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Analog VLSI Circuits for the Perception of Visual Motion by Alan A. Stocker

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Appendix A

Variational Calculus

A.1 Optimization Problem

Consider the following minimization problem. Given the Lagrange function imagesimages which is sufficiently regular (e.g. ∈ C2) and the function images, find function images such that

images

images

Definition 1. A function images is called a candidate for a solution of (A.1) if it is defined on Ω, obeys the boundary condition, and is piece-wise differentiable.

A necessary condition for a candidate images, images to be a solution of (A.1) is that the following system of differential equations applies:

This fundamental theorem was proven by Leonhard Euler in 1744. With this proof, he created ...

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