Mesh optimization

Abstract

We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh M0, produce a mesh M, of the same topological type as M0, that fits the data well and has a small number of vertices. Our approach is to minimize an energy function that explicitly models the competing desires of conciseness of representation and fidelity to the data. We show that mesh optimization can be effectively used in at least two applications: surface reconstruction from unorganized points, and mesh simplification (the reduction of the number of vertices in an initially dense mesh of triangles).

Exploring Facial Expression Effects in 3D Face Recognition Using Partial ICP

“…(1) To compensate for the effect of resolution,we simplify trimmed models using mesh optimization [15]. Then, all facial surface meshes put into experiments have about 2000 vertices.…”

“…Each facial mesh then have about 25000 points and 50000 triangles and the resolution is 0.04 mm. After mesh simplification [15], each scan has about 2000 points and about 4000 triangles. Figure 3(b) shows 3 subjects and 27 scans of face models.…”

Adaptive real-time level-of-detail based rendering for polygonal models

“…Case (b) can arise because in determining a parent-child relationship we are essentially collapsing an edge and not all edge collapses are considered legal. For a detailed discussion on legality of edge collapses the interested reader can refer to [26].…”

“…The global algorithms optimize the simplification process over the whole object, and are not necessarily limited to Contact Address: Department of Computer Science, State University of New York at Stony Brook, Stony Brook, NY 11794-4400, Email: chaoyu jihad varshney@cs.sunysb.edu the small neighborhood regions on the object. Some of the local approaches have been -vertex deletion by Schroeder et al [32], vertex collapsing by Rossignac and Borrel [31], edge collapsing by Hoppe et al [26] and Guéziec [20], triangle collapsing by Hamann [21], and polygon merging by Hinker and Hansen [24]. Some of the global approaches have been -redistributing vertices over the surface by Turk [35], minimizing global energy functions by Hoppe et al [26], using simplification envelopes by Varshney [36] and Cohen et al [10], and wavelets by DeRose et al [14].…”

“…Some of the local approaches have been -vertex deletion by Schroeder et al [32], vertex collapsing by Rossignac and Borrel [31], edge collapsing by Hoppe et al [26] and Guéziec [20], triangle collapsing by Hamann [21], and polygon merging by Hinker and Hansen [24]. Some of the global approaches have been -redistributing vertices over the surface by Turk [35], minimizing global energy functions by Hoppe et al [26], using simplification envelopes by Varshney [36] and Cohen et al [10], and wavelets by DeRose et al [14]. The issue of preservation or simplification of the genus of the object is independent of whether an algorithm uses local rules, or global rules, or both, to simplify.…”