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Direct analytical methods for solving Poisson equations in computer vision problems
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Direct analytical methods are discussed for solving Poisson equations of the general form Delta u=f on a rectangular domain and experiments indicate that results comparable to those using multigrid can be obtained in a very small number of iterations.Abstract:
Direct analytical methods are discussed for solving Poisson equations of the general form Delta u=f on a rectangular domain. Some embedding techniques that may be useful when boundary conditions (obtained from stereo and occluding boundary) are defined on arbitrary contours are described. The suggested algorithms are computationally efficient owing to the use of fast orthogonal transforms. Applications to shape from shading, lightness and optical flow problems are also discussed. A proof for the existence and convergence of the flow estimates is given. Experiments using synthetic images indicate that results comparable to those using multigrid can be obtained in a very small number of iterations. >read more
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Height and gradient from shading
TL;DR: In this paper, the shape-from-shading problem is solved by linearization of the reflectance map about the current estimate of the surface orientation at each picture cell, which can find an exact solution of a given shape from shading problem even though a regularizing term is included.
References
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Journal ArticleDOI
Determining optical flow
TL;DR: In this paper, a method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image, and an iterative implementation is shown which successfully computes the Optical Flow for a number of synthetic image sequences.
Book
Numerical solution of partial differential equations : finite difference methods
TL;DR: In this article, the standard finite difference methods of parabolic, hyperbolic, and elliptic equations are discussed, together with the concomitant theoretical work on consistency, stability, and convergence.
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