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.
- SourceAvailable from: Arjan Kuijper
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
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ABSTRACT: In this paper a novel method to derive the Medial Axis of a shape is presented. The property that the Medial Axis is a subset of the Symmetry Set is used. The latter allows a formulation in terms of two equations, based on geometrical arguments. From the set that solves the equations, the subset that yields the Medial Axis can be taken. An algorithm is given that performs these tasks. The Medial Axis can easily be labelled with respect to main axis and branches, as this information follows directly from the Symmetry Set.Pattern Recognition Letters. 01/2007; 28:2011-2018.
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ABSTRACT: Among the many attempts made to represent families of 2D shapes in a simpler way, the Medial Axis (MA) takes a prominent place. Its graphical representation is intuitively appealing and can be computed efficiently. Small perturbations of the shape can have large impact on the MA and are regarded as instabilities, although these changes are mathematically known from the investigations on a super set, the Symmetry Set (SS). This set has mainly been in a mathematical research stage, partially due to computational aspects, and partially due to its unattractive representation in the plane. In this paper novel methods are introduced to overcome both aspects. As a result, it is possible to represent the SS as a string is presented. The advantage of such a structure is that it allows fast and simple query algorithms for comparisons. Second, alternative ways to visualize the SS are presented. They use the distances from the shape to the set as extra dimension as well as the so-called pre-Symmetry Set and anti-Symmetry Set. Information revealed by these representations can be used to calculate the linear string representation structure. Example shapes from a data base are shown and their data structures derived.Journal of Mathematical Imaging and Vision 01/2006; 26:127-147. · 1.77 Impact Factor