I had the pleasure of meeting Irwin Sobel back in 2017. He said that he devised the “Sobel Operators,” as they were called, because similar filters that left out the row (or column) of zeros did not have what Andrew referred to as a “central pixel.” As Irwin told me, he was unsure how to map a pixel in the filtered result back to a pixel in the unfiltered source, and that bothered him.
It is interesting to note that the Sobel filters actually perform two separable operations. The most obvious is, of course, the detection of edges. The second is more subtle, and can be significant in the presence of noise. The Sobel filters perform some smoothing in the direction parallel to the edge. This smoothing reduces the noise in this direction, making edge detection more robust. The transfer function of this smoothing operation is a half raised cosine (called the “halversine” decades ago), and is the impulse response of the von Hann window.
Using convolution filters does have a connection to neural visual processing. David Hubel and Torsten Wiesel shared a Nobel Prize for their work on neural visual processing. A key discovery was that there are neurons in the visual cortex that respond to edges at certain angles (they called these “simple cells”), as well as ones that respond to more complicated patterns. In either case, the operation of the neuron could be characterized by a convolution. (While I never met David Hubel, I do know his son, Paul, and I pinch-hit (so to speak) for him at a 2014 conference held at Harvard University, where his father did some of this significant work!)
Some of the neural processing is done in the retina of the eye. There are specialized neurons in the retina that perform a convolution-like operation using cone cells in what are called their “receptive field.” Again, this lends some credence to the use of convolutions in this context.