Questions tagged [variational-methods]
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3
questions
1
vote
1answer
31 views
Justification for Squared $ {L}_{2} $ Data and Smoothness Term as an Error Bound
Often in variational methods (and not only) we have an energy that is of the form:
$$E(u) = \frac{1}{2}\|f-u\|^2_2 + \frac{\alpha}{2}\|\psi(u)\|^2_2,$$
where the first term is referred to as the data ...
1
vote
0answers
35 views
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 ...
1
vote
1answer
438 views
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 ...
