A Variational Approach to the Design of Early Vision Algorithms

A Variational Approach to the Design of Early Vision Algorithms. A mathematical model for the design of early vision processing stages is presented. The model comprises a “generic” class of abstract minimization problems from which specific nonlinear diffusion processes can be derived for various kinds of visual data. Each smoothing process results in a one-parameter family of segmentations of the underlying domain and thus provides a basis for the segmentation of “general” scenes. A wide range of numerical realizations can be implemented using standard Galerkin discretization. Theoretically, each algorithm can also be implemented as a globally convergent network using analog VLSI-hardware. The approach is illustrated by deriving nonlinear diffusion schemes for the processing of greyvalue data and for the processing of locally computed image motion data.

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