Premium
Geometry Processing Problems Using the Total Variation of the Normal Vector Field
Author(s) -
Bergmann Ronny,
Herrmann Marc,
Herzog Roland,
Schmidt Stephan,
Vidal-Núñez José
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900189
Subject(s) - geodesic , piecewise , mathematics , normal , noise reduction , vertex (graph theory) , algorithm , geometry , total variation denoising , vector field , unit vector , constant (computer programming) , quadratic equation , mathematical analysis , computer science , surface (topology) , combinatorics , artificial intelligence , graph , programming language
This paper presents a novel approach to the formulation and solution of discrete geometry processing problems including mesh denoising. The main quantity of interest is the piecewise constant unit normal vector field, which we consider on piecewise flat, triangulated surfaces. In a similar fashion as one does for images defined on ‘flat’ domains, our goal is to remove noise while preserving shape features such as sharp edges. To this end, we model a denoising problem via a quadratic vertex tracking term and a regularizer based on the total variation of the normal vector field. Since the latter has values on the unit sphere, its total variation reduces to a finite sum of the geodesic distances of neighboring normals. We solve the model numerically by applying split‐Bregmann iterations and provide results for the ‘fandisk’ benchmark.