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A new method for the deformation of curves is presented. It is based upon a decomposition of the linear elasticity problem into basic physical laws. Unlike other methods which solve the partial differential equation arising from the physical laws by numerical techniques, we encode the basic laws using computational algebraic topology. Conservative laws use… (More)

This paper proposes an alternative to partial differential equations (PDEs) for the solution of the optical flow problem. The problem is modeled using the heat transfer process. Instead of using PDEs, we propose to use the global equation of heat conservation. We use a computational algebraic topology-based image model which allows us to encode some… (More)

- Andrew S. Rhoades, Glenn Schrader, Paul Poulin
- 2007

Opinions, interpretations, conclusions and recommendations are those of the authors and are not necessarily endorsed by the United States Government.

This paper proposes an alternative to partial differential equations (PDEs) for the solution of diffusion modeled using the heat transfer problem. Traditionally, the method for solving such physics-based problems is to discretize and solve a PDE by a purely mathematical process. Instead of using the PDE, we use the global heat equation and decompose it into… (More)

We present a new method for the deformation of curve based upon a decomposition of the elasticity problem into basic physical laws. We encode the basic laws using computational algebraic topology. Each basic law uses exact global values and makes approximations only when they are needed. The deformations computed with our approach have a physical… (More)

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