Geometry Gurus Needed (First Order Geodesics on Surface Pairs)
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COULD really use the advice of some people who are interested in computer graphics and vision — inverse but complementary fields, which are largely related to geometry and mathematics at large. The challenge is to compare surfaces based on their 3-D characteristics, using Euclidean, geodesic or another non-Euclidean metrics.
Here is what the surfaces look like.
The following image represents a performance ROC curve we have.
In simple terms, this means that we’re able to classify correctly about 70% of the time. Having summarised a year’s work, culminating in mostly unsuccessful experiments around diffusion (around 97^ recognition rate, the above is poor, So I return to working with geodesic distances as the Swiss army knife for measurement of distances. But the approach being explored at the moment is different and with further enhancement it can hopefully yield performance higher than 97% (matching rate). The sources of limitation are generally well understood in the sense that they can be visualised and overlaid on top of the image pairs. There is no trivial and reliable way to establish multiple landmark points around which to measure distances consistently, so I am trying another way, which at a very coarse level has a matching rate of about 80% (can be significantly improved soon).
The approach attempted at this stage involves triangle comparison post- and pre-marking, but the performance attained so far is not satisfactory.
The limitation is likely inherent in the measuring of distances in FMM and the sub-sampling that results from triangulation (see image for the size of triangles to be fully appreciated).
One particular weakness of the diffusion approach to masking is that it leads to holes in the data, which invalidates some of the measures that were used routinely beforehand. In order to fuse together both geodesic and spectral measures, we now attempt to get a more symbiotic approach that carves out surfaces based on geodesic properties and then uses spectral features on these surfaces. Since ordering does not exist (e.g. point-to-point correspondences), the histogram of images is used to describe the sub-surfaces (carved out around a known correspondence). By increasing the number of rings and bins in the histogram, the performance can be varied somewhat. I was running overnight experiment to test this and got some other appalling ROC curves, such as this:
The results from the last experiment were disappointing because they did not provide good separability. So the following morning I designed and started running an experiment that explores the potential of measuring diffusion distance between furthest points in the surface carved in accordance with geodesic boundaries (several rings). This too did not give good results. Generally speaking, diffusion distance as a measurement has not proven to be anywhere as useful as FMM so far (since December). It seems to be insensitive to small differences and it does not seem to degrade linearly, either. The next experimental design will explore another new approach, perhaps conceding the potential of diffusion being integrated into the framework’s pipeline.
So the question is this: given two surfaces that are geodetically craves around the surface, what approach would you use to compare them for similarity? We’ve tried a variety of known methods, but none seems to yield very encouraging results thus far. Thanks for any advice or pointers you may have.
ith recent milestones reached and a change in publication strategy, I decided to unleash some easy-to-run code along with the 535 pages which document the code as well as experiments that have been run using this code over the past year or so. The document is not as organised as it ought to be, but I hereby make a lot of stuff available in fairly raw form. I made an HTML version to overcome file size issues that are associated with PDF, not to mention accessibility issues. 
AST year (or at the end of 2010 to be more accurate) I started posting a lot more often about my work in this blog. I resumed what I had done years beforehand, even if that meant a loss of focus for this personal blog. But then again, this blog hardly ever had any single point of focus, so after the upcoming release of one gigantic PDF I will resume posting updates about my research on a more regular basis. This ought to achieve a more transparent communication of ideas. It is also a departure from the disappointing pace of blogging (about a post per week as of late).
O, TODAY was a little dull. In the midst of boredom scripts were produced to turn a sequence of images into an animation of small size with an example of crop, border, and resize (ImageMagick required). Let’s go through this one step at a time. Put all the images from the sequence in a working directory.
HE FOLLOWING research notes have just been uploaded, hopefully to help others understand the work undertaken and what ideas are being tested (generalised to the extent of being applicable to any type of data, including biomedical). The 200+ pages long document which is more complete is still work in progress and it will be published at a later date. Thanks to the 
INALLY, after nearly a week since taking and returning from a break, I received the server I have been waiting for. It arrived on Monday afternoon and today I finished configuring it, running alongside the triple-head workstation which I will use to do computer vision jobs and other development/admin work. The research requires a lot of screen space and sometimes the RAM/CPUload goes rather high, which helps not at all unless there is a second motherboard at hand (and a fallback machine.
