A variational formulation-based edge focussing algorithm

A variational formulation-based edge focussing algorithm

Many edge detection techniques exhibit scale-dependent distortion of edges. We develop two ideas, which may also be of independent interest, to produce sharp edge localization at all scales. The first is approximation of the functional associated with the variational formulation via epi-convergence, replacing the edge set with a function. We provide a fast algorithm for minimizing the approxima...

A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration

Variational models with 1-norm based regularization, in particular total variation (TV) and its variants, have long been known to offer superior image restoration quality, but processing speed remained a bottleneck, preventing their widespread use in the practice of color image processing. In this paper, by extending the grayscale image deblurring algorithm proposed in [Y. Wang, J. Yang, W. Yin...

A variational formulation for PDEs

Definition 1. A classic solution (sometimes called strong solution) to the problem is a function u ∈ C2([a, b]) such that it vanishes at the endpoints and pointwise it satisfies the equation −u′′(x)+ u(x) = f(x). Let’s change approach. Suppose that we formally multiply the differential equation by an arbitrary function φ ∈ C1([a, b]) with φ(a) = φ(b) = 0 and we integrate over the interval [a, b...

Variational Formulation of Problems and Variational Methods

A FUZZY DIFFERENCE BASED EDGE DETECTOR

In this paper, a new algorithm for edge detection based on fuzzyconcept is suggested. The proposed approach defines dynamic membershipfunctions for different groups of pixels in a 3 by 3 neighborhood of the centralpixel. Then, fuzzy distance and -cut theory are applied to detect the edgemap by following a simple heuristic thresholding rule to produce a thin edgeimage. A large number of experime...