Variational shape approximation

Abstract

A method for concise, faithful approximation of complex 3D datasets is key to reducing the computational cost of graphics applications. Despite numerous applications ranging from geometry compression to reverse engineering, efficiently capturing the geometry of a surface remains a tedious task. In this paper, we present both theoretical and practical contributions that result in a novel and versatile framework for geometric approximation of surfaces. We depart from the usual strategy by casting shape approximation as a variational geometric partitioning problem. Using the concept of geometric proxies, we drive the distortion error down through repeated clustering of faces into best-fitting regions. Our approach is entirely discrete and error-driven, and does not require parameterization or local estimations of differential quantities. We also introduce a new metric based on normal deviation, and demonstrate its superior behavior at capturing anisotropy.

Feature-aligned segmentation using correlation clustering

“…Ideally, the feature lines emerge implicitly as the boundaries of the patches. The regularity condition can be low approximation error by an analytical primitive [5,[22][23][24][25], developability [26,27], or similarity using a variety of shape descriptors, including curvature [6,[28][29][30][31], normal voting tensor [32], slippage [33], and diffusion-type distances to a set of seed locations [34,35]. However, implicit methods can oversegment surface regions that are void of prominent feature lines, if the region fails the regularity conditions.…”

Isotropic 2D Quadrangle Meshing with Size and Orientation Control

“…Discrete partitioning is achieved by flooding the domain one triangle at a time from their generators with a dynamic priority queue [12]. Each tile is initialized to be its triangle generator, and a priority queue is filled with (up to three) incident triangles (candidates for flooding) per generator.…”

Generating Segmented Quality Meshes from Images

“…Traditionally, methods devoted to segment meshes make use of geometrical attributes, such as curvature, in order to identify the structures of interest [21,23,5,11]. In fact, the problem of segmenting meshes generated from images has not been largely investigated, being the work by Bertin et al [2] one of the few examples described in the literature.…”