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Monday, February 20th, 2012, 1:28 am

State-of-the-art Results for Verification in 3-D Alone

THE task of comparing atomically-meaningful 3-D surfaces is not simple. The plethora of diffusion-based techniques have not managed to overcome the drawbacks and ever surpass the performance attained through geodesic distances. The main issue, to summarise this very briefly, is that when the differences are very small between one subject and another (no topological differences) there is not enough that can be done to distinguish by kernel-based score.

I have meanwhile returned to geodesics again. Based on literature surveys from a few years ago (I read three with great interest), for 3-D in isolation the verification rates are almost always worse than for 2-D (and of course 3-D plus 2-D), which brings up the question, what type of performance levels are expected from 3-D alone in order to make a technique publishable? With our best methods we hover around the mid-nineties. With further refinements that do not require 2-D data we can make further improvements, but there are inherent difficulties. For example, as I showed a colleague at the lab some pairs of different range image (in 3-D) she was unable to tell if there were the same or not. When the similarity is high it becomes almost about gut feeling or guesswork, even for verification as opposed to identification (one-to-many or many-to-many).

Additionally, spectral methods degrade poorly compared to geodesics, as shown in the images below (first a meaningful slicing, then improper).

Spectral examples

Spectral examples

Spectral problems

Spectral problems

I am currently working on a concise report about this project (which has exceeded a year in duration so far). There’s a lot more coming. I also added some list of side projects (totally unrelated) I’ve been working on recently. I hope to focus more on ERC-funded work and not whatever pays more (industry pays more than academic). But all these are a matter to be discussed another day.

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