VER the past few days progress has been made primarily by exploring diffusion-based methods, having come to the point where geodesics cannot quite have their resultant performance improved any further. So far I got just one mistake in the GMDS-based approach and none in the other FMM-based approach, so it is looking similar to what I saw before. If I can rid myself of all errors (even in hard cases), that will be great, but it depends on the inherent limitations and strengths of the methodology, not the will.

The latest experiment showed comparable performance (w.r.t. prior experiments) but it is a lot slower, so I switched back to 2000 vertices and tried 300 points (to find correspondence for) rather than just 100 as before.

This aforementioned approach did indeed seem to improve things somewhat, but it would take longer experiments to provide good empirical evidence for it (need for harder pairs to distinguish based on many false negatives/positives). The only pair that causes trouble at the moment (among about 60 pairs that are being tested) is one that looks similar but is actually of different subjects. GMDS also detects it as being similar enough to fall near the border but at the side of true pairs rather than false ones. Let’s just take a face example (the methods are generic and can be applied to other data).

Some of my more recent modifications did not succeed at resolving the more problematic cases — ones where pairs are too similar/dissimilar to make an accurate assessment (it would be interesting to know how other methods cope with those as even a human observer would struggle, despite our brains being well wired to recognise faces). Doing 2D+3D or just 2D might in some sense be easier than 3D only, depending on the methods tested.

The other issue is, very consistently I find that GMDS is outperformed by a simpler FMM-based method that I implemented, without exceptions (the latter is a lot faster). But the mask continues to be modified in accordance with prior results and some observation of the stress (shown in different shades of grey upon points inside Voronoi cells) studied. If we hit a recognition barrier at around 97% (depending on the datasets), then perhaps using a mixture of methods would help, e.g. shape descriptors where the photometric data is encoded as geometric. I will revisit heat kernel signature and see if I can make those work better than before, then incorporate newer code like the stuff most recently published.

Now, moving on to heat kernel signatures we get some encouraging early results. With improvements to the code and to the masks, I have reimplemented the diffusion-based thresholding around landmark points and preliminary tests suggest high recognition performance. However, at this stage, the code is not stable, so it takes a lot of effort to produce a ROC curve. Performance of the diffusion-based comparator seems to have been vastly improved since last month, but there are still some issues to overcome. Heat kernels, being less dependent on the plane’s surface than geodesics calculated upon triangles, sometimes leave isolated patches that penalise and significantly increase the dissimilarity score, removing much of its signal. Maybe both distance types can be fused to resolve this in an ad hoc fashion. The first image just shows what happens if the surface if fragmented, the second shows what happens when it’s all in one unit. The third and fourth images provide examples of diffusion-based cutoffs leaving small ‘islands’ that pose a challenge.

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