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Comparing Images Using the Hausdorff Distance
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1993
"... The Hausdorff distance measures the extent to which each point of a `model' set lies near some point of an `image' set and vice versa. Thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. In this paper we provide ef ..."
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Cited by 659 (10 self)
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The Hausdorff distance measures the extent to which each point of a `model' set lies near some point of an `image' set and vice versa. Thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. In this paper we provide
QUANTIZED GROMOVHAUSDORFF DISTANCE
, 2005
"... Abstract. A quantized metric space is a matrix order unit space equipped with an operator space version of Rieffel’s Lipnorm. We develop for quantized metric spaces an operator space version of quantum GromovHausdorff distance. We show that two quantized metric spaces are completely isometric if a ..."
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Cited by 2 (0 self)
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Abstract. A quantized metric space is a matrix order unit space equipped with an operator space version of Rieffel’s Lipnorm. We develop for quantized metric spaces an operator space version of quantum GromovHausdorff distance. We show that two quantized metric spaces are completely isometric
A Modified Hausdorff Distance for Object Matching
, 1994
"... The 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. Based on our experim ..."
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Cited by 200 (1 self)
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The 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. Based on our
Bounding the Fréchet distance by the Hausdorff distance
 In Proceedings of the Seventeenth European Workshop on Computational Geometry
, 2001
"... We consider planar curves where the arclength between any two points on the curve is at most a constant times their Euclidean distance, which we call κstraight curves. We show that the Frechet distance of such curves is at most (1 + κ) times their Hausdorff distance. ..."
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Cited by 6 (2 self)
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We consider planar curves where the arclength between any two points on the curve is at most a constant times their Euclidean distance, which we call κstraight curves. We show that the Frechet distance of such curves is at most (1 + κ) times their Hausdorff distance.
Robust Face Detection Using the Hausdorff Distance
, 2001
"... The localization of human faces in digital images is a fundamental step in the process of face recognition. This paper presents a shape comparison approach to achieve fast, accurate face detection that is robust to changes in illumination and background. The proposed method is edgebased and works o ..."
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Cited by 212 (1 self)
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on grayscale still images. The Hausdorff distance is used as a similarity measure between a general face model and possible instances of the object within the image. The paper describes an efficient implementation, making this approach suitable for realtime applications. A twostep process that allows both
On Hausdorff Distance Measures
, 2004
"... ABSTRACT A number of Hausdorffbased algorithms have been proposed for finding objects in images. We evaluate different measures and argue that the Hausdorff Average distance measure outperforms other variants for model detection. This method has improved robustness properties with respect to noise ..."
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Cited by 2 (0 self)
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ABSTRACT A number of Hausdorffbased algorithms have been proposed for finding objects in images. We evaluate different measures and argue that the Hausdorff Average distance measure outperforms other variants for model detection. This method has improved robustness properties with respect
Gromovhausdorff distances in Euclidean spaces
 In Proc. Computer Vision and Pattern Recognition (CVPR
"... The purpose of this paper is to study the relationship between measures of dissimilarity between shapes in Euclidean space. We first concentrate on the pair GromovHausdorff distance (GH) versus Hausdorff distance under the action of Euclidean isometries (EH). Then, we (1) show they are comparable i ..."
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Cited by 18 (6 self)
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The purpose of this paper is to study the relationship between measures of dissimilarity between shapes in Euclidean space. We first concentrate on the pair GromovHausdorff distance (GH) versus Hausdorff distance under the action of Euclidean isometries (EH). Then, we (1) show they are comparable
Lower bounds for the complexity of the Hausdorff distance
, 1993
"... We describe new lower bounds for the complexity of the directed Hausdorff distance under translation and rigid motion. We exhibit lower bound constructions of \Omega\Gamma n 3 ) for point sets under translation, for the L 1 , L 2 and L1 norms, \Omega\Gamma n 4 ) for line segments under transl ..."
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Cited by 8 (0 self)
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We describe new lower bounds for the complexity of the directed Hausdorff distance under translation and rigid motion. We exhibit lower bound constructions of \Omega\Gamma n 3 ) for point sets under translation, for the L 1 , L 2 and L1 norms, \Omega\Gamma n 4 ) for line segments under
Results 1  10
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810