The variational method is a way to solve problems given in the form of a variational model, i.e., as an energy minimization problem on an infinite-dimensional space which is typically a function space. It employs tools from the mathematical framework of variational analysis.
Ikeuchi and Horn's shape-from-shading paper and Horn and Schunck's optical flow paper, which appeared in AIJ simultaneously, are the earliest representative works to introduce a variational method to computer vision . Inspired by the extraordinary success of the idea, variational methods have been extensively studied in computer vision and become a very popular tool for a wide variety of problems. They are particularly successful in mathematical image processing, where they are used to describe fundamental low-level problems, like image segmentation [9, 11], denoising , and deblurring , but have also been employed for...
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