Can atrous (dilated) convolution ever ignore a pixel in the original image?

Atrous (dilated) convolution expands the receptive field of the filter by skipping pixels between kernel elements. However, when considering a single layer with a fixed input size and convolution parameters, theoretically each pixel of the input image could be used, but not necessarily — it depends on the input size, stride, kernel size, and dilation rate.

If the dilation rate is too large and the input size is small, some pixels may not fall under the convolution kernel in any position, meaning they will not be used in computations. This is especially noticeable with large dilations and small input images.

Thus, in general, atrous convolution may not utilize some pixels of the original image if the convolution parameters and input size are such that these pixels do not fall under the kernel in any shift.

Example: for a 1D signal of length 10, with a kernel size of 3 and dilation of 4, the kernel will look at positions [i, i+4, i+8]. For i=0, these are positions 0, 4, 8; for i=1, positions 1, 5, 9; for i=2, positions 2, 6, 10 (which is out of bounds). The pixel with index 3 will not be used in any position.