Energy-Based Image Simplification with Nonlocal Data and Smoothness Terms
نویسندگان
چکیده
Image simplification and smoothing is a very important basic ingredient of a lot of practical applications. In this paper we compare different numerical approaches to solve this image approximation task within a unifying variational approach presented in [8]. For methods based on fixed point iterations we show the existence of fixed points. To speed up the convergence we also use two approaches involving Newton’s method which is only applicable for convex penalisers. The running time in practice is studied with numerical examples in 1-D and 2-D.
منابع مشابه
On Robust Estimation and Smoothing with Spatial and Tonal Kernels∗
This paper deals with establishing relations between a number of widely-used nonlinear filters for digital image processing. We cover robust statistical estimation with (local) M-estimators, local mode filtering in image or histogram space, bilateral filtering, nonlinear diffusion, and regularisation approaches. Although these methods originate in different mathematical theories, we show that t...
متن کاملA Novel Image Structural Similarity Index Considering Image Content Detectability Using Maximally Stable Extremal Region Descriptor
The image content detectability and image structure preservation are closely related concepts with undeniable role in image quality assessment. However, the most attention of image quality studies has been paid to image structure evaluation, few of them focused on image content detectability. Examining the image structure was firstly introduced and assessed in Structural SIMilarity (SSIM) measu...
متن کاملDiscrete Regularization on Weighted Graphs for Image and Mesh Filtering
We propose a discrete regularization framework on weighted graphs of arbitrary topology, which unifies image and mesh filtering. The approach considers the problem as a variational one, which consists in minimizing a weighted sum of two energy terms: a regularization one that uses the discrete p-Laplace operator, and an approximation one. This formulation leads to a family of simple nonlinear f...
متن کاملImage Deblurring using Split Bregman Iterative Algorithm
This paper presents a new variational algorithm for image deblurring by characterizing the properties of image local smoothness and nonlocal self-similarity simultaneously. Specifically, the local smoothness is measured by a Total Variation method, enforcing the local smoothness of images, while the nonlocal self similarity is measured by transforming the 3D array generated by grouping similar ...
متن کاملA Linear Scale-Space Theory for Continuous Nonlocal Evolutions
Most scale-space evolutions are described in terms of partial differential equations. In recent years, however, nonlocal processes have become an important research topic in image analysis. The goal of our paper is to establish well-posedness and scale-space properties for a class of nonlocal evolutions. They are given by linear integro-differential equations with measures. In analogy to Weicke...
متن کامل