Abstract
Given a collection of similar signals that have been deformed with respect to each other, the general signal-matching problem is to recover the deformation. We formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term. The minimization reduces to a dynamic system governed by a set of coupled, first-order differential equations. The dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale. Among the major themes in recent work on visual signal matching have been the notions of matching as constrained optimization, of variational surface reconstruction, and of coarse-to-fine matching. Our solution captures these in a precise, succinct, and unified form. Results are presented for one-dimensional signals, a motion sequence, and a stereo pair.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Witkin, “Scale Space Filtering,” in PROC. INT. JOINT CONF. ARTIF. INTELL., Karlsruhe, FRG, 1983, pp. 1019–1021.
L.R. Rabiner and R.W. Schafer, DIGITAL PROCESSING OF SPEECH SIGNALS. Prentice-Hall: Englewood Cliffs, NJ, 1978.
D. Sankoff and J.B. Kruskal (eds.), TIME WARPS, STRING EDITS AND MACROMOLECULES: THE THEORY AND PRACTICE OF SEQUENCE COMPARISON. Addison-Wesley: Reading, MA, 1983.
W.E.L. Grimson, “An implementation of a computational theory of visual surface interpolation,” COMPUT. VISION, GRAPHICS, IMAGE PROCESSING vol. 22, pp. 39–69, 1983.
D. Terzopoulos, “Multilevel computational processes for visual surface reconstruction,” COMPUT. VISION, GRAPHICS, IMAGE PROCESSING vol. 24 pp. 52–96, 1983.
D. Terzopoulos, “The role of constraints and discontinuities in visible-surface reconstruction,” in PROC. 8TH INT. JOINT CONF. ARTIF. INTELL., Karlsruhe, FRG, 1983, pp. 1073–1077.
D. Terzopoulos, “Regularization of inverse visual problems involving discontinuities,” IEEE TRANS. PAMI vol. PAMI-8, pp. 413–424, 1986.
C. Broit, “Optimal registration of deformed images,” PhD thesis, Computer and Information Science Department, University of Pennsylvania, Philadelphia, PA, 1981.
M.A. Fischler, and R.A. Elschlager, “The representation and matching of pictorial structures,” IEEE TRANS. COMPUT. vol. C-22, pp. 67–92, 1973.
D.J. Burr, “A dynamic model for image registration,” COMPUT. GRAPHICS IMAGE PROCESSING vol. 15, pp. 102–112, 1981.
B.K.P. Horn, ROBOT VISION. M.I.T. Press: Cambridge, MA, 1986.
T. Poggio, V. Torre, and C. Koch, “Computational vision and regularization theory,” NATURE vol. 317, pp. 314–319, 1985.
J.L. Marroquin, “Probabilistic solution of inverse problems,” M.I.T. Artif. Intell. Lab., Cambridge, MA, A.I.-TR 860, 1985.
S.T. Barnard, “A stochastic approach to stereo vision,” in PROC. NATL. CONF. ARTIF. INTELL. AAAI-86, Philadelphia, PA, 1976, pp. 676–680.
K. Mori, M. Kidodi, and H. Asada, “An iterative prediction and correction method for automatic stereo comparison,” COMPUT. GRAPHICS IMAGE PROCESSING vol. 2, pp. 393–401, 1973.
M.J. Hannah, “Computer matching of areas in stereo images,” Stanford Artif. Intell. Lab., A.I. Memo. AIM-239, July 1974.
H.P. Moravec, “Towards automatic visual obstacle avoidance,” in PROC. FIFTH INT. JOINT CONF. ARTIF. INTELL. Cambridge, MA. 1977, p. 584.
D. Marr and T. Poggio, “A theory of human stereo vision,” PROC. R. SOC. LOND. [B] vol. 204, pp. 301–328, 1979.
D.B. Gennery, “Modeling the environment of an exploring vehicle by means of stereo vision,” PhD thesis, Stanford Artif. Intell. Lab., A.I. Memo. 339, 1980.
20.L.H. Quam, “Hierarchical warp stereo,” in PROC. IMAGE UNDERSTANDING WORKSHOP, New Orleans, LA, October 1984, pp. 149–155.
N.S. Bakhvalov, NUMERICAL METHODS. Mir: Moscow, 1977.
G. Dahlquist and A. Björck, NUMERICAL METHODS, N. Anderson (trans.). Prentice-Hall: Englewood Cliffs, NJ, 1974.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Witkin, A., Terzopoulos, D. & Kass, M. Signal matching through scale space. Int J Comput Vision 1, 133–144 (1987). https://doi.org/10.1007/BF00123162
Issue Date:
DOI: https://doi.org/10.1007/BF00123162