Towards a singularity-based shape language: ridges, ravines, and skeletons for polygonal surfaces.
ABSTRACT High demands on digital contents have posing strong needs on visual languages on three-dimensional (3D) shapes for improved
human communication. For a visual language to effectively communicate essential 3D shape information, shape features defined
in terms of singularity signs have been recognized as key shape descriptors. In this paper, we study salient shape features
defined via distance function singularities: ridges, ravines, and a skeleton. We propose a method for robust extraction of
the 3D skeleton of a polygonal surface and detection of salient surface features, ridges and ravines, corresponding to the
skeletal edges. The method adapts the three-dimensional Voronoi diagram technique for skeleton extraction, explores singularity
theory for ridge and ravine detection, and combines several filtering methods for skeleton denoising and for selecting perceptually
salient ridges and ravines. We demonstrate that the ridges and ravines convey important shape information and, in particular,
can be used for face recognition purposes.
- International Journal of Shape Modeling - IJSM. 01/1994;
- [show abstract] [hide abstract]
ABSTRACT: The Ball-Pivoting Algorithm (BPA) computes a triangle mesh interpolating a given point cloud. Typically, the points are surface samples acquired with multiple range scans of an object. The principle of the BPA is very simple: Three points form a triangle if a ball of a user-specified radius p touches them without containing any other point. Starting with a seed triangle, the ball pivots around an edge (i.e., it revolves around the edge while keeping in contact with the edge's endpoints) until it touches another point, forming another triangle. The process continues until all reachable edges have been tried, and then starts from another seed triangle, until all points have been considered. The process can then be repeated with a ball of larger radius to handle uneven sampling densities. We applied the BPA to datasets of millions of points representing actual scans of complex 3D objects. The relatively small amount of memory required by the BPA, its time efficiency, and the quality of the results obtained compare favorably with existing techniquesIEEE Transactions on Visualization and Computer Graphics 11/1999; · 1.90 Impact Factor
Conference Proceeding: Topology matching for fully automatic similarity estimation of 3D shapes.[show abstract] [hide abstract]
ABSTRACT: There is a growing need to be able to accurately and efficiently search visual data sets, and in particular, 3D shape data sets. This paper proposes a novel technique, called Topology Matching, in which similarity between polyhedral models is quickly, accurately, and automatically calculated by comparing Multiresolutional Reeb Graphs (MRGs). The MRG thus operates well as a search key for 3D shape data sets. In particular, the MRG represents the skeletal and topological structure of a 3D shape at various levels of resolution. The MRG is constructed using a continuous function on the 3D shape, which may preferably be a function of geodesic distance because this function is invariant to translation and rotation and is also robust against changes in connectivities caused by a mesh simplification or subdivision. The similarity calculation between 3D shapes is processed using a coarse-to-fine strategy while preserving the consistency of the graph structures, which results in establishing a correspondence between the parts of objects. The similarity calculation is fast and efficient because it is not necessary to determine the particular pose of a 3D shape, such as a rotation, in advance. Topology Matching is particularly useful for interactively searching for a 3D object because the results of the search fit human intuition well.01/2001