## Matching: Invariant to Translations, Rotations and Scale Changes (1992)

Venue: | Pattern Recognition |

Citations: | 39 - 5 self |

### BibTeX

@ARTICLE{Li92matching:invariant,

author = {S. Z. Li},

title = {Matching: Invariant to Translations, Rotations and Scale Changes},

journal = {Pattern Recognition},

year = {1992},

volume = {25},

pages = {583--594}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present an approach to invariant matching. In this approach, an object or a pattern is invariantly represented by an object-centered description called an attributed relational structure (ARS) embedding invariant properties and relations between the primitives of the pattern such as line segments and points. Noise effect is taken into account such that a scene can consist of noisy sub-parts of a model. The matching is then to find the optimal mapping between the ARSs of the scene and the model. A gain functional is formulated to measure the goodness of fit and is to be maximized by using the relaxation labeling method. Experiments are shown to illustrate the matching algorithm and to demonstrate that the approach is truly invariant to arbitrary translations, rotations, and scale changes under noise. Index terms --- Attributed relational structures, invariance, pattern recognition, relaxation labeling, sub-graph matching. Pattern Recognition, 25(6):583--594, June 1992 2 Contents 1...

### Citations

3921 |
Pattern Classification and Scene Analysis
- Duda, Hart
- 1973
(Show Context)
Citation Context ...s section, we discuss such the problem of optimal matching between two ARGs based on their relations. 3.1 Optimal Morphic Mapping The simplest example of such mapping is feature vector classification =-=[8]-=-. It is based on the similarity between the unary attributes of two ARSs while each ARS is made up of a set of nodes and associated feature vectors. A more sophisticated example is relaxation labeling... |

3719 |
Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images
- Geman, Geman
- 1984
(Show Context)
Citation Context ...mum n-ary constraints g for n = 2; :::; N (36) The condition i 1 6= i 2 ; :::; 6= i n in the above means that a match does not support itself. Our definition of ! n is an extension to that defined in =-=[12]-=-. The n th order gain is defined by E n (f jsn ; ! n ) = \Gamma X (i 1 ;I 1 ;i 2 ;I 2 ;:::;i n ;I n )2!nsn (i 1 ; I 1 ; i 2 ; I 2 ; :::; i n ; I n )f(i 1 ; I 1 )f(i 2 ; I 2 ):::f (i n ; I n ) (37) (cf... |

828 |
Computer Vision
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- 1982
(Show Context)
Citation Context ...sed as a constraint for matching. For example, by using such inequality, Liu et al. [17] allow \Sigma20% scale changes. ARS or the like has been used in computer vision to represent models and scenes =-=[1, 2, 7, 20, 23]-=-. Many problems in computer vision, such as image sequence analysis, stereo correspondence, feature labeling, object recognition, scene understanding, etc. can be seen as examples of ARS matching. Ine... |

737 | Visual Reconstruction
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- 1987
(Show Context)
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467 |
The interpretation of visual motion
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- 1979
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Citation Context ... unary term is E 1 (f js1 ; ! 1 ) = X (i;I)2!1s1 (i; I)f(i; I) (38) The unary term measures the gain incurred by mapping unary relations. It corresponds to the cost energy in a minimal mapping theory =-=[24]-=-, and is similar to the criterion for the simplest perceptron [21]. The binary term is E 2 (f js2 ; ! 2 ) = X (i;I;j;J)2!2s2 (i; I; j; J)f(i; I)f(j; J) (39) It measures the gain incurred by mapping bi... |

349 |
Scene labeling by relaxation operations
- Rosenfeld, Hummel, et al.
- 1976
(Show Context)
Citation Context ... It is based on the similarity between the unary attributes of two ARSs while each ARS is made up of a set of nodes and associated feature vectors. A more sophisticated example is relaxation labeling =-=[9, 15, 16, 22]-=-. This is is based on the similarity between the binary relations of two ARSs while each ARS consists of a set of nodes and associated binary relations between them. The formulation in this paper is t... |

286 |
Principles of Neurodynamics
- Rosenblatt
- 1962
(Show Context)
Citation Context ...) The unary term measures the gain incurred by mapping unary relations. It corresponds to the cost energy in a minimal mapping theory [24], and is similar to the criterion for the simplest perceptron =-=[21]-=-. The binary term is E 2 (f js2 ; ! 2 ) = X (i;I;j;J)2!2s2 (i; I; j; J)f(i; I)f(j; J) (39) It measures the gain incurred by mapping binary relations. It is the criterion known as the average local con... |

281 |
The representation and matching of pictorial structures
- Fischler, Elschlager
- 1973
(Show Context)
Citation Context ...1 3.3 Computation of Optimal Mapping Finding solution of Equation 18 is a combinatorial optimization problem. To perform this, we could use methods such as maximal cliques [1, 6], dynamic programming =-=[11]-=-, constraint search [10, 14], etc. However, a disadvantage common to these methods is that thresholds may have to be used to determine whether a match is acceptable otherwise the search could be exhau... |

252 |
On the Foundations of Relaxation Labeling Processes
- Hummel, Zucker
- 1983
(Show Context)
Citation Context ... It is based on the similarity between the unary attributes of two ARSs while each ARS is made up of a set of nodes and associated feature vectors. A more sophisticated example is relaxation labeling =-=[9, 15, 16, 22]-=-. This is is based on the similarity between the binary relations of two ARSs while each ARS consists of a set of nodes and associated binary relations between them. The formulation in this paper is t... |

229 |
The representation, recognition, and locating of 3-d objects
- Faugeras, Hebert
- 1986
(Show Context)
Citation Context ...feature labeling, object recognition, scene understanding, etc. can be seen as examples of ARS matching. Inexact matching between images and models is commonly performed by explicit search approaches =-=[1, 6, 7, 10, 13, 14, 20, 23]-=-, or by using implicit search methods such as relaxation labeling [4]. A goodness of fit is usually formulated to measure the optimality of matching. This paper is organized as follows. Section 2 disc... |

175 |
Structural descriptions and inexact matching
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- 1981
(Show Context)
Citation Context ...sed as a constraint for matching. For example, by using such inequality, Liu et al. [17] allow \Sigma20% scale changes. ARS or the like has been used in computer vision to represent models and scenes =-=[1, 2, 7, 20, 23]-=-. Many problems in computer vision, such as image sequence analysis, stereo correspondence, feature labeling, object recognition, scene understanding, etc. can be seen as examples of ARS matching. Ine... |

163 |
Localizing overlapping parts by searching the interpretation tree
- Grimson, Lozano-Pérez
- 1987
(Show Context)
Citation Context ...feature labeling, object recognition, scene understanding, etc. can be seen as examples of ARS matching. Inexact matching between images and models is commonly performed by explicit search approaches =-=[1, 6, 7, 10, 13, 14, 20, 23]-=-, or by using implicit search methods such as relaxation labeling [4]. A goodness of fit is usually formulated to measure the optimality of matching. This paper is organized as follows. Section 2 disc... |

49 |
Shape matching using relaxation techniques
- Davis
- 1979
(Show Context)
Citation Context ...s intrinsic and is meant to be invariant to viewpoints. Invariant properties and relations have been suggested and utilized for matching, such as curvature properties [3], relative angle and distance =-=[7]-=-. Since the distance itself is dependent on scale, some inequality of the ratio of distances or line length is used as a constraint for matching. For example, by using such inequality, Liu et al. [17]... |

42 |
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- Ambler, Barrow, et al.
- 1982
(Show Context)
Citation Context ...sed as a constraint for matching. For example, by using such inequality, Liu et al. [17] allow \Sigma20% scale changes. ARS or the like has been used in computer vision to represent models and scenes =-=[1, 2, 7, 20, 23]-=-. Many problems in computer vision, such as image sequence analysis, stereo correspondence, feature labeling, object recognition, scene understanding, etc. can be seen as examples of ARS matching. Ine... |

40 |
Improving consistency and reducing ambiguity in stochastic labeling: an optimization approach
- Faugeras, Berthod
- 1981
(Show Context)
Citation Context ... It is based on the similarity between the unary attributes of two ARSs while each ARS is made up of a set of nodes and associated feature vectors. A more sophisticated example is relaxation labeling =-=[9, 15, 16, 22]-=-. This is is based on the similarity between the binary relations of two ARSs while each ARS consists of a set of nodes and associated binary relations between them. The formulation in this paper is t... |

28 |
Partial shape classification using contour matching in distance transformation
- Liu, Srinath
- 1990
(Show Context)
Citation Context ... [7]. Since the distance itself is dependent on scale, some inequality of the ratio of distances or line length is used as a constraint for matching. For example, by using such inequality, Liu et al. =-=[17]-=- allow \Sigma20% scale changes. ARS or the like has been used in computer vision to represent models and scenes [1, 2, 7, 20, 23]. Many problems in computer vision, such as image sequence analysis, st... |

24 | Relaxation labeling algorithms – a review - Kittler, Illingworth - 1985 |

17 |
Image sequence analysis using relational structures
- Radig
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11 |
Intrinsic and extrinsic surface characteristics
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- 1985
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Citation Context ...ecognition. This representation is intrinsic and is meant to be invariant to viewpoints. Invariant properties and relations have been suggested and utilized for matching, such as curvature properties =-=[3]-=-, relative angle and distance [7]. Since the distance itself is dependent on scale, some inequality of the ratio of distances or line length is used as a constraint for matching. For example, by using... |

11 |
Robust feature matching through maximal cliques
- Bolles
- 1979
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Citation Context ...feature labeling, object recognition, scene understanding, etc. can be seen as examples of ARS matching. Inexact matching between images and models is commonly performed by explicit search approaches =-=[1, 6, 7, 10, 13, 14, 20, 23]-=-, or by using implicit search methods such as relaxation labeling [4]. A goodness of fit is usually formulated to measure the optimality of matching. This paper is organized as follows. Section 2 disc... |

5 |
A feasible direction operator for relaxation methods
- Mohammed, Hummel, et al.
- 1983
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Citation Context ...by an appropriate amount in the appropriate direction. Here the computation of the length and the direction of the updating vector \Psi is based on the gradient projection (GP) operation described in =-=[15, 19]-=-. More specifically, f is updated by a vector of ju f (t+1) / f (t) + ju (43) where u is the direction vector computed by the GP operation and j is a factor which ensures that the updated vector f (t+... |

4 |
Faugeras. "Shape matching of two-dimensional objects
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- 1984
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Citation Context ...matching. Inexact matching between images and models is commonly performed by explicit search approaches [1, 6, 7, 10, 13, 14, 20, 23], or by using implicit search methods such as relaxation labeling =-=[4]-=-. A goodness of fit is usually formulated to measure the optimality of matching. This paper is organized as follows. Section 2 discusses proper selection of invariant properties and relations and intr... |

4 |
Graph optimal monomorphism algorithms
- Ghahraman, Wong, et al.
- 1980
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