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When using the BRIEF algorithm to generate a feature vector, 5 methods are provided for selecting 2 random points inside a feature point patch. The 3rd method is described as follows:

Let consider the size of patch p is (S x S) and assuming keypoint is located in the center of the patch.

The first pixel(x) in the random pair is drawn from a Gaussian distribution centered around the keypoint with a stranded deviation or spread of 0.04 * S². The second pixel(y) in the random pair is drawn from a Gaussian distribution centered around the first pixel(x) with a standard deviation or spread of 0.01 * S². This forces the test(pair) to be more local. Test(pair) locations outside the patch are clamped to the edge of the patch.

I fail to understand how the distributions are chosen and how the points are chosen from them. Are they distributions of the pixel intensities? Assuming I have a 50x50 pixel patch and the keypoint is in the center, how is my first Gaussian decided? From the selected patch, the mean intensity might not be the one of the keypoint pixel yet it says that the distribution is centered around that. Also how does the size of the patch S come into play in the standard deviation?

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