## Signal Matching Through Scale Space (1987)

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Venue: | International Journal of Computer Vision |

Citations: | 75 - 3 self |

### BibTeX

@ARTICLE{Witkin87signalmatching,

author = {Andrew Witkin and Demetri Terzopoulos and Michael Kass},

title = {Signal Matching Through Scale Space},

journal = {International Journal of Computer Vision},

year = {1987},

volume = {1},

pages = {133--144}

}

### Years of Citing Articles

### OpenURL

### 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 opti-mization, 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

### Citations

326 | A theory of human stereo vision - Marr, Poggio - 1979 |

281 |
The representation and matching of pictorial structures
- Fischler, Elschlager
- 1973
(Show Context)
Citation Context ...nvolves the strain energy of a globally smooth elastic body, is more elaborate than the deformation constraints inherent in the spring-loaded subtemplate matching technique of Fischler and Elschlager =-=[9]-=- or the iterative Gaussiansmoothed deformation models proposed by Burr [10]. Our controlled-continuity deformation model provides us with the additional capability to regulate the order of smoothness ... |

239 |
Computational Vision and Regularization Theory
- Poggio, Koch, et al.
- 1985
(Show Context)
Citation Context ...lates an approach to stereo matching that involves the minimization of a cost functional that combines a global smoothness constraint and a squared difference image similarity measure. Poggio et al. (=-=[12]-=- table 1) consider a similar cost functional for stereo in the context of the regularization approach. Neither of these sources presents an implementation, but mention is made of low-pass or band-pass... |

237 |
Regularization of inverse visual problems involving discontinuities
- Terzopoulos
- 1986
(Show Context)
Citation Context ...tant problem of stereo matching. In the past, dense disparity maps have been computed through a two-step process of local matching followed by smooth [4], multiresolution [5], or piecewise continuous =-=[6, 7]-=- surface reconstruction from the sparse disparities. The approach in the present report unifies matching and piecewise smooth reconstruction into a single iterative optimization process. Broit's work ... |

186 | Towards automatic visual obstacle avoidance - Moravec - 1977 |

140 |
Scale Space Filtering
- Witkin
- 1983
(Show Context)
Citation Context ...al minimization problem is then obtained by continuously tracking the minimum as tr tends to zero. This is analogous to a coarse-to-fine tracking of extrema through scale space in the sense of Witkin =-=[1]-=-. The entire procedure consists of solving the first-order dynamic system 6, --- -cx exp(-cat Wo~ (V, ~r)[), V= - ~7~ยข (V, o') where the dot denotes a time derivative, a is the scale parameter and Cl ... |

83 |
Optimal registration of deformed images
- Broit
- 1981
(Show Context)
Citation Context ... surface reconstruction from the sparse disparities. The approach in the present report unifies matching and piecewise smooth reconstruction into a single iterative optimization process. Broit's work =-=[8]-=- in registering a deformed image to a model image resembles ours in that matching is explicitly formulated as a minimization problem involving a cost functional that combines both a deformation constr... |

73 |
Multilevel computational processes for visual surface reconstruction
- Terzopoulos
- 1983
(Show Context)
Citation Context ...al vision. Consider the important problem of stereo matching. In the past, dense disparity maps have been computed through a two-step process of local matching followed by smooth [4], multiresolution =-=[5]-=-, or piecewise continuous [6, 7] surface reconstruction from the sparse disparities. The approach in the present report unifies matching and piecewise smooth reconstruction into a single iterative opt... |

62 |
A Computational Theory of Visual Surface Interpolation
- Grimson
- 1982
(Show Context)
Citation Context ...opular in computational vision. Consider the important problem of stereo matching. In the past, dense disparity maps have been computed through a two-step process of local matching followed by smooth =-=[4]-=-, multiresolution [5], or piecewise continuous [6, 7] surface reconstruction from the sparse disparities. The approach in the present report unifies matching and piecewise smooth reconstruction into a... |

55 |
Hierarchical warp stereo
- Quam
- 1984
(Show Context)
Citation Context ...ing the signals according to the current approximation of the deformation. This concern has also been addressed by the matching algorithms described by Mori et al. [15] Burr [10], Broit [8], and Quam =-=[20]-=-. 2 Framework Consider a vector of n similar signals f*(x) = [f~a(x) .... ,j~(x)] defined in d dimensional space x --- [xl .... , Xd] e ~ d and a deformation mapping V: ~d _~ ~/nd, such that V(x) = [v... |

48 |
Probabilistic solution of inverse problems
- Marroquin
- 1985
(Show Context)
Citation Context ...d-pass filtering of images as a means of simplifying the minimization. Stochastic optimization is the usually expensive alternative. Monte Carlo algorithms for signal matching are given by Marroquin (=-=[13]-=- chapter 6) and a simulated annealing algorithm for stereo matching is offered by Barnard [14]; both employ cost functionals very similar to Horn and Poggio. Coarse-to-fine matching schemes have previ... |

40 |
A dynamic Model for Image Registration
- Burr
- 1981
(Show Context)
Citation Context ...rate than the deformation constraints inherent in the spring-loaded subtemplate matching technique of Fischler and Elschlager [9] or the iterative Gaussiansmoothed deformation models proposed by Burr =-=[10]-=-. Our controlled-continuity deformation model provides us with the additional capability to regulate the order of smoothness and to preserve discontinuities in the deformation. Horn ([11] section 13.9... |

26 | Computer matching of areas in stereo images - Hannah - 1974 |

23 | Modelling the Environment of an Exploring Vehicle by means of Stereo Vision - Gennery - 1980 |

21 | A stochastic approach to stereo vision
- Barnard
- 1986
(Show Context)
Citation Context ... is the usually expensive alternative. Monte Carlo algorithms for signal matching are given by Marroquin ([13] chapter 6) and a simulated annealing algorithm for stereo matching is offered by Barnard =-=[14]-=-; both employ cost functionals very similar to Horn and Poggio. Coarse-to-fine matching schemes have previously been treated as a multistage process in which a matching operation is performed at each ... |

19 |
The role of constraints and discontinuities in visible-surface reconstruction
- Terzopoulos
- 1983
(Show Context)
Citation Context ...tant problem of stereo matching. In the past, dense disparity maps have been computed through a two-step process of local matching followed by smooth [4], multiresolution [5], or piecewise continuous =-=[6, 7]-=- surface reconstruction from the sparse disparities. The approach in the present report unifies matching and piecewise smooth reconstruction into a single iterative optimization process. Broit's work ... |

19 |
An Iterative Prediction and Correction Method for Automatic Stereocomparison
- Mori, Kidode, et al.
- 1973
(Show Context)
Citation Context ...he similarity measurements by deforming the signals according to the current approximation of the deformation. This concern has also been addressed by the matching algorithms described by Mori et al. =-=[15]-=- Burr [10], Broit [8], and Quam [20]. 2 Framework Consider a vector of n similar signals f*(x) = [f~a(x) .... ,j~(x)] defined in d dimensional space x --- [xl .... , Xd] e ~ d and a deformation mappin... |