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.
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ABSTRACT: In this paper we discuss the implementation of 3D Symmetry Sets. It describes how the Symmetry Set can be derived given a parametrized shape, as well as given an unorganized point cloud. It presents a geometric method to derive the Symmetry Set, that is an extension of the one given in deliverable 10. Just as in the 2D case, level set methods cannot be applied. Although the mathematics are a simple extension of the 2D case, the visualization, numerical computations and their stability are complicated. An example is give by means of a ellipsoid. In this example the Symmetry Set can be computed exactly and results can be compared to the ground truth.
Conference Paper: Computing 3D Symmetry Sets; A Case Study.[Show abstract] [Hide abstract]
ABSTRACT: In this paper we discuss the implementation of methods to derive 3D Symmetry Sets, given a parameterized shape, as well as an unorganized point cloud. It presents a geometric method to derive the Symmetry Set, that is an extension of the one given in (6). Although the mathematics is a simple extension of the 2D case, the visualization, nu- merical computations and their stability are much more complicated. An example is given by means of an ellipsoid. In this example the Symmetry Set can be computed exactly and results can be compared to the ground truth.Deep Structure, Singularities, and Computer Vision, First International Workshop, DSSCV 2005, Maastricht, The Netherlands, June 9-10, 2005, Revised Selected Papers; 01/2005