doi:10.1016/j.imavis.2004.06.004 
Copyright © 2004 Elsevier B.V. All rights reserved.
Computing and analysing convex deficiencies to characterise 3D complex objects
aIstituto di Cibernetica ‘E. Caianiello’, CNR, Pozzuoli (Napoli), Italy
bCentre for Image Analysis, Uppsala, Sweden
Received 16 January 2004;
revised 30 April 2004;
accepted 29 June 2004.
Available online 23 November 2004.
References and further reading may be available for this article. To view references and further reading you must
purchase this article.
Abstract
Entities such as object components, cavities, tunnels and concavities in 3D digital images can be useful in the framework of object analysis. For each object component, we first identify its convex deficiencies, by subtracting the object component from a covering polyhedron approximating the convex hull. Watershed segmentation is then used to decompose complex convex deficiencies into simpler parts, corresponding to individual cavities, concavities and tunnels of the object component. These entities are finally described by means of a representation system accounting for the shape features characterising them.
Keywords: Volume image; Distance transform; Watershed; Topological erosion
Fig. 1. An object with a concavity, a tunnel and a cavity (left), and a cross-section of the object (right).
Fig. 2. Two cross-sections of an object with a cavity shaped as a torus.
Fig. 3. Convex deficiencies relative to the object in Fig. 1.
Fig. 4. An object with a concatenation of tunnels and concavities close to each other that would originate a single, complex, convex deficiency (top); cross-section (bottom).
Fig. 5. A cube with a tunnel, rotated 30° in the z-direction with respect to the upright position (left), and the convex deficiencies before cleaning (right).
Fig. 6. Top: from left to right, an object, its covering polyhedron, and the convex deficiencies before cleaning. Bottom: the covering polyhedron, left, and the convex deficiencies, right, after cleaning.
Fig. 7. An object shown in two different views (top); a cross-section and the convex deficiencies (bottom).
Fig. 8. Decomposition of the concatenations of tunnels and concavities shown in Fig. 4 (top) and in Fig. 7 (bottom).
Fig. 9. Cross-section of a Y-shaped tunnel with two diaphragms (left), decomposition of the corresponding CD before merging (middle), and after merging (right).
Fig. 10. Cross-section of an object with a tunnel having a significant protrusion, (left), decomposition of the corresponding CD before merging (middle), and after merging (right).
Fig. 11. Identifiers (180° rotated) for the entities shown in Fig. 3.
Fig. 12. An object with two tunnels (top left) and its cross-section (top right). The entities (bottom left) and the tunnel-identifiers (bottom right).
Fig. 13. Cross-section of an object with a Y-shaped tunnel and two cavities (top), and the corresponding entities (bottom).
Fig. 14. Darker voxels are end points and branch points.
Table 1.
Features for the entities in Fig. 13
Table 2.
Features for the tunnels in Fig. 14
Abstract
Purchase PDF (263 K)
E-mail Article
Add to my Quick Links
Cited By in Scopus (2)
Purchase PDF (541 K)
