I'm reading through BRIEF and one point isn't clear to me. If we are randomly sampling the pixel-vs-pixel tests, how is it that we obtain a reproducible descriptor?
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It looks to me as if they came up with a random pixel patch vs pixel patch set of points and they used this to train their system. The system then recognizes different transformations by looking at the database of transformations and seeing how the transformations would affect the match. It then picks the transformation with the best score (lowest Hamming distance). The random pixel locations are only random once during the system design.