Improving Consistency and Reducing Ambiguity in Stochastic Labeling: An Optimization Approach

Faugeras, Olivier; Berthod, Marc-Antoine

doi:10.1109/tpami.1981.4767127

Cited by 160 publications

(54 citation statements)

References 9 publications

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“…In this case, nodes and edges may have vector attributes or labels. There is a vast literature addressing the graph matching problem in pattern recognition, which can be divided generally into work on search methods [14], [17], [18], [19], [20], [21], [22], [23], and work on nonsearch methods, such as probabilistic relaxation [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], spectral and least-squares methods [5], [36], [37], [38], [39], [40], graduated assignment [13], genetic optimization [41] and other principles [15], [16], [42], [43]. For a recent comprehensive review on graph matching for pattern recognition, see [44].…”

Section: Problem Description and Related Problemsmentioning

confidence: 99%

Graphical Models and Point Pattern Matching

Caetano

Caelli

Schuurmans

et al. 2006

IEEE Trans. Pattern Anal. Mach. Intell.

117

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Abstract-This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless case. First, we model point pattern matching as a weighted graph matching problem, where weights correspond to Euclidean distances between nodes. We then formulate graph matching as a problem of finding a maximum probability configuration in a graphical model. By using graph rigidity arguments, we prove that a sparse graphical model yields equivalent results to the fully connected model in the noiseless case. This allows us to obtain an algorithm that runs in polynomial time and is provably optimal for exact matching between noiseless point sets. For inexact matching, we can still apply the same algorithm to find approximately optimal solutions. Experimental results obtained by our approach show improvements in accuracy over current methods, particularly when matching patterns of different sizes.

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Section: Problem Description and Related Problemsmentioning

confidence: 99%

Graphical Models and Point Pattern Matching

Caetano

Caelli

Schuurmans

et al. 2006

IEEE Trans. Pattern Anal. Mach. Intell.

117

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“…Equations (4) and (6) can be combined into to to to to (8) Since (5) and (7) (10) where . Equations (9) and (10) form a consistent system of linear equations that can be easily solved.…”

Section: Fgm Algorithmmentioning

confidence: 99%

“…Once and are computed, we can use to update memberships using (8). The FGM algorithm is presented below.…”

Section: Fgm Algorithmmentioning

confidence: 99%

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Graph matching by relaxation of fuzzy assignments

Medasani

Krishnapuram

Choi

2001

IEEE Trans. Fuzzy Syst.

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Abstract-Graphs are very powerful and widely used representational tools in computer applications. In this paper, we present a relaxation approach to (sub)graph matching based on a fuzzy assignment matrix. The algorithm has a computational complexity of ( 2 2 ) where and are the number of nodes in the two graphs being matched, and can perform both exact and inexact matching. To illustrate the performance of the algorithm, we summarize the results obtained for more than 12 000 pairs of graphs of varying types (weighted graphs, attributed graphs, and noisy graphs). We also compare our results with those obtained using the Graduated Assignment algorithm.

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“…The model described above should be contrasted with those adopted by Berthod and Faugeras [11] and by Zucker et al [12] in their applications of probabilistic relaxation to edge-labelling. According to both of these approaches, the initial label probabilities are assigned on the basis of the responses to a set of directional difference masks; no attempt is made to justify the way in which the raw measurements originate from realistic edge or noise processes.…”

Section: Other Relaxation Approachesmentioning

confidence: 99%

Edge Postprocessing - A Comparative Study

Hancock¹,

Kittler²

1989

Procedings of the Alvey Vision Conference 1989

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The use of contextual information is a vital ingredient in the successful postprocessing of edge information. Edge postprocessing is concerned with locating and labelling consistent edge-structures given confused or noisy response information. The available contextual information exists in the form of measurements provided by the gradient-vectors in pixel neighbourhoods and knowledge of acceptable edge structure which is expressed symbolically. We compare various approaches to the use of this information.Robust edge detection has been a goal of computer vision for almost three decades. Edge-detection algorithms reported in the literature are invariably multistage. Early stages are concerned with the characterisation of the raw edge information; this frequently involves filtering the raw pixel grey scale values to remove the effects of noise or produce a multiscale representation of the image data. Intermediate stages are concerned with the localisation of the edge response. Finally, the edges of physical objects are located by assigning labels to structures which exhibit desirable properties such as strong spatial connectivity. Canny [l] and Spacek [2] adhere to this multistage philosophy. Both authors derive filters for the optimal characterisation of step responses in the presence of noise. However, they adopt rather different methods for the postprocessing of the edge information. Canny performs non-maximum suppression by interpolating gradient vectors from an image neighbourhood and later draws upon connectivity information in the hysteresis linking stage. Spacek, on the other hand, imposes analytic continuity on the gradient magnitudes by fitting of a second-order polynomial surface to achieve non-maximum suppression without drawing directly on connectivity information.The point that we wish to make in this paper is that although the characterisation of raw edge information has been addressed in a number of systematic ways, the postprocessing of this information has been treated less objectively. The postprocessing task is concerned with locating and labelling consistent edge-structures given confused or noisy response information. In practice it invariably draws on various sources of contextual information such as the meaurements provided by the gradient-vectors available in a neighbourhood of the image or the symbolic information conveyed by the connectivity of candidate edge structures. Although a number of schemes reported in the literature, including those described above, are certainly effective solutions to the problem, they do not objectively quantify the available contextual information. It is in this respect that contextual labelling schemes can be profitably applied to the edge-detection problem. Our aim in this paper is to stress the conceptual differences between the way in which edge postprocessing techniques draw on the available contextual information and the objective quantification of this information.A host of contextual labelling strategies are described in the literature. The bulk of t...

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Improving Consistency and Reducing Ambiguity in Stochastic Labeling: An Optimization Approach

Cited by 160 publications

References 9 publications

Graphical Models and Point Pattern Matching

Graphical Models and Point Pattern Matching

Graph matching by relaxation of fuzzy assignments

Edge Postprocessing - A Comparative Study

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