Self-adaptive regularization

Abstract

Often an image g(x,y) is regularized and even restored by minimizing the Mumford-Shah functional. Properties of the regularized image u(x,y) depends critically on the numerical value of the two parameters alpha and gamma controlling smoothness and fidelity. When alpha and gamma are constant over the image, small details are lost when an extensive filtering is used in order to remove noise. In this paper, it is shown how the two parameters alpha and gamma can be made self-adaptive. In fact, alpha and gamma are not constant but automatically adapt to the local scale and contrast of features in the image. In this way, edges at all scales are detected and boundaries are well-localized and preserved. In order to preserve trihedral junctions alpha and gamma become locally small and the regularized image u(x,y) maintains sharp and well-defined trihedral junctions. Images regularized by the proposed procedure are well-suited for further processing, such as image segmentation and object recognition.

Enhancing precision in time-domain fluorescence lifetime imaging

“…Other TV or non-TV denoising methods have also been developed either to handle Poisson noise or to have varying regularization parameters that can potentially be used to remove Poisson noise. [19][20][21][22] However, although Poisson-distributed noise is a common form of noise for photon-counting devices, other forms of noise may appear due to nonunity gain and sometimes nonideal behaviors of real imaging systems. In addition, to directly denoise FLIM lifetime maps, the deformed noise distribution after lifetime determination and the dependence of this distribution on intensity and lifetime need to be considered as well.…”

Automatic Scale Detection for Contour Fragment Based on Difference of Curvature

“…One is the MPEG-7 contour shape descriptor that is based on the curvature scale-space. The other is the gradient-based curvature that is based on the intensity image of contour [9], [11]. In the following, these conventional methods are called CSS and GbC, whereas the proposed method is called DoC.…”

Multiplierless Mumford and Shah Functional Implementation

“…As far as the Mumford and Shah functional implementation is concerned, several works deal with iterative algorithms [4,9,15,17,18,31,32]. Furthermore, since the Mumford and Shah functional is very computationally intensive, different solutions have been proposed to tackle its complexity [4,9,17,31,32].…”

“…Furthermore, since the Mumford and Shah functional is very computationally intensive, different solutions have been proposed to tackle its complexity [4,9,17,31,32]. In particular, as the computation of the Mumford and Shah functional is based on iterative algorithms, most of the proposed studies have focused on reducing the number of required iterations.…”

“…Other solutions are based on the Steepest Descent (e.g., [4] and [31]) to reduce the number of iterations. The Preconditioned Conjugate Gradient method is a very effective technique for solving sparse linear equation systems as Ax = b.…”