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Why has SIFT been so successful? Why its extension, DSP-SIFT, can furtherimprove SIFT? Is there a theory that can explain both? How can such theorybenefit real applications? Can it suggest new algorithms with reducedcomputational complexity or new descriptors with better accuracy for matching?We construct a general theory of local descriptors for visual matching. Ourtheory relies on concepts in energy minimization and heat diffusion. We showthat SIFT and DSP-SIFT approximate the solution the theory suggests. Inparticular, DSP-SIFT gives a better approximation to the theoretical solution;justifying why DSP-SIFT outperforms SIFT. Using the developed theory, we derivenew descriptors that have fewer parameters and are potentially better inhandling affine deformations.

A Theory of Local Matching: SIFT and Beyond