Shape Recovery Using Stochastic Heat Flow

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We consider the problem of depth estimation from multiple images based on the defocus cue. For a Gaussian defocus blur, the observations can be shown to be the solution of a deterministic but inhomogeneous diffusion process. However, the diffusion process does not sufficiently address the case in which the Gaussian kernel is deformed. This deformation happens due to several factors like self-occlusion, possible aberrations and imperfections in the aperture. These issues can be solved by incorporating a stochastic perturbation into the heat diffusion process. The resultant flow is that of an inhomogeneous heat diffusion perturbed by a stochastic curvature driven motion. The depth in the scene is estimated from the coefficient of the stochastic heat equation without actually knowing the departure from the Gaussian assumption. Further, the proposed method also takes into account the non-convex nature of the diffusion process. The method provides a strong theoretical framework for handling the depth from defocus problem.

Recommended citation: V.P. Namboodiri and S. Chaudhuri (2007) “Shape Recovery Using Stochastic Heat Flow“ Proceedings of the British Machine Vision Conference 2007, University of Warwick, UK, September 10-13, 2007