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I am currently studying the FREAK descriptor and I read the article published by its designers. It states that the aim was to mimic the retinal topology, and one of the advantages that could be gained is the fact that retinal receptive fields overlap, which increases the performance.

I thought about it a lot, and the only explanation I was able to come up with is the fact that, looking at this problem from an implementation point of view, a receptive field is the ensemble of an image patch centred around a pixel, plus the standard deviation of the Gaussian filter applied to this patch. The size of the receptive field represents the value of the standard variation. The bigger the size is, the more pixels will be taken into consideration when Gaussian filtering, and so we "mix" more information in a single value.

But this guess of mine is very amateurish, I would appreciate it if someone could give an explanation from what goes on in the field of image processing-computer vision-neuroscience.

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As a neuroscientist/engineer who teaches vision in a physiology course for engineers, but who hasn't read any of the FREAK docs, I'd point people to the works of David Marr, or maybe Kuffler. I found a nice review at Introduction to visual computation and the primate visual system - 11MB PDF.

Retinal receptive fields (or more properly, ganglion cell receptive fields, where ganglion cells are the output layer of the retina) have a center-surround topology, where the outer portions of the receptive fields behave opposite to the central part of the visual field. Thus, a point of light shined on the center of the field might excite the ganglion cell, and if shined on the periphery of the field it might inhibit the same cell. This image (mostly images from a physiology text by Purves) shows this idea in a couple of ways, and also shows an interesting illusion that results from this center-surround antagonism in the lower right (the center bar is a constant shade of grey). enter image description here

This arrangement (approximately a difference of gaussians) has the benefit of increasing the dynamic range of the ganglion cell, and it also enhances the edges in images received by the retina.

The output from the ganglion cells projects fairly directly to the lateral geniculate nucleus, and from there to the visual cortex of the brain. There, the roughly circular receptive fields of the ganglion cells can be joined up in interesting ways to respond to lines of contrast. This is one of the reasons why overlapping fields can be so powerful. From there, you can use overlapping "line" fields to detect x's, +'s, and so on, with increasing complexity. enter image description here

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Interesting question! Thanks for introducing me to FREAK!

The paper just says that overlapping fields "increases redundancy", my interpretation is that like most detectors, FREAK is essentially scrolling a detection window over the image. If you arbitrarily break the image into non-overlapping windows then there's a good chance you'll break a useful image patch into multiple pieces. Visual examples are better than wordy explanations. Let's assume I have a smiley-detector and I'm running it on the image below. The strongest response from my smiley-detector will come from the blue window, but if I had broken the image into non-overlapping windows (the red regions) then instead of one strong face descriptor, I'd have four crappy face descriptors.

Smiley detector example

As I said, I don't know the details of FREAK, but in general for scrolling-window-type detectors that's the reason to have overlapping windows.

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