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1

Wu, Wei. "Quantized Gromov–Hausdorff distance." Journal of Functional Analysis 238, no. 1 (2006): 58–98. http://dx.doi.org/10.1016/j.jfa.2005.02.017.

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Ali, Mehboob, Zahid Hussain, and Miin-Shen Yang. "Hausdorff Distance and Similarity Measures for Single-Valued Neutrosophic Sets with Application in Multi-Criteria Decision Making." Electronics 12, no. 1 (2022): 201. http://dx.doi.org/10.3390/electronics12010201.

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Hausdorff distance is one of the important distance measures to study the degree of dissimilarity between two sets that had been used in various fields under fuzzy environments. Among those, the framework of single-valued neutrosophic sets (SVNSs) is the one that has more potential to explain uncertain, inconsistent and indeterminate information in a comprehensive way. And so, Hausdorff distance for SVNSs is important. Thus, we propose two novel schemes to calculate the Hausdorff distance and its corresponding similarity measures (SMs) for SVNSs. In doing so, we firstly develop the two forms o
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Kraft, Daniel. "Computing the Hausdorff Distance of Two Sets from Their Distance Functions." International Journal of Computational Geometry & Applications 30, no. 01 (2020): 19–49. http://dx.doi.org/10.1142/s0218195920500028.

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The Hausdorff distance is a measure of (dis-)similarity between two sets which is widely used in various applications. Most of the applied literature is devoted to the computation for sets consisting of a finite number of points. This has applications, for instance, in image processing. However, we would like to apply the Hausdorff distance to control and evaluate optimisation methods in level-set based shape optimisation. In this context, the involved sets are not finite point sets but characterised by level-set or signed distance functions. This paper discusses the computation of the Hausdor
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BERINDE, VASILE, and MADALINA PACURAR. "The role of the Pompeiu-Hausdorff metric in fixed point theory." Creative Mathematics and Informatics 24, no. 2 (2015): 143–50. http://dx.doi.org/10.37193/cmi.2015.02.17.

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The main aim of this note is to highlight the role of the Pompeiu-Hausdorff metric in fixed point theory and, subsidiarily, to touch some issues related to the history of this fundamental concept in modern mathematics. This will allow us to conclude that what is nowadays almost generally called Hausdorff metric (distance) and very seldom Hausdorff-Pompeiu metric (distance) or Pompeiu-Hausdorff metric (distance), should be fairly and correctly named Pompeiu-Hausdorff metric (distance).
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BERINDE, VASILE, and MADALINA PACURAR. "The role of the Pompeiu-Hausdorff metric in fixed point theory." Creative Mathematics and Informatics 22, no. 2 (2013): 143–50. http://dx.doi.org/10.37193/cmi.2013.02.13.

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The main aim of this note is to highlight the role of the Pompeiu-Hausdorff metric in fixed point theory and, subsidiarily, to touch some issues related to the history of this fundamental concept in modern mathematics. This will allow us to conclude that what is nowadays almost generally called Hausdorff metric (distance) and very seldom Hausdorff-Pompeiu metric (distance) or Pompeiu-Hausdorff metric (distance), should be fairly and correctly named Pompeiu-Hausdorff metric (distance).
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BERINDE, VASILE, and MĂDĂLINA PĂCURAR. ""Why Pompeiu-Hausdorff metric instead of Hausdorff metric?"." Creative Mathematics and Informatics 31, no. 1 (2022): 33–41. http://dx.doi.org/10.37193/cmi.2022.01.03.

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"The distance between two sets, commonly called Hausdorff metric, is a very important mathematical concept, with plenty of applications in almost all scientific research areas. We suggest in this paper an update of its name as Pompeiu-Hausdorff metric (distance). Based on historical evidence, this proposal follows the contemporary manner of appointing concepts in scientific writings, especially in mathematics."
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7

Cai, Wei, Wen Chen, and Fajie Wang. "Three-dimensional Hausdorff derivative diffusion model for isotropic/anisotropic fractal porous media." Thermal Science 22, Suppl. 1 (2018): 1–6. http://dx.doi.org/10.2298/tsci170630265c.

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The anomalous diffusion in fractal isotropic/anisotropic porous media is characterized by the Hausdorff derivative diffusion model with the varying fractal orders representing the fractal structures in different directions. This paper presents a comprehensive understanding of the Hausdorff derivative diffusion model on the basis of the physical interpretation, the Hausdorff fractal distance and the fundamental solution. The concept of the Hausdorff fractal distance is introduced, which converges to the classical Euclidean distance with the varying orders tending to 1. The fundamental solution
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8

Bo, Guan, Liang Xu Liu, Jian Bo Fan, and Jin Yang Chen. "An Efficient Trajectory Clustering Framework Based Relative Distance." Applied Mechanics and Materials 241-244 (December 2012): 3209–12. http://dx.doi.org/10.4028/www.scientific.net/amm.241-244.3209.

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along with more and more trajectory dataset being collected into application servers, the research in trajectory clustering has become increasingly important topic. This paper proposes a new mobile object trajectory Clustering algorithm (Trajectory Clustering based Improved Minimum Hausdorff Distance under Translation, TraClustMHD). In this framework, improved Minimum Hausdorff Distance under Translation is presented to measure the similarity between sub-segments. In additional, R-Tree is employed to improve the efficiency. The experimental results showed that this algorithm better than based
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9

Herron, David A., Abigail Richard, and Marie A. Snipes. "Chordal Hausdorff Convergence and Quasihyperbolic Distance." Analysis and Geometry in Metric Spaces 8, no. 1 (2020): 36–67. http://dx.doi.org/10.1515/agms-2020-0104.

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AbstractWe study Hausdorff convergence (and related topics) in the chordalization of a metric space to better understand pointed Gromov-Hausdorff convergence of quasihyperbolic distances (and other conformal distances).
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10

Ronse, Christian, Loic Mazo, and Mohamed Tajine. "Correspondence between Topological and Discrete Connectivities in Hausdorff Discretization." Mathematical Morphology - Theory and Applications 3, no. 1 (2019): 1–28. http://dx.doi.org/10.1515/mathm-2019-0001.

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Abstract We consider Hausdorff discretization from a metric space E to a discrete subspace D, which associates to a closed subset F of E any subset S of D minimizing the Hausdorff distance between F and S; this minimum distance, called the Hausdorff radius of F and written rH(F), is bounded by the resolution of D. We call a closed set F separated if it can be partitioned into two non-empty closed subsets F1 and F2 whose mutual distances have a strictly positive lower bound. Assuming some minimal topological properties of E and D (satisfied in ℝn and ℤn), we show that given a non-separated clos
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11

Bîrsan, Temistocle. "Convexity and Hausdorff-Pompeiu distance." Mathematica Moravica 15, no. 1 (2011): 17–23. http://dx.doi.org/10.5937/matmor1101017b.

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12

Beer, Gerald, and Luzviminda Villar. "Borel measures and Hausdorff distance." Transactions of the American Mathematical Society 307, no. 2 (1988): 763. http://dx.doi.org/10.1090/s0002-9947-1988-0940226-0.

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13

Kerr, David. "Matricial quantum Gromov–Hausdorff distance." Journal of Functional Analysis 205, no. 1 (2003): 132–67. http://dx.doi.org/10.1016/s0022-1236(03)00195-2.

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14

Sendov, Bl. "Hausdorff distance and image processing." Russian Mathematical Surveys 59, no. 2 (2004): 319–28. http://dx.doi.org/10.1070/rm2004v059n02abeh000721.

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15

Bourgain, Jean. "Hausdorff dimension and distance sets." Israel Journal of Mathematics 87, no. 1-3 (1994): 193–201. http://dx.doi.org/10.1007/bf02772994.

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16

Prus-Wiśniowski, Franciszek. "λ-Variation and Hausdorff Distance". Mathematische Nachrichten 158, № 1 (2006): 283–97. http://dx.doi.org/10.1002/mana.19921580120.

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17

Wang, Hui, Guo Jia Li, Jun Hui Pan, and Fu Hua Shang. "An Improved Algorithm of Improved Computation Efficiency on LTS Hausdorff Distance." Applied Mechanics and Materials 347-350 (August 2013): 3217–21. http://dx.doi.org/10.4028/www.scientific.net/amm.347-350.3217.

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The computation efficiency of traditional algorithm is not high, and there is more time consuming. This paper presents an effective method for improved hausdorff distance, depth correction of logging curves is based on improved Hausdorff distance. In this method. On the basis of existing LTS hausdorff distance, the contrast curve segment is divided into neighborhood in an area, the LTS hausdorff distance is calculated by using engineering approximate, and the improving methods of search path is put forward, which ensures that the improved algorithm is better than the original algorithm has hig
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18

Vegter, Gert, and Mathijs Wintraecken. "Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes." Studia Scientiarum Mathematicarum Hungarica 57, no. 2 (2020): 193–99. http://dx.doi.org/10.1556/012.2020.57.2.1454.

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AbstractFejes Tóth [3] studied approximations of smooth surfaces in three-space by piecewise flat triangular meshes with a given number of vertices on the surface that are optimal with respect to Hausdorff distance. He proves that this Hausdorff distance decreases inversely proportional with the number of vertices of the approximating mesh if the surface is convex. He also claims that this Hausdorff distance is inversely proportional to the square of the number of vertices for a specific non-convex surface, namely a one-sheeted hyperboloid of revolution bounded by two congruent circles. We ref
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19

WANG, FAJIE, WEN CHEN, CHUANZENG ZHANG, and QINGSONG HUA. "KANSA METHOD BASED ON THE HAUSDORFF FRACTAL DISTANCE FOR HAUSDORFF DERIVATIVE POISSON EQUATIONS." Fractals 26, no. 04 (2018): 1850084. http://dx.doi.org/10.1142/s0218348x18500846.

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This study proposes the radial basis function (RBF) based on the Hausdorff fractal distance and then applies it to develop the Kansa method for the solution of the Hausdorff derivative Poisson equations. The Kansa method is a meshless global technique promising for high-dimensional irregular domain problems. It is, however, noted that the shape parameter of the RBFs can have a significant influence on the accuracy and robustness of the numerical solution. Based on the leave-one-out cross-validation algorithm proposed by Rippa, this study presents a new technique to choose the optimal shape par
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20

van Kreveld, Marc, Tillmann Miltzow, Tim Ophelders, Willem Sonke, and Jordi L. Vermeulen. "Between shapes, using the Hausdorff distance." Computational Geometry 100 (January 2022): 101817. http://dx.doi.org/10.1016/j.comgeo.2021.101817.

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21

Kim, Kyeongtaek, and Ji Hun Kyung. "Character Matching Using a Hausdorff Distance." Journal of Society of Korea Industrial and Systems Engineering 38, no. 2 (2015): 56–62. http://dx.doi.org/10.11627/jkise.2015.38.2.56.

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22

Huttenlocher, D. P., G. A. Klanderman, and W. J. Rucklidge. "Comparing images using the Hausdorff distance." IEEE Transactions on Pattern Analysis and Machine Intelligence 15, no. 9 (1993): 850–63. http://dx.doi.org/10.1109/34.232073.

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23

Kwon, Oh-Kyu. "Nonparametric hierarchical Hausdorff distance matching algorithm." Optical Engineering 39, no. 7 (2000): 1917. http://dx.doi.org/10.1117/1.602576.

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24

Lim, Sunhyuk, Facundo Mémoli, and Zane Smith. "The Gromov–Hausdorff distance between spheres." Geometry & Topology 27, no. 9 (2023): 3733–800. http://dx.doi.org/10.2140/gt.2023.27.3733.

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25

Nutanong, Sarana, Edwin H. Jacox, and Hanan Samet. "An incremental Hausdorff distance calculation algorithm." Proceedings of the VLDB Endowment 4, no. 8 (2011): 506–17. http://dx.doi.org/10.14778/2002974.2002978.

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26

Van Rooij, Arnoud. "Fourier inversion and the Hausdorff distance." Statistica Neerlandica 56, no. 2 (2002): 206–13. http://dx.doi.org/10.1111/1467-9574.00194.

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27

Rieffel, Marc A. "Vector Bundles and Gromov–Hausdorff Distance." Journal of K-Theory 5, no. 1 (2009): 39–103. http://dx.doi.org/10.1017/is008008014jkt080.

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AbstractWe show how to make precise the vague idea that for compact metric spaces that are close together for Gromov–Hausdorff distance, suitable vector bundles on one metric space will have counterpart vector bundles on the other. Our approach employs the Lipschitz constants of projection-valued functions that determine vector bundles. We develop some computational techniques, and we illustrate our ideas with simple specific examples involving vector bundles on the circle, the two-torus, the two-sphere, and finite metric spaces. Our topic is motivated by statements concerning “monopole bundle
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28

Attouch, Hedy, Roberto Lucchetti та Roger J. B. Wets. "The topology of theρ-hausdorff distance". Annali di Matematica Pura ed Applicata 160, № 1 (1991): 303–20. http://dx.doi.org/10.1007/bf01764131.

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29

Belogay, E., C. Cabrelli, U. Molter, and R. Shonkwiler. "Calculating the Hausdorff distance between curves." Information Processing Letters 64, no. 1 (1997): 17–22. http://dx.doi.org/10.1016/s0020-0190(97)00140-3.

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30

Li, Hanfeng. "Order-unit quantum Gromov–Hausdorff distance." Journal of Functional Analysis 231, no. 2 (2006): 312–60. http://dx.doi.org/10.1016/j.jfa.2005.03.016.

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31

Liu, Luo-fei. "Zero asymptotic Lipschitz distance and finite Gromov-Hausdorff distance." Science in China Series A: Mathematics 50, no. 3 (2007): 345–50. http://dx.doi.org/10.1007/s11425-007-0009-4.

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32

Ishiki, Yoshito. "Branching Geodesics of the Gromov-Hausdorff Distance." Analysis and Geometry in Metric Spaces 10, no. 1 (2022): 109–28. http://dx.doi.org/10.1515/agms-2022-0136.

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Abstract In this paper, we first evaluate topological distributions of the sets of all doubling spaces, all uniformly disconnected spaces, and all uniformly perfect spaces in the space of all isometry classes of compact metric spaces equipped with the Gromov–Hausdorff distance.We then construct branching geodesics of the Gromov–Hausdorff distance continuously parameterized by the Hilbert cube, passing through or avoiding sets of all spaces satisfying some of the three properties shown above, and passing through the sets of all infinite-dimensional spaces and the set of all Cantor metric spaces
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BRANDENBURG, FRANZ J., ANDREAS GLEIßNER, and ANDREAS HOFMEIER. "COMPARING AND AGGREGATING PARTIAL ORDERS WITH KENDALL TAU DISTANCES." Discrete Mathematics, Algorithms and Applications 05, no. 02 (2013): 1360003. http://dx.doi.org/10.1142/s1793830913600033.

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Comparing and ranking information is an important topic in social and information sciences, and in particular on the web. Its objective is to measure the difference of the preferences of voters on a set of candidates and to compute a consensus ranking. Commonly, each voter provides a total order or a bucket order of all candidates, where bucket orders allow ties. In this work we consider the generalization of total and bucket orders to partial orders and compare them by the nearest neighbor and the Hausdorff Kendall tau distances. For total and bucket orders these distances can be computed in
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34

Dang, Chau Nguyen, and Tuan Hong Do. "A modification of line Hausdorff distance for face recognition to reduce computational cost." Science and Technology Development Journal 20, K3 (2017): 152–58. http://dx.doi.org/10.32508/stdj.v20ik3.1106.

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Face recognition, that has a lot of applications in modern life, is still an attractive research for pattern recognition community. Due to the similarity of human faces, face recognition presents a significant challenge for pattern recognition researchers. Hausdorff distance is an efficient parameter for measuring the similarity between objects. Line Hausdorff distance (LHD) technique, which is the applying of Hausdorff distance for face recognition, gives high accuracy in comparing with common methods for face recognition. For fast screen techniques such as LHD, the computational cost is a ke
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PAPADOPOULOU, EVANTHIA, and D. T. LEE. "THE HAUSDORFF VORONOI DIAGRAM OF POLYGONAL OBJECTS: A DIVIDE AND CONQUER APPROACH." International Journal of Computational Geometry & Applications 14, no. 06 (2004): 421–52. http://dx.doi.org/10.1142/s0218195904001536.

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We study the Hausdorff Voronoi diagram of a set S of polygonal objects in the plane, a generalization of Voronoi diagrams based on the maximum distance of a point from a polygon, and show that it is equivalent to the Voronoi diagram of S under the Hausdorff distance function. We investigate the structural and combinatorial properties of the Hausdorff Voronoi diagram and give a divide and conquer algorithm for the construction of this diagram that improves upon previous results. As a byproduct we introduce the Hausdorff hull, a structure that relates to the Hausdorff Voronoi diagram in the same
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Qiang, He Qun, Chun Hua Qian, and Sheng Rong Gong. "Similarity Measure for Image Retrieval Based on Hausdorff Distance." Applied Mechanics and Materials 635-637 (September 2014): 1039–44. http://dx.doi.org/10.4028/www.scientific.net/amm.635-637.1039.

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In general, it is difficult to segment accurately image regions or boundary contours and represent them by feature vectors for shape-based image query. Therefore, the object similarity is often computed by their boundaries. Hausdorff distance is nonlinear for computing distance, it can be used to measure the similarity between two patterns of points of edge images. Classical Hausdorff measure need to express image as a feature matrix firstly, then calculate feature values or feature vectors, so it is time-consuming. Otherwise, it is difficult for part pattern matching when shadow and noise exi
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KNAUER, CHRISTIAN, and MARC SCHERFENBERG. "APPROXIMATE NEAREST NEIGHBOR SEARCH UNDER TRANSLATION INVARIANT HAUSDORFF DISTANCE." International Journal of Computational Geometry & Applications 21, no. 03 (2011): 369–81. http://dx.doi.org/10.1142/s0218195911003706.

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We present an embedding and search reduction which allow us to build the first data structure for the nearest neighbor search among small point sets with respect to the directed Hausdorff distance under translation. The search structure is non-heuristic in the sense that the quality of the results, the performance, and the space bound are guaranteed. Let n denote the number of point sets in the data base, s the maximal size of a point set, and d the dimension of the points. The nearest neighbor of a query point set under the translation invariant directed Hausdorff distance can be approximated
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38

De, Sujit Kumar, and Shib Sankar Sana. "Two-layer supply chain model for Cauchy-type stochastic demand under fuzzy environment." International Journal of Intelligent Computing and Cybernetics 11, no. 2 (2018): 285–308. http://dx.doi.org/10.1108/ijicc-10-2016-0037.

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Purpose The purpose of this paper is to deal with profit maximization problem of two-layer supply chain (SC) under fuzzy stochastic demand having finite mean and unknown variance. Buyback policy is employed from the retailer to supplier. The profit of the supplier solely depends on the order size of the retailers. However, the loss of shortage items is related to loss of profit and goodwill dependent. The authors develop the profit function separately for both the retailer and supplier, first, for a decentralized system and, second, joining them, the authors get a centralized system (CS) of de
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39

Yu, Yongbo, Hong Jiang, Xiangfeng Zhang, and Yutong Chen. "Identifying Irregular Potatoes Using Hausdorff Distance and Intersection over Union." Sensors 22, no. 15 (2022): 5740. http://dx.doi.org/10.3390/s22155740.

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Further processing and the added value of potatoes are limited by irregular potatoes. An ellipse-fitting-based Hausdorff distance and intersection over union (IoU) method for identifying irregular potatoes is proposed to solve the problem. First, the acquired potato image is resized, translated, segmented, and filtered to obtain the potato contour information. Secondly, a least-squares fitting method fits the extracted contour to an ellipse. Then, the similarity between the irregular potato contour and the fitted ellipse is characterized using the perimeter ratio, area ratio, Hausdorff distanc
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40

Li, Yinlong, and Tianshu Zhang. "A hybrid Hausdorff distance track correlation algorithm based on time sliding window." MATEC Web of Conferences 336 (2021): 07015. http://dx.doi.org/10.1051/matecconf/202133607015.

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In multi-sensor target tracking, track correlation is the key to the unification of global situation. Hausdorff distance has been applied to power fault elimination, point cloud data, medical measurement, image segmentation, vehicle trajectory recognition and other directions. To solve the problem of track correlation, a hybrid Hausdorff distance track correlation algorithm based on time sliding window is proposed. The hybrid Hausdorff distance based on position, speed and azimuth is defined, and the time sliding window is added on this basis. Simulation results show that the proposed algorith
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41

ALT, HELMUT, and LUDMILA SCHARF. "COMPUTING THE HAUSDORFF DISTANCE BETWEEN CURVED OBJECTS." International Journal of Computational Geometry & Applications 18, no. 04 (2008): 307–20. http://dx.doi.org/10.1142/s0218195908002647.

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The Hausdorff distance between two sets of curves is a measure for the similarity of these objects and therefore an interesting feature in shape recognition. If the curves are algebraic computing the Hausdorff distance involves computing the intersection points of the Voronoi edges of the one set with the curves in the other. Since computing the Voronoi diagram of curves is quite difficult we characterize those points algebraically and compute them using the computer algebra system SYNAPS. This paper describes in detail which points have to be considered, by what algebraic equations they are c
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HUANG, Hua, Kai YAN, and Chun QI. "Adaptive Hausdorff Distance Based on Similarity Weighting." Acta Automatica Sinica 35, no. 7 (2009): 882–87. http://dx.doi.org/10.3724/sp.j.1004.2009.00882.

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43

Ji, Yibo, and Alexey A. Tuzhilin. "Gromov–Hausdorff distance between interval and circle." Topology and its Applications 307 (February 2022): 107938. http://dx.doi.org/10.1016/j.topol.2021.107938.

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44

Falconer, K. J. "On the Hausdorff dimensions of distance sets." Mathematika 32, no. 2 (1985): 206–12. http://dx.doi.org/10.1112/s0025579300010998.

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45

Qiu, Derong. "Geometry of non-Archimedean Gromov-Hausdorff distance." P-Adic Numbers, Ultrametric Analysis, and Applications 1, no. 4 (2009): 317–37. http://dx.doi.org/10.1134/s2070046609040050.

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46

Liu, Hui, Zhichun Zhang, and Dong Wei. "A Hausdorff Distance Based Image Registration Algorithm." International Journal of Signal Processing, Image Processing and Pattern Recognition 8, no. 1 (2015): 125–34. http://dx.doi.org/10.14257/ijsip.2015.8.1.13.

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47

Noldus, Johan. "A Lorentzian Gromov–Hausdorff notion of distance." Classical and Quantum Gravity 21, no. 4 (2004): 839–50. http://dx.doi.org/10.1088/0264-9381/21/4/007.

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48

Malysheva, O. S. "Estimates for Modified (Euclidean) Gromov–Hausdorff Distance." Moscow University Mathematics Bulletin 79, no. 4 (2024): 201–5. http://dx.doi.org/10.3103/s002713222470027x.

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49

Donoso-Aguirre, F., J. P. Bustos-Salas, M. Torres-Torriti, and A. Guesalaga. "Mobile robot localization using the Hausdorff distance." Robotica 26, no. 2 (2008): 129–41. http://dx.doi.org/10.1017/s0263574707003657.

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SUMMARYThis paper presents a novel method for localization of mobile robots in structured environments. The estimation of the position and orientation of the robot relies on the minimisation of the partial Hausdorff distance between ladar range measurements and a floor plan image of the building. The approach is employed in combination with an extended Kalman filter to obtain accurate estimates of the robot's position, heading and velocity. Good estimates of these variables were obtained during tests performed using a differential drive robot, thus demonstrating that the approach provides an a
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50

Gao, Yongsheng, and Maylor K. H. Leung. "Line segment Hausdorff distance on face matching." Pattern Recognition 35, no. 2 (2002): 361–71. http://dx.doi.org/10.1016/s0031-3203(01)00049-8.

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