Families of tuned scale-space kernels
We propose a formalism for deriving parametrised ensembles of local neighbourhood operators on the basis of a complete family of scale-space kernels, which are apt for the measurement of a specific physical observable. The parameters are introduced in order to associate a continuum of a priori equivalent kernels with each scale-space kernel, each of which is tuned to a particular parameter value.
Ensemble averages, or other functional operations in parameter space, may provide robust information about the physical observable of interest. The approach gives a possible handle on incorporating multi-valuedness (transparancy) and visual coherence into a single model.
We consider the case of velocity tuning to illustrate the method. The emphasis, however, is on the formalism, which is more generally applicable.
KeywordsStimulus Velocity Complete Family Functional Operation Point Stimulus Stereo Disparity
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- 1.A. Witkin, “Scale space filtering,” in Proc. International Joint Conference on Artificial Intelligence, (Karlsruhe, W. Germany), pp. 1019–1023, 1983.Google Scholar
- 4.B. M. ter Haar Romeny, L. M. J. Florack, J. J. Koenderink, and M. A. Viergever, “Scalespace: Its natural operators and differential invariants,” in International Conf. on Information Processing in Medical Imaging, vol. 511 of Lecture Notes in Computer Science, (Berlin), pp. 239–255, Springer-Verlag, July 1991.Google Scholar
- 5.L. Florack, B. ter Haar Romeny, J. Koenderink, and M. Viergever, “Scale-space.” Submitted to IEEE PAMI, November 1991.Google Scholar
- 7.P. Bijl, Aspects of Visual Contrast Detection. PhD thesis, University of Utrecht, University of Utrecht, Dept. of Med. Phys., Princetonplein 5, Utrecht, the Netherlands, May 1991.Google Scholar
- 10.J. J. Koenderink and A. J. van Doom, “Receptive field families,” Biol. Cybern., vol. 63, pp. 291–298, 1990.Google Scholar
- 11.P. Werkhoven, Visual Perception of Successive Order. PhD thesis, University of Utrecht, University of Utrecht, Dept. of Med. Phys., Princetonplein 5, Utrecht, the Netherlands, May 1990.Google Scholar
- 12.D. J. Heeger, “Model for the extraction of image flow,” Journal of the Optical Society of America-A, vol. 4, no. 8, pp. 1455–1471, 1987.Google Scholar
- 13.D. Heeger, “Optical flow using spatiotemporal filters,” International Journal of Computer Vision, vol. 1, pp. 279–302, 1988.Google Scholar
- 14.E. H. Adelson and J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” Journal of the Optical Society of America-A, vol. 2, no. 2, pp. 284–299, 1985.Google Scholar
- 16.P. J. Olver, Applications of Lie Groups to Differential Equations, vol. 107 of Graduate Texts in Mathematics. Springer-Verlag, 1986.Google Scholar
- 17.J. J. Koenderink, “Scale-time,” Biol. Cybern., vol. 58, pp. 159–162, 1988.Google Scholar
- 18.A. J. Noest and J. J. Koenderink, “Visual coherence despite transparency or partial occlusion,” Perception, vol. 19, p. 384, 1990. Abstract of poster presented at the ECVP 1990, Paris.Google Scholar