Gauge Invariant Framework for Shape Analysis of Surfaces


This paper describes a completely unique framework for computing geodesic methods in shape spaces of spherical surfaces below an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) area, rather than inheriting it from pre-form area, and using it to formulate a path energy that measures solely the conventional parts of velocities along the trail. In alternative words, this paper defines and solves for geodesics directly on the shape space and avoids complications ensuing from the quotient operation. This comprehensive framework is invariant to arbitrary parameterizations of surfaces along ways, a phenomenon termed as gauge invariance. Additionally, this paper makes a link between totally different elastic metrics used in the computer science literature on one hand, and also the mathematical literature on the other hand, and provides a geometrical interpretation of the terms involved. Examples using real and simulated 3D objects are provided to assist illustrate the most concepts.

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