Signal matching through scale space

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.

[1]  A. Booth.  Numerical Methods , 1957, Nature.

[2]  Masatsugu Kidode,et al.  An iterative prediction and correction method for automatic stereocomparison , 1973, Comput. Graph. Image Process..

[3]  Martin A. Fischler,et al.  The Representation and Matching of Pictorial Structures , 1973, IEEE Transactions on Computers.

[4]  Marsha Jo Hannah,et al.  Computer matching of areas in stereo images. , 1974 .

[5]  Åke Björck,et al.  Numerical Methods , 2021, Markov Renewal and Piecewise Deterministic Processes.

[6]  Hans P. Moravec.  Towards Automatic Visual Obstacle Avoidance , 1977, IJCAI.

[7]  Tomaso Poggio,et al.  A Theory of Human Stereo Vision , 1977 .

[8]  Ronald W. Schafer,et al.  Digital Processing of Speech Signals , 1978 .

[9]  T. Poggio,et al.  A computational theory of human stereo vision , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[10]  Donald Bernard Gennery,et al.  Modelling the environment of an exploring vehicle by means of stereo vision , 1980 .

[11]  D. Burr.  A dynamic model for image registration , 1981 .

[12]  C. Broit.  Optimal registration of deformed images , 1981 .

[13]  David Sankoff,et al.  Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison , 1983 .

[14]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[15]  Demetri Terzopoulos,et al.  Multilevel computational processes for visual surface reconstruction , 1983, Comput. Vis. Graph. Image Process..

[16]  Demetri Terzopoulos,et al.  The Role of Constraints and Discontinuities in Visible-Surface Reconstruction , 1983, IJCAI.

[17]  W. Eric L. Grimson,et al.  An implementation of a computational theory of visual surface interpolation , 1983, Comput. Vis. Graph. Image Process..

[18]  Tomaso Poggio,et al.  Computational vision and regularization theory , 1985, Nature.

[19]  José L. Marroquín,et al.  Probabilistic solution of inverse problems , 1985 .

[20]  Demetri Terzopoulos,et al.  Regularization of Inverse Visual Problems Involving Discontinuities , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  Stephen T. Barnard,et al.  A Stochastic Approach to Stereo Vision , 1986, AAAI.

[22]  Berthold K. P. Horn.  Robot vision , 1986, MIT electrical engineering and computer science series.

[23]  L. Quam.  Hierarchical warp stereo , 1987 .