A Modification of Diffusion Distance for Clustering and Image Segmentation
Measuring the distances is an important problem in many image-segmentation algorithms. The distance should tell whether two image points belong to a single or, respectively, to two different image segments. The simplest approach is to use the Euclidean distance. However, measuring the distances along the image manifold seems to take better into account the facts that are important for segmentation. Geodesic distance, i.e. the shortest path in the corresponding graph or k shortest paths can be regarded as the simplest way how the distances along the manifold can be measured. At a first glance, one would say that the resistance and diffusion distance should provide the properties that are even better since all the paths along the manifold are taken into account. Surprisingly, it is not often true. We show that the high number of paths is not beneficial for measuring the distances in image segmentation. On the basis of analysing the problems of diffusion distance, we introduce its modification, in which, in essence, the number of paths is restricted to a certain chosen number. We demonstrate the positive properties of this new metrics.
KeywordsImage segmentation diffusion distance geodesic distance
Unable to display preview. Download preview PDF.
- 4.Fiorio, C., Mercat, C., Rieux, F.: Adaptive Discrete Laplace Operator. In: International Symposium on Visual Computing, pp. 567–577 (2011)Google Scholar
- 7.Huang, H., Yoo, S., Qin, H., Yu, D.: A Robust Clustering Algorithm Based on Aggregated Heat Kernel Mapping. In: International Conference on Data Mining, pp. 270–279 (2011)Google Scholar
- 10.Lipman, Y., Rustamov, R.M., Funkhouser, T.A.: Biharmonic Distance. ACM Transactions on Graphics 29, 1–11 (2010)Google Scholar
- 11.Martin, D., Fowlkes, C., Tal, D., Malik, J.: A Database of Human Segmented Natural Images and its Application to Evaluating Segmentation Algorithms and Measuring Ecological Statistics. In: International Conference of Computer Vision, pp. 416–423 (2001)Google Scholar
- 12.Nadler, B., Lafon, S., Coifman, R.R., Kevrekidis, I.G.: Diffusion Maps, Spectral Clustering and Eigenfunctions of Fokker-Planck Operators. Advances in Neural Information Processing Systems 18, 955–962 (2005)Google Scholar
- 16.Yen, L., Fouss, F., Decaestecker, C., Francq, P., Saerens, M.: Graph Nodes Clustering Based on the Commute-Time Kernel. In: Pacific-Asia Conference on Knowledge Discovery and Data Mining, pp. 1037–1045 (2007)Google Scholar