Geometry Processing Problems Using the Total Variation of the Normal Vector Field. Issue 1 (18th November 2019)

• Record Type: Journal Article
• Authors: Bergmann, Ronny; Herrmann, Marc; Herzog, Roland; Schmidt, Stephan; Vidal-Núñez, José
• Other Names: Eberhardsteiner J. guestEditor.; Schöberl M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 19:Issue 1(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-11-18
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201900189
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: 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.