What matters more for image matching and the comparison of descriptors: invariance and causality requirements or repeatability criteria?

Jean-Michel Morel (work in progress with Vicent Caselles, Mauricio Delbracio, Ives Rey Otero, Rida Sadek)

We are trying very hard since years to understand scale invariant/affine invariant/illumination invariant pattern recognition. There is by now a variety of image mathcing methods combining a detector and a descriptor. The first one to have been seriously successful is the SIFT method. This method is based on a rather rigorous application of linear scale space theory and Lindeberg's ideas to detect scale invariant features. It claims to be "scale invariant" and is so to some extent, but it is not fully scale invariant. Nevertheless several more or less recent competitors (MSER, SURF, ASIFT, SIFER,) claim better results while several of them are being "less invariant" or "less causal" than SIFT.

Better from which viewpoint? Using coupled repeatability/detection rates on datasets. In short, theory lets one hope or surmise that a method should be better when it is more invariant, all things equal, and practice tells that a pragmatical not-invariant method performs better!

At the state of our inquiry, we found that the repeatability criteria are provably biased, and that the non-invariant methods are in no way "better" than the invariant ones. Their bias is very simple: using their lack of causality they create new features and a plethore of matching descriptors that overlap. In short, they create redundant descriptors. Thus they seem to win for simplistic repeatability criteria, but an examination of simple examples shows that this is rather an illusion. This leads me to regret that mathematical analysis and invariance requirements are so neglected while the community is more and more adept to blind pragmatism and benchmark data. I would like to oppose to biased benchmarks made of plenty of uncontrolled material the elaborate choice of test patterns, and restore a role to theoretical invariance analysis.