Abstract
This article presents a scale-space theory for spatio-temporal data. Starting from the main assumptions that (i) the scale-space should be generated by convolution with a semi-group of filter kernels and that (ii) local extrema must not be enhanced when the scale parameter increases, a complete taxonomy is given of the linear scale-space concepts that satisfy these conditions on spatial, temporal and spatio-temporal domains, including the cases with continuous as well as discrete data.
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J. J. Barron, D. J. Fleet, and S. S. Beachemin. Performance of optical flow techniques. IJCV, 12(1), 1994.
P. J. Burt. Fast filter transforms for image processing. CVGIP, 16:20–51, 1981.
J. L. Crowley. A Representation for Visual Information. PhD thesis., Carnegie-Mellon University, Robotics Institute, Pittsburgh, Pennsylvania, 1981.
G. C. DeAngelis, I. Ohzawa, and R. D. Freeman. Receptive field dynamics in the central visual pathways. Trends in Neuroscience, 18(10):451–457, 1995.
D. J. Fleet and K. Langley. Recursive filters for optical flow. IEEE-PAMI, 17(1):61–67, 1995.
L. M. J. Florack, B. M. ter Haar Romeny, J. J. Koenderink, and M. A. Viergever. Families of tuned scale-space kernels. In 2nd ECCV, pages 19–23, 1992.
L. M. J. Florack. The Syntactical Structure of Scalar Images. PhD thesis., Dept. Med. Phys. Physics, Univ. Utrecht, NL-3508 Utrecht, Netherlands, 1993.
E. Hille and R. S. Phillips. Functional Analysis and Semi-Groups, volume XXXI. American Mathematical Society Colloquium Publications, 1957.
J. J. Koenderink and A. J. van Doorn. Generic neighborhood operators. IEEE-PAMI, 14(6):597–605, 1992.
J. J. Koenderink. The structure of images. Biol. Cyb., 50:363–370, 1984.
J. J. Koenderink. Scale-time. Biol. Cyb., 58:159–162, 1988.
T. Lindeberg and D. Fagerström. Scale-space with causal time direction. In 4th ECCV, volume 1064, pages 229–240, Cambridge, UK, 1996.
T. Lindeberg. Scale-space for discrete signals. IEEE-PAMI, 12(3):234–254, 1990.
T. Lindeberg. On the axiomatic foundations of linear scale-space: Combining semigroup structure with causality vs. scale invariance. Technical Report ISRN KTH/NA/P-94/20-SE, KTH, 1994. Extended version to appear in J. Sporring et al. (eds.) Gaussian Scale-Space Theory, Kluwer, May 1996.
T. Lindeberg. Scale-Space Theory in Computer Vision. Kluwer, Netherlands, 1994.
T. Lindeberg. Linear spatio-temporal scale-space. Technical report, KTH, 1996.
A. P. Witkin. Scale-space filtering. In 8th IJCAI, pages 1019–1022, 1983.
R. A. Young. The Gaussian derivative model for spatial vision: I. Retinal mechanisms. Spatial Vision, 2:273–293, 1987.
A. L. Yuille and T. A. Poggio. Scaling theorems for zero-crossings. IEEE-PAMI, 8:15–25, 1986.
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© 1997 Springer-Verlag Berlin Heidelberg
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Lindeberg, T. (1997). Linear spatio-temporal scale-space. In: ter Haar Romeny, B., Florack, L., Koenderink, J., Viergever, M. (eds) Scale-Space Theory in Computer Vision. Scale-Space 1997. Lecture Notes in Computer Science, vol 1252. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63167-4_44
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DOI: https://doi.org/10.1007/3-540-63167-4_44
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