On Volumetric Shape Reconstruction from Implicit Forms
In this paper we report on the evaluation of volumetric shape reconstruction methods that consider as input implicit forms in 3D. Many visual applications build implicit representations of shapes that are converted into explicit shape representations usin
- PDF / 4,637,330 Bytes
- 16 Pages / 439.37 x 666.142 pts Page_size
- 82 Downloads / 204 Views
Abstract. In this paper we report on the evaluation of volumetric shape reconstruction methods that consider as input implicit forms in 3D. Many visual applications build implicit representations of shapes that are converted into explicit shape representations using geometric tools such as the Marching Cubes algorithm. This is the case with image based reconstructions that produce point clouds from which implicit functions are computed, with for instance a Poisson reconstruction approach. While the Marching Cubes method is a versatile solution with proven efficiency, alternative solutions exist with different and complementary properties that are of interest for shape modeling. In this paper, we propose a novel strategy that builds on Centroidal Voronoi Tessellations (CVTs). These tessellations provide volumetric and surface representations with strong regularities in addition to provably more accurate approximations of the implicit forms considered. In order to compare the existing strategies, we present an extensive evaluation that analyzes various properties of the main strategies for implicit to explicit volumetric conversions: Marching cubes, Delaunay refinement and CVTs, including accuracy and shape quality of the resulting shape mesh.
1
Introduction
Visual computing applications usually consider explicit representations for 3D shapes, in the form of surface or volume meshes in general. This is true for most visualization applications and also for applications that require local neighboring information within the shape or on its surface, as often the case with shape optimization or shape deformation applications for example. In order to generate such explicit representations from visual observations many methods consider as input an implicit representation that identifies the shape as being a region V within an observation domain Ω ∈ R3 . Such implicit representation is typically given as a scalar function f : Ω → R which takes different values inside and outside V, for instance an indicator function or a distance function in 3D. These implicit representations f are often encountered in reconstruction applications that consider point clouds, as obtained with for instance stereo, multi-stereo and depth scanning apparatus, e.g. [18,24] (see Fig. 1). They can also be built directly from image primitives, for instance the implicit visual hull form, e.g. [15] with image silhouettes. The conversion then from implicit to explicit representations c Springer International Publishing AG 2016 B. Leibe et al. (Eds.): ECCV 2016, Part III, LNCS 9907, pp. 173–188, 2016. DOI: 10.1007/978-3-319-46487-9 11
174
L. Wang et al.
Fig. 1. The Gargoyle multi-view point cloud and the associated Poisson reconstructions with Marching Cubes and CVT. Distances to the implicit form are color encoded on the right, from low (blue) to high (red). (Color figure online)
usually consists in the polyhedrization of the region V, where both the resulting polyhedral volume and the associated polygonal surface approximations are potentially conside
Data Loading...
