Last update : Dec. 3, 2002

BACK

Papers by the Aizu University team on Ridges & related topics :

• A Skeleton-based Approach for Detection of Perceptually Salient Features on Polygonal Surfaces, 2002+
• A 3D Voronoi-based Skeleton and Associated Surface Features, 2001.
• Ridges and ravines on implicit surfaces, 1998.
• Ridges and Ravines: A Singularity Approach, 1994.
• Detection of Ridges and Ravines Based on Caustic Singularities, 1994.

BibTeX references.

Link to Yoshihisa Shinagawa et al. list of related papers.

Web links:

• Shape Modeling Laboratory @ Aizu University.
• Shape Modeling & Computer Graphics with Real Functions.
• Shape Modeling International '99.
• Shape Modeling International '97.

NB: Journal version of the 2001 Conference paper at Pacific Graphics.

The paper presents a skeleton-based approach for robust detection of perceptually salient shape features. Given a shape approximated by a polygonal surface, its skeleton is extracted using a three-dimensional Voronoi diagram technique proposed recently by Amenta et al. [3]. Shape creases, ridges and ravines, are detected as curves corresponding to skeletal edges. Salient shape regions are extracted via skeleton decomposition into patches. The approach explores the singularity theory for ridge and ravine detection, combines several filtering methods for skeleton denoising and for selecting perceptually important ridges and ravines, and uses a topological analysis of the skeleton for detection of salient shape regions.

The paper proposes an approach for stable extraction of the skeleton of a polygonal surface and detection of surface features, ridges and ravines, corresponding to skeletal edges. The approach adapts the three-dimensional Voronoi diagram technique for skeleton extraction, explores the singularity theory for ridge and ravine detection, and combines several filtering methods for skeleton denoising and for selecting perceptually salient ridges and ravines. Rather than extract the skeleton as a CW-complex, we approximate it by a two-sided surface. It allows us to use standard mesh editing tools for skeleton denoising and achieve stably extract the ridges and ravines.

Index Terms: polygonal surface, 3D Voronoi diagram, skeleton, ridges and ravines.

Notes:

Requires a surface mesh to begin with. In fact this method depends strongly on the quality of the initial surface mesh. Also, their skeletal surfaces are connected IF the original surface is connected it seems.

Because they throw away the intrinsic graph structure of the MA (what they call the CW-complex) they have to somehow reconstruct it in the end (e.g., to approximate ridges and ravines).

The skeletal points are themselves obtained using Amenta et al.'s method.

We propose a new approach for recognition, description and extraction of ridges and ravines based on singularity theory; the approach may be used for shape coding and animation.

A new concept of ridges, ravines and related structures (skeletons) associated with a surface in three-dimensional space is introduced. The concept is based on the investigation of relationships between the singularities of the distance function from the surface and singularities of caustic of the normals to the surface. It involves both local and global geometric surface properties and leads to the effective procedure for ridges and ravines recognition.

BACK

Page created & maintained by Frederic Leymarie, 2000-2
Comments, suggestions, etc., mail to: leymarie@lems.brown.edu