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Monday, July 11th, 2011, 1:06 am

Multidimesional Scaling – Animated Example

Canonical forms animation

As a demonstration of canonical forms and stress reduction complemented/guided by multidimesional scaling, I’ve created an animation which shows the process applied to each image in the Face Recognition Grand Challenge (FRGC) 2.0 set — albeit Fall Semester only in this case — in turn, in order to approach a more mutually-isometric and pose-agnostic state where distances are tied to inherent surface details (curvature, size, etc.) and the accompanying static image, as seen below, shows the original image too (added at the top). To use this within an objective function it will need to be clearer how points are selected consistently and where correspondences can autonomously be chosen to improve overall performance. The triangulation in this case is Delaunay-based although 3 methods have been implemented and they offer room for further experimental work. The factors affecting performance may be the PCA component, the triangulation, the placement of points, the optimisation of lengths, the pre-processing (ICP for instance), and few minor technicalities less worthy of consideration. Each one of these represents one parameter among many but feasibility tests — those exploring whether the overall framework is effective in the first place (distances as an encoded signature resistant to expressions) — must come first. Based on a preliminary look, this ought to serve as a reasonable discriminant, but many of the pertinent parts of the framework may need tweaking based on trials and errors.

Note: this is an except from an ongoing project and a document exceeding 200 pages so far. It will be released later this year.

MDS-stress and canonical forms

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