Sub-Riemannian Mean Curvature Flow for Image Processing

被引：18

作者：

Citti, G. ^{[1
]}

Franceschiello, B. ^{[2
]}

Sanguinetti, G. ^{[3
]}

Sarti, A. ^{[2
]}

机构：

[1] Univ Bologna, Dipartimento Matemat, I-40126 Bologna, Italy

[2] CNRS, EHESS, Ctr Math, F-75244 Paris, France

[3] Tech Univ Eindhoven, Dept Math & Comp Sci, POB 513, NL-5600 MB Eindhoven, Netherlands

来源：

SIAM JOURNAL ON IMAGING SCIENCES | 2016年 / 9卷 / 01期

基金：

欧洲研究理事会;

关键词：

image completion; sub-Riemannian models; existence result; INVARIANT PARABOLIC EVOLUTIONS; INVERTIBLE ORIENTATION SCORES; FUNCTIONAL ARCHITECTURE; CONTOUR ENHANCEMENT; VISCOSITY SOLUTIONS; MINIMAL-SURFACES; REGULARITY; DIFFUSION; FIELDS; CONNECTIONS;

D O I：

10.1137/15M1013572

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

In this paper we reconsider the sub-Riemannian cortical model of image completion introduced in [G. Citti and A. Sarti, J. Math. Imaging Vision, 24 (2006), pp. 307-326]. This model combines two mechanisms, the sub-Riemannian diffusion and the concentration, giving rise to a diffusion driven motion by curvature. In this paper we give a formal proof of the existence of viscosity solutions of the sub-Riemannian motion by curvature. Furthermore we illustrate the sub-Riemannian finite difference scheme used to implement the model and we discuss some properties of the algorithm. Finally results of completion and enhancement on a number of natural images are shown and compared with other models.

引用

页码：212 / 237

页数：26

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