A Part‐aware Surface Metric for Shape Analysis

By Rong Liu, Hao Zhang, Ariel Shamir, Daniel Cohen-Or. 2009

96 citations recorded by the source corpus.

The notion of parts in a shape plays an important role in many geometry problems, including segmentation, correspondence, recognition, editing, and animation. As the fundamental geometric representation of 3D objects in computer graphics is surface‐based, solutions of many such problems utilize a surface metric, a distance function defined over pairs of points on the surface, to assist shape analysis and understanding. The main contribution of our work is to bring together these two fundamental concepts: shape parts and surface metric. Specifically, we develop a surface metric that is part‐aware. To encode part information at a point on a shape, we model its volumetric context – called the volumetric shape image (VSI) – inside the shape's enclosed volume, to capture relevant visibility information. We then define the part‐aware metric by combining an appropriate VSI distance with geodesic distance and normal variation. We show how the volumetric view on part separation addresses certain limitations of the surface view, which relies on concavity measures over a surface as implied by the well‐known minima rule. We demonstrate how the new metric can be effectively utilized in various applications including mesh segmentation, shape registration, part‐aware sampling and shape retrieval.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computer Graphics and Computer-Aided Design

In Computer Vision and Pattern Recognition

Citations in the corpus

PointGrid: A Deep Network for 3D Shape Understanding (2018, background): “), dihedral angles between triangles [58], curvatures (Gaussian curvature or mean curvature) [30], geodesic distances on a mesh [17, 64], slippage [61], symmetry, convexity, medial axis [33], shape diameter [44] and motion characteristics [43], shape contexts [4], spin images [21], etc.”
The wave kernel signature: A quantum mechanical approach to shape analysis (2011, background): “Such descriptors also include the Integral Invariants [19], the Multiscale Local Signature [14] and the Point-Aware Metric [18].”
Learning 3D mesh segmentation and labeling (2010, background): “In Press], distances from medial surface points [Liu et al. 2009], average geodesic distances [Hilaga et al.”
3D Mesh Labeling via Deep Convolutional Neural Networks (2015, background): “…2006], PCA feature (PCA) [Kalogerakis et al. 2010], shape diameter function (SDF) [Shapira et al. 2010], distance from medial surface (DIS) [Liu et al. 2009], average geodesic distance (AGD) [Hilaga et al. 2001 shape context (SC) [Belongie et al. 2002], and spin image (SI [Johnson and…”