The Isophotic Metric and Its Application to Feature Sensitive Morphology on Surfaces
We introduce the isophotic metric, a new metric on surfaces, in which the length of a surface curve is not just dependent on the curve itself, but also on the variation of the surface normals along it. A weak variation of the normals brings the isophotic length of a curve close to its Euclidean length, whereas a strong normal variation increases the isophotic length. We actually have a whole family of metrics, with a parameter that controls the amount by which the normals influence the metric. We are interested here in surfaces with features such as smoothed edges, which are characterized by a significant deviation of the two principal curvatures. The isophotic metric is sensitive to those features: paths along features are close to geodesics in the isophotic metric, paths across features have high isophotic length. This shape effect makes the isophotic metric useful for a number of applications. We address feature sensitive image processing with mathematical morphology on surfaces, feature sensitive geometric design on surfaces, and feature sensitive local neighborhood definition and region growing as an aid in the segmentation process for reverse engineering of geometric objects.
KeywordsPrincipal Curvature Parameter Domain Mathematical Morphology Implicit Surface Triangle Mesh
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- 1.Bertalmio, M., Mémoli, F., Cheng, L.T., Sapiro, G., Osher, S.: Variational problems and partial differential equations on implicit surfaces, CAM Report 02-17, UCLA (April 2002)Google Scholar
- 2.Beucher, S., Blosseville, J.M., Lenoir, F.: Traffic spatial measurements using video image processing. In: Proc. SPIE, Intelligent Robots and Computer Vision, vol. 848, pp. 648–655 (1987)Google Scholar
- 4.Cheng, L.T., Burchard, P., Merriman, B., Osher, S.: Motion of curves constrained on surfaces using a level set approach. UCLA CAM Report 00-36 (September 2000)Google Scholar
- 7.Haider, C., Hönigmann, D.: Efficient computation of distance functions on manifolds by parallelized fast sweeping, Advanced Computer Vision, Technical Report 116, Vienna (2003)Google Scholar
- 8.Hanbury, A.: Mathematical morphology applied to circular data. In: Hawkes, P.W. (ed.) Advances in Imaging and Electron Physics, vol. 128, pp. 123–205. Academic Press, London (2003)Google Scholar
- 13.Loménie, N., Gallo, L., Cambou, N., Stamon, G.: Morphological operations on Delaunay triangulations. In: Proc. Intl. Conf. on Pattern Recognition, Barcelona, vol. 3, pp. 3556–3560 (2000)Google Scholar
- 17.Roerdink, J.B.T.M.: Mathematical morphology on the sphere. In: Proc. SPIE Conf. Visual Communications and Image Processing 1990, Lausanne, pp. 263–271 (1990)Google Scholar
- 18.Reimers, M.: Computing geodesic distance functions on triangle meshes, Technical Report, Dept. of Informatics, Univ. of Oslo (2003) in preparationGoogle Scholar
- 19.Roerdink, J.B.T.M.: Manifold Shape: from Differential Geometry to Mathematical Morphology. In: Y.L. O et al. (eds.) Shape in Picture, pp. 209–223. Springer, Berlin (1994)Google Scholar
- 20.Rössl, C., Kobbelt, L., Seidel, H.-P.: Extraction of feature lines on triangulated surfaces using morphological operators. In: Proc. Smart Graphics 2000, AAAI Spring Symposium. Stanford University, Stanford (2000)Google Scholar