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Fourier inversion and the Hausdorff distance
Statistica Neerlandica, 2002This paper continues research done by F.H. Ruymgaart and the author. For a function f on Rd we consider its Fourier transform Ff and the functions fM(M>0) derived from Ff by the formula fM(x)=(F(εM·Ff))(−x);, where the εM are suitable integrable functions tending to 1 pointwise as M→∞. It was shown earlier that, relative to a metric dH, analogous to
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Hausdorff distance and image processing
Russian Mathematical Surveys, 2004This paper based on the report at the conference is dedicated to the centenary of the birth of Kolmogorov. Sendov gives the brief exposition of the theory of approximations of functions of two variables with the Hausdorff metric. He considers images as bounded functions on the unit square and argues that the Hausdorff distance is more natural to ...
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Measuring Closeness of Graphs—The Hausdorff Distance
Bulletin of the Malaysian Mathematical Sciences Society, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Banič, Iztok, Taranenko, Andrej
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Robust Hausdorff distance for shape matching
SPIE Proceedings, 2002The Hausdorff distance can be used to measure the similarity of two point sets. In matching the two point sets, one of them is translated, rotated and scaled in order to obtain an optimal matching, which is a computationally intensive process. In this paper, a robust line-feature-based approach for model-based recognition is presented, which can ...
Wai-Pak Choi +2 more
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Calculating the Hausdorff distance between curves
Information Processing Letters, 1997CARLOS Cabrelli +2 more
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An incremental Hausdorff distance calculation algorithm
Proceedings of the VLDB Endowment, 2011The Hausdorff distance is commonly used as a similarity measure between two point sets. Using this measure, a set X is considered similar to Y iff every point in X is close to at least one point in Y . Formally, the Hausdorff distance HausDist(
Sarana Nutanong +2 more
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A modified Hausdorff distance for object matching
Proceedings of 12th International Conference on Pattern Recognition, 2002The purpose of object matching is to decide the similarity between two objects. This paper introduces 24 possible distance measures based on the Hausdorff distance between two point sets. These measures can be used to match two sets of edge points extracted from any two objects.
Marie-Pierre Dubuisson +1 more
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Hausdorff Distance and Digital Filters
1987One of the main steps for designing digital filters is the problem for approximation of the amplitude-frequency characteristic of the filter. As a rule it is necessary to approximate a functions with jumps (step function) by means of polynomials or rational functions. There exist many approaches for solving that problem under different restrictions and
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Gromov-Hausdorff distances in Euclidean spaces
2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, 2008The purpose of this paper is to study the relationship between measures of dissimilarity between shapes in Euclidean space. We first concentrate on the pair Gromov-Hausdorff distance (GH) versus Hausdorff distance under the action of Euclidean isometries (EH). Then, we (1) show they are comparable in a precise sense that is not the linear behaviour one
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Evaluation of Hausdorff distances in interval mathematics
Computing, 1990For a class of metrics in \({\mathbb{R}}^ n\) including the Hölder metrics explicit expressions are developed for evaluating the values of the corresponding Hausdorff metrics.
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