doi:10.1016/S0167-8655(01)00143-X
Copyright © 2002 Elsevier Science B.V. All rights reserved.
A new shape descriptor for surfaces in 3D images
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Gabriella Sanniti di Bajaa and Stina Svensson
, 
, b
a Istituto di Cibernetica, National Research Council of Italy (CNR), Pozzuoli (Naples), Italy
b Centre for Image Analysis, Swedish University of Agricultural Sciences, Lägerhyddvägen 17, 75237 Uppsala, Sweden
Available online 17 October 2001.
Abstract
We introduce a linear shape descriptor for (open) surfaces in 3D images. To extract the shape descriptor, the border of the surface is first identified. Then, the distance transform of the surface is computed, where each voxel in the surface is labelled with the minimum distance to its closest border voxel. On the distance transform, the centres of the maximal geodesic discs (CMGDs) are detected. These voxels are suitably linked to each other by growing paths in the direction of the steepest gradient, to finally obtain the linear shape descriptor of the surface. The shape descriptor can be extracted from any open surface-like object, i.e., an object with thickness at most two-voxel.
Author Keywords: Surface; Distance transform; Volume image; Shape descriptor; Linear representation
Fig. 1. Surface that cannot be transformed into an “ideal” surface, one-voxel thick everywhere.
Fig. 2. The 27-neighbourhoody of v.
Fig. 3. Voxels with (•) have N26
1 and .
Fig. 4. Voxels with (•) have N261 and .
Fig. 5. Voxels with (•) and with (
) are detected as in L-shaped configuration during the first and the second check, respectively.
Fig. 6. Voxel with (•) is an isolated candidate border voxel.
Fig. 7. Curve voxels, (•), and edge voxels connecting the curve to the surface, ().
Fig. 8. A surface consisting of four planes meeting each other along segments aligned in face, edge, and point directions (top). Geodesic discs centred at the intersection of the above segments, with radius 25, and using DT6, DT26 and 3–4–5 DT, respectively, (bottom) from left to right.
Fig. 9. A surface and its shape descriptor. Close up showing a path consisting of alternating single voxels and pairs of edge connected voxels.
Fig. 10. A two-voxel thick surface and its shape descriptor.
Fig. 11. A surface and its shape descriptor, not topologically equivalent to the surface.
Fig. 12. A cupboard, a chair, and their shape descriptors.
Fig. 13. A table, a table top, and their shape descriptors.
Fig. 14. A surface (a), the intrinsic voxels (saddle voxels placed in junctions are pointed out) (b), the shape descriptors where saddle voxels placed in junctions are considered (c), and disregarded (d).
Fig. 15. Two surfaces and their shape descriptors.
Corresponding author. Tel.: +46-18-4713465; fax: +46-18-553447; email: stina@cb.uu.se
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