resolution.