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Questions tagged [variational-methods]

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Linear equation set construction for Brox et al. optical flow optimization

I'm trying to implement an optical flow calculation program for two successive images based on this article by Brox et al. The Euler-Lagrange combined with a fixed point iteration loop yields two ...
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Is the behaviour of the following filter plausible?

I've designed a filter based on this equation $$ E(u) = \frac{1}{2}\int_{\Omega} \left[(u-f)^2 + g(\lVert \nabla u \rVert)\right]dxdy $$ Euler-Lagrange equations in this case are (should be) given ...
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Laplacian of Gaussian Approximation and Gaussian Blur as the Solution of Heat Equation

While I was reading SIFT paper(Lowe, 2004), I came across the method that he apply "heat diffusion equation" to Gaussian function to derive that $$ \frac{∂G}{∂σ} = σ∇^2G $$ I searched Wikipedia and ...