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Solving Ill-Conditioned Problems by Minimizing Equation Error - Softcover

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9780259174127: Solving Ill-Conditioned Problems by Minimizing Equation Error

Synopsis

This book presents a groundbreaking method for solving inverse problems in computer vision, where the goal is to infer the structure of objects from incomplete or degraded data. The author presents a method rooted in numerical analysis for solving ill-posed problems, where a known equation models a sequence of steps that have degraded the scene. Reconstruction is attempted by finding a solution that minimizes the deviation from that equation. The book exemplifies this method through its application to the deblurring problem, where deblurring is achieved by computing a succession of images, each slightly deblurred from the previous, such that the complete set satisfies the equations specifying the diffusion process of blurring. This approach is a novel method of regularization for problems where a scale-space parameter can be used to separate the information extracted from the image. The author argues that this method has great promise for a number of applications in computer vision, including interpolation of sparse data, feature extraction, and the investigation of the information content of zero-crossings in the raw primal sketch. The book's insights on the main subject significantly contribute to the field of computer vision and will be of great interest to researchers and practitioners alike.

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