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Автор: Grafiati
Опубліковано: 6 вересня 2023

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Статті в журналах з теми "Hausdorff distance measures"

1

Beer, Gerald, and Luzviminda Villar. "Borel measures and Hausdorff distance." Transactions of the American Mathematical Society 307, no. 2 (February 1, 1988): 763. http://dx.doi.org/10.1090/s0002-9947-1988-0940226-0.

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2

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 (December 31, 2022): 201. http://dx.doi.org/10.3390/electronics12010201.

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Анотація:
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 of Hausdorff distance between SVNSs based on the definition of Hausdorff metric between two sets. We then use these new distance measures to construct several SMs for SVNSs. Some mathematical theorems regarding the proposed Hausdorff distances for SVNSs are also proven to strengthen its theoretical properties. In order to show the exact calculation behavior and distance measurement mechanism of our proposed methods in accordance with the decorum of Hausdorff metric, we utilize an intuitive numerical example that demonstrate the novelty and practicality of our proposed measures. Furthermore, we develop a multi-criteria decision making (MCDM) method under single-valued neutrosophic environment using the proposed SMs based on our defined Hausdorff distance measures, called as a single-valued neutrosophic MCDM (SVN-MCDM) method. In this connection, we employ our proposed SMs to compute the degree of similarity of each option with the ideal choice to identify the best alternative as well as to perform an overall ranking of the alternatives under study. We then apply our proposed SVN-MCDM scheme to solve two real world problems of MCDM under single-valued neutrosophic environment to show its effectiveness and application.
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3

Dong-Gyu Sim, Oh-Kyu Kwon, and Rae-Hong Park. "Object matching algorithms using robust Hausdorff distance measures." IEEE Transactions on Image Processing 8, no. 3 (March 1999): 425–29. http://dx.doi.org/10.1109/83.748897.

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4

XU, Z. S., and J. CHEN. "AN OVERVIEW OF DISTANCE AND SIMILARITY MEASURES OF INTUITIONISTIC FUZZY SETS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 16, no. 04 (August 2008): 529–55. http://dx.doi.org/10.1142/s0218488508005406.

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The Intuitionistic Fuzzy Sets (IFSs), originated by Atanassov [1], is a useful tool to deal with vagueness and ambiguity. In the short time since their first appearance, many different distance and similarity measures of IFSs have been proposed, but they are scattered through the literature. In this paper, we give a comprehensive overview of distance and similarity measures of IFSs. Based on the weighted Hamming distance, the weighted Euclidean distance, and the weighted Hausdorff distance, respectively, we define some continuous distance and similarity measures for IFSs. We also utilize geometric distance model to define some continuous distance and similarity measures for IFSs, which are the various combinations and generalizations of the weighted Hamming distance, the weighted Euclidean distance and the weighted Hausdorff distance. Then we extend these distance and similarity measures for Interval-Valued Intuitionistic Fuzzy Sets (IVIFSs).
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5

Hung, Wen-Liang, and Miin-Shen Yang. "Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance." Pattern Recognition Letters 25, no. 14 (October 2004): 1603–11. http://dx.doi.org/10.1016/j.patrec.2004.06.006.

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6

Jee, Hana, Monica Tamariz, and Richard Shillcock. "Quantified Grapho-Phonemic Systematicity in Korean Hangeul." Asian Culture and History 15, no. 1 (February 2, 2023): 25. http://dx.doi.org/10.5539/ach.v15n1p25.

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Hangeul, the Korean orthography is well known for its scientific design that emphasizes the link between sounds and letter shapes. However, it hasn’t been asked so far ‘how systematic’ it is. We quantify, for the first time, the grapho-phonemic systematicity of hangeul. We defined Korean phonemes as binary vectors according to articulatory features and then measured the pairwise phonemic distance between phonemes using multiple methods. We measured the pairwise visual distance between letter shapes by (a) stroke share rate, which reflects the original principles of hangeul’s creation, and (b) Hausdorff distance (Huttenlocher et al., 1993), which measures topological difference between images. We then tested the correlation between the phonological distances and the corresponding orthographical distances. Positive correlations clearly indicated that similar letters tend to have similar pronunciations in Korean hangeul. Stroke share rate maximizes hangeul’s grapho-phonemic systematicity. Hausdorff distance, an initial step in the detailed quantifying of visual distance, allows similar calculations to be carried out with any hangeul font and with any other orthography (Jee, Tamariz, & Shillcock, 2021; 2022a; 2022b). Consciously designed to be phonologically transparent, hangeul can be considered as the gold standard of grapho-phonemic systematicity. We discuss the implications of this systematicity.
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7

Banaś, Józef, and Antonio Martinón. "Some properties of the Hausdorff distance in metric spaces." Bulletin of the Australian Mathematical Society 42, no. 3 (December 1990): 511–16. http://dx.doi.org/10.1017/s0004972700028677.

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8

Ren, Wenjuan, Zhanpeng Yang, and Xipeng Li. "Distance Measures Based on Metric Information Matrix for Atanassov’s Intuitionistic Fuzzy Sets." Axioms 12, no. 4 (April 14, 2023): 376. http://dx.doi.org/10.3390/axioms12040376.

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The metric matrix theory is an important research object of metric measure geometry and it can be used to characterize the geometric structure of a set. For intuitionistic fuzzy sets (IFS), we defined metric information matrices (MIM) of IFS by using the metric matrix theory. We introduced the Gromov–Hausdorff metric to measure the distance between any two MIMs. We then constructed a kind of metric information matrix distance knowledge measure for IFS. The proposed distance measures have the ability to measure the distance between two incomplete intuitionistic fuzzy sets. In order to reduce the information confusion caused by the disorder of MIM, we defined a homogenous metric information matrix distance by rearranging MIM. Some theorems are given to show the properties of the constructed distance measures. At the end of the paper, some numerical experiments are given to show that the proposed distances can recognize different patterns represented by IFS.
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9

Schwedler, Benjamin R. J., and Michael E. Baldwin. "Diagnosing the Sensitivity of Binary Image Measures to Bias, Location, and Event Frequency within a Forecast Verification Framework." Weather and Forecasting 26, no. 6 (December 1, 2011): 1032–44. http://dx.doi.org/10.1175/waf-d-11-00032.1.

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Abstract While the use of binary distance measures has a substantial history in the field of image processing, these techniques have only recently been applied in the area of forecast verification. Designed to quantify the distance between two images, these measures can easily be extended for use with paired forecast and observation fields. The behavior of traditional forecast verification metrics based on the dichotomous contingency table continues to be an area of active study, but the sensitivity of image metrics has not yet been analyzed within the framework of forecast verification. Four binary distance measures are presented and the response of each to changes in event frequency, bias, and displacement error is documented. The Hausdorff distance and its derivatives, the modified and partial Hausdorff distances, are shown only to be sensitive to changes in base rate, bias, and displacement between the forecast and observation. In addition to its sensitivity to these three parameters, the Baddeley image metric is also sensitive to additional aspects of the forecast situation. It is shown that the Baddeley metric is dependent not only on the spatial relationship between a forecast and observation but also the location of the events within the domain. This behavior may have considerable impact on the results obtained when using this measure for forecast verification. For ease of comparison, a hypothetical forecast event is presented to quantitatively analyze the various sensitivities of these distance measures.
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10

Meng, Lingyan, and Xiaoyan Wei. "Research on Evaluation of Sustainable Development of New Urbanization from the Perspective of Urban Agglomeration under the Pythagorean Fuzzy Sets." Discrete Dynamics in Nature and Society 2021 (August 16, 2021): 1–11. http://dx.doi.org/10.1155/2021/2445025.

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In this study, considering the traditional geometric operation laws and Pythagorean fuzzy information, we propose a variety of new distance measures of Pythagorean fuzzy sets such as generalized Pythagorean fuzzy geometric distance (GPFGD) measures and generalized Pythagorean fuzzy weighted geometric distance (GPFWGD) measures. Besides, some special issues including Hamming distance, Euclidean distance, and Hausdorff distance of these raised geometric distance measures are investigated. To testify the valid of these new presented distance measures, we build a decision-making model illustrated by a mathematical calculation example to evaluate the sustainable development of new urbanization from the perspective of urban agglomeration using Pythagorean fuzzy information.
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Більше джерел

Дисертації з теми "Hausdorff distance measures"

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Ryvkin, Leonie [Verfasser], Maike [Gutachter] Buchin, and Carola [Gutachter] Wenk. "On distance measures for polygonal curves bridging between Hausdorff and Fréchet distance / Leonie Ryvkin ; Gutachter: Maike Buchin, Carola Wenk ; Fakultät für Mathematik." Bochum : Ruhr-Universität Bochum, 2021. http://d-nb.info/1239418930/34.

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2

SURIANO, LUCA. "A Quantum distance for noncommutative measure spaces and an application to quantum field theory." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2010. http://hdl.handle.net/2108/1326.

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Nella prima parte della Tesi, presentiamo una versione "puntata" della topologia di Gromov-Hausdorff quantistica introdotta da Rieffel per spazi metrici quantistici compatti (cioè, spazi con unità d'ordine e una seminorma Lipschitz che metrizza la topologia *-debole sullo spazio dei funzionali positivi normalizzati). In particolare, proporremo una nozione di cono tangente quantistico di uno spazio metrico quantistico, come analogo noncommutativo del cono tangente di Gromov in un punto di uno spazio metrico ordinario, basata su una opportuna procedura di riscalamento della seminorma Lipschitz definita su uno spazio metrico quantistico. Tale costruzione estende effettivamente la corrispondente costruzione valida per spazi metrici ordinari. Infine, a titolo di esempio, descriveremo il cono tangente quantistico del toro noncommutativo bidimensionale. Nella seconda parte, invece, introduciamo una particolare distanza quantistica sull'insieme delle algebre di von Neumann Lip-normate (cioè, dotate di una ulteriore norma che metrizza la topologia debole sui sottoinsiemi limitati nella norma C*). Come avviene per le distanze di tipo Gromov-Hausdorff, anche questa distanza G.-H. duale è una pseudo-distanza, e diviene una vera distanza solo sulle classi di equivalenza isometrica (rispetto alla norma Lip) delle algebre di von Neumann Lip-normate. Inoltre, dimostreremo un criterio di precompatteza per famiglie di algebre di vN Lip-normate (fortemente) uniformemente limitate, utilizzando la nozione di ultraprodotto (ristretto) di algebre di vN Lip-normate. Infine, nell'ambito del'approccio algebrico alla teoria quantistica dei campi, applicheremo tale costruzione allo studio del limite di scala (cioè, quando si fanno tendere a un punto le regioni dello spaziotempo su cui sono definiti gli osservabili della teoria) di una rete locale di algebre di vN (le algebre degli osservabili), confrontando l'approccio tramite ultraprodotti (e con la convergenza nella distanza quantistica) con la costruzione delle algebre "limite di scala" di Buchholz e Verch, mostrando che nel caso del campo libero bosonico le due procedure forniscono lo stesso risultato.
In the first part of this dissertation, we study a pointed version of Rieffel's quantum Gromov-Hausdorff topology for compact quantum metric spaces (i.e, order-unit spaces with a Lipschitz-like seminorm inducing a distance on the space of positive normalized linear functionals which metrizes the w*-topology). In particular, in analogy with Gromov's notion of metric tangent cone at a point of an (abstract) proper metric space, we propose a similar construction for (compact) quantum metric spaces, based on a suitable procedure of rescaling the Lipschitz seminorm on a given quantum metric space. As a result, we get a quantum analogue of the Gromov tangent cone, which extends the classical (say, commutative) construction. As a case study, we apply this procedure to the two-dimensional noncommutative torus, and we obtain what we call a noncommutative solenoid. In the second part, we introduce a quantum distance on the set of dual Lip-von Neumann algebras (i.e., vN algebras with a dual Lip-norm which metrizes the w*-topology on bounded subset). As for the other G.-H. distances (classical or quantum), this dual quantum Gromov-Hausdorff (pseudo-)distance turns out to be a true distance on the (Lip-)isometry classes of Lip-vN algebras. We give also a precompactness criterion, relating the limit of a (strongly) uniform sequence of Lip-vN algebras to the (restricted) ultraproduct, over an ultrafilter, of the same sequence. As an application, we apply this construction to the study of the Buchholz-Verch scaling limit theory of a local net of (algebras of) observables in the algebraic quantum field theory framework, showing that the two approaches lead to the same result for the (real scalar) free field model.
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3

Suzuki, Kohei. "Convergence of stochastic processes on varying metric spaces." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215281.

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4

George, Greegar. "Global and combined global-local response sensitivity analyses of uncertain structures based on model distance measures." Thesis, 2018. https://etd.iisc.ac.in/handle/2005/4750.

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The work reported in this thesis is in the area of global response sensitivity analysis (GRSA) of engineering systems in which the uncertainties associated with external actions and/or system parameters need to be explicitly modelled using a suitable mathematical framework. The uncertainties in loads and system parameters propagate through the relevant input-output relationship and manifest as uncertainties in the response variables of interest. The problem of GRSA consists of decomposing a measure of uncertainty in a chosen response variable into a set of constituents each of which quantifies the influence of a specified input or load variable or their group wise interactions. The quantification of relative importance of different input variables in a model enables the ranking of input variables according to their relative importance. This facilitates effective model reductions and also helps in planning experiments while gathering empirical data for arriving at the uncertainty models. The thesis pursues two intertwining themes, within the context of GRSA of structural systems: a) development of notions of global response sensitivity indices based on the concept of measures of distance between two mathematical models (viz., a fiducial model in which all the sources of uncertainties are included in characterising the response, and a set of altered models, in which uncertainties in one or more of the input variables are deliberately suppressed), and b) embedding these developments within the context of alternative uncertainty modelling frameworks, namely, probabilistic, non-probabilistic (including intervals, convex functions, and fuzzy variables), combined probabilistic and non-probabilistic modelling (within the context of a given problem), and polymorphic modelling frameworks. The studies involving probabilistic models allow for uncertain variables to be modelled as a set of random variables (which could, in general, be dependent and non-Gaussian distributed) and/or as a set of random processes evolving space and/or time. The model distance measures considered include norm, Hellinger distance, Kullback-Leibler divergence, and Kantorovich distance. The study demonstrates the equivalence of Sobol’s indices and norm based indices for the special case when the uncertain variables are modelled as a set of independent random variables. The studies involving non-probabilistic uncertain input variables employ Hausdorff distance measures to characterize the global response sensitivity indices. Newer definitions of model distance measures are introduced when dealing with polymorphic uncertain variables. This part of the study allows for different forms of polymorphic uncertain variable modelling, namely, fuzzy random variables, probability-box variables, fuzzy probability based random variables, and fuzzy probability based fuzzy random variables. The study also involves development of appropriate computational strategies (which combine Monte Carlo simulations and numerical optimization schemes) for evaluating the various global response sensitivity indices. The illustrations are drawn mainly from problems of structural mechanics involving static/dynamic and linear/nonlinear behaviours.
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5

Akhvlediani, Andrei. "Hausdorff and Gromov distances in quantale-enriched categories /." 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR45921.

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Анотація:
Thesis (M.A.)--York University, 2008. Graduate Programme in Mathematics and Statistics.
Typescript. Includes bibliographical references (leaves 166-167). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR45921
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6

Maitra, Sayantan. "The Space of Metric Measure Spaces." Thesis, 2017. http://etd.iisc.ac.in/handle/2005/3588.

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This thesis is broadly divided in two parts. In the first part we give a survey of various distances between metric spaces, namely the uniform distance, Lipschitz distance, Hausdor distance and the Gramoz Hausdor distance. Here we talk about only the most basic of their properties and give a few illustrative examples. As we wish to study collections of metric measure spaces, which are triples (X; d; m) consisting of a complete separable metric space (X; d) and a Boral probability measure m on X, there are discussions about some distances between them. Among the three that we discuss, the transportation and distortion distances were introduced by Sturm. The later, denoted by 2, on the space X2 of all metric measure spaces having finite L2-size is the focus of the second part of this thesis. The second part is an exposition based on the work done by Sturm. Here we prove a number of results on the analytic and geometric properties of (X2; 2). Beginning by noting that (X2; 2) is a non-complete space, we try to understand its completion. Towards this end, the notion of a gauged measure space is useful. These are triples (X; f; m) where X is a Polish space, m a Boral probability measure on X and f a function, also called a gauge, on X X that is symmetric and square integral with respect to the product measure m2. We show that, Theorem 1. The completion of (X2; 2) consists of all gauged measure spaces where the gauges satisfy triangle inequality almost everywhere. We denote the space of all gauged measure spaces by Y. The space X2 can be embedded in Y and the transportation distance 2 extends easily from X2 to Y. These two spaces turn out to have similar geometric properties. On both these spaces 2 is a strictly intrinsic metric; i.e. any two members in them can be joined by a shortest path. But more importantly, using a description of the geodesics in these spaces, the following result is proved. Theorem 2. Both (X2; 2) and (Y; 2) have non-negative curvature in the sense of Alexandrov.
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7

Maitra, Sayantan. "The Space of Metric Measure Spaces." Thesis, 2017. http://etd.iisc.ernet.in/2005/3588.

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Анотація:
This thesis is broadly divided in two parts. In the first part we give a survey of various distances between metric spaces, namely the uniform distance, Lipschitz distance, Hausdor distance and the Gramoz Hausdor distance. Here we talk about only the most basic of their properties and give a few illustrative examples. As we wish to study collections of metric measure spaces, which are triples (X; d; m) consisting of a complete separable metric space (X; d) and a Boral probability measure m on X, there are discussions about some distances between them. Among the three that we discuss, the transportation and distortion distances were introduced by Sturm. The later, denoted by 2, on the space X2 of all metric measure spaces having finite L2-size is the focus of the second part of this thesis. The second part is an exposition based on the work done by Sturm. Here we prove a number of results on the analytic and geometric properties of (X2; 2). Beginning by noting that (X2; 2) is a non-complete space, we try to understand its completion. Towards this end, the notion of a gauged measure space is useful. These are triples (X; f; m) where X is a Polish space, m a Boral probability measure on X and f a function, also called a gauge, on X X that is symmetric and square integral with respect to the product measure m2. We show that, Theorem 1. The completion of (X2; 2) consists of all gauged measure spaces where the gauges satisfy triangle inequality almost everywhere. We denote the space of all gauged measure spaces by Y. The space X2 can be embedded in Y and the transportation distance 2 extends easily from X2 to Y. These two spaces turn out to have similar geometric properties. On both these spaces 2 is a strictly intrinsic metric; i.e. any two members in them can be joined by a shortest path. But more importantly, using a description of the geodesics in these spaces, the following result is proved. Theorem 2. Both (X2; 2) and (Y; 2) have non-negative curvature in the sense of Alexandrov.
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Книги з теми "Hausdorff distance measures"

1

Efficient visual recognition using the Hausdorff distance. Berlin: Springer, 1996.

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Rucklidge, William. Efficient visual recognition using the Hausdorff distance. Berlin: Springer, 1996.

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Частини книг з теми "Hausdorff distance measures"

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Feydy, Jean, and Alain Trouvé. "Global Divergences Between Measures: From Hausdorff Distance to Optimal Transport." In Shape in Medical Imaging, 102–15. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-04747-4_10.

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2

Fedorov, Andriy, Eric Billet, Marcel Prastawa, Guido Gerig, Alireza Radmanesh, Simon K. Warfield, Ron Kikinis, and Nikos Chrisochoides. "Evaluation of Brain MRI Alignment with the Robust Hausdorff Distance Measures." In Advances in Visual Computing, 594–603. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-89639-5_57.

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3

Sudha, N., and E. P. Vivek. "A High-Speed VLSI Array Architecture for Euclidean Metric-Based Hausdorff Distance Measures Between Images." In Lecture Notes in Computer Science, 180–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11602569_22.

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Park, Bo Gun, Kyoung Mu Lee, and Sang Uk Lee. "A New Similarity Measure for Random Signatures: Perceptually Modified Hausdorff Distance." In Advanced Concepts for Intelligent Vision Systems, 990–1001. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11864349_90.

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5

"Hausdorff Distance for Face Recognition." In Similarity Measures for Face Recognition, edited by Enrico Vezzetti and Federica Marcolin, 39–46. BENTHAM SCIENCE PUBLISHERS, 2015. http://dx.doi.org/10.2174/9781681080444115010006.

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When two sets are differently sized, the Hausdorff distance can be computed between them, even if the cardinality of one set is infinite. Different versions of this distance have been proposed and employed for face verification, among which the modified Hausdorff distance is the most famous. The important point to be noted is that, among the most commonly used similarity measures, the Hausdorff distance is the only one that has been widely applied to 3D data.
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Тези доповідей конференцій з теми "Hausdorff distance measures"

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Andreev, Andrey, and Nikolay Kirov. "Text search in document images based on Hausdorff distance measures." In the 9th International Conference. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1500879.1500892.

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2

Verma, Nishchal K., Esha Dutta, and Yan Cui. "Hausdorff distance and global silhouette index as novel measures for estimating quality of biclusters." In 2015 IEEE International Conference on Bioinformatics and Biomedicine (BIBM). IEEE, 2015. http://dx.doi.org/10.1109/bibm.2015.7359691.

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Ji, Pu, and Hong-yu Zhang. "A subsethood measure with the hausdorff distance for interval neutrosophic sets and its relations with similarity and entropy measures." In 2016 Chinese Control and Decision Conference (CCDC). IEEE, 2016. http://dx.doi.org/10.1109/ccdc.2016.7531710.

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4

Song, Y., J. S. M. Vergeest, and C. Wang. "Identifying and Tracking Features in Freeform Shape." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57174.

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Анотація:
Building a smooth and well structured surface to fit unstructured 3-D data is always an interesting topic in Computer-Aided Design (CAD). In this paper, a method of approximating complex freeform shapes with parameterized freeform feature templates is proposed. To achieve this, a portion of a digitized 3-Dimensional (3-D) shape should be matched, or fitted, to a deformable shape feature template, where the deformation is a function of intrinsic feature parameters. 3-D shape matching to, possibly sparse, inaccurate or otherwise degraded, freeform surface data is known to be hard. Using a variant of the directed Hausdorff distance measure of shapes, it is shown that convergence towards a shape match is feasible. Based on sensitivity analyses of the shape distance measures, it is determined that adjusting coefficients of the optimization function in different stages of optimizations can accelerate the optimization procedure. By the matching results, a standard deviation-like function is proposed to achieve automatic feature recognition. With the proposed extendable concept, complex freeform shapes are tracked and fitted automatically. Based on a defined interference ratio, interfered feature can also be identified. Numerical experiments were conducted in order to verify the proposed method and to find the maximal degree of feature interference for which matching is successful. It is also described how the presented technique can be applied in shape modeling applications.
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Enayatifar, Rasul, and Rosalina Abdul Salam. "Similarity Measure Using Hausdorff Distance in 2D Shape Recognition System." In 2nd International Symposium on Computer, Communication, Control and Automation. Paris, France: Atlantis Press, 2013. http://dx.doi.org/10.2991/3ca-13.2013.49.

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Chi, Jing, DuanSheng Chen, XiaoJing Lu, and XiaoLi Li. "Robust face recognition using gradient map and Hausdorff distance measure." In International Symposium on Multispectral Image Processing and Pattern Recognition, edited by S. J. Maybank, Mingyue Ding, F. Wahl, and Yaoting Zhu. SPIE, 2007. http://dx.doi.org/10.1117/12.753405.

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Balakrishnan, Ramadoss, Rajkumar Kannan, Suresh Kannaiyan, and Sridhar Swaminathan. "Deity face recognition using schur decomposition and hausdorff distance measure." In 2013 IEEE 56th International Midwest Symposium on Circuits and Systems (MWSCAS). IEEE, 2013. http://dx.doi.org/10.1109/mwscas.2013.6674865.

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Yuankui Hu and Zengfu Wang. "A Similarity Measure Based on Hausdorff Distance for Human Face Recognition." In 18th International Conference on Pattern Recognition (ICPR'06). IEEE, 2006. http://dx.doi.org/10.1109/icpr.2006.174.

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Rodrigues, Rodrigo, Rubens Pasa, Karine Kavalco, and João Fernando Mari. "Segmentation of fish chromosomes in microscopy images: A new dataset." In Workshop de Visão Computacional. Sociedade Brasileira de Computação - SBC, 2020. http://dx.doi.org/10.5753/wvc.2020.13481.

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Анотація:
The chromosome segmentation is the most important step in automatic karyotype assembling. In this work, we presented a brand new chromosome image dataset and proposed methods for segmenting the chromosomes. Chromosome images are usually low quality, especially fish chromosomes. In order to overcome this issue, we tested three filters to reduce noise and improve image quality. After filtering, we applied adaptive threshold segmentation combined with mathematical morphology and supervised classification methods. Support Vector Machine and k-nearest neighbors were applied to discriminate between chromosomes and image background. The proposed method was applied to segment chromosomes in a new dataset. To enable measure the performance of the methods all chromosomes were manually delineated. The results are evaluated considering the Hausdorff distance and normalized sum of distances between segmented and reference images.
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Xu, Jinbo, and Yong Dou. "Robust and real-time automatic target recognition using partial hausdorff distance measure on reconfigurable hardware." In 2006 IEEE International Conference on Field Programmable Technology. IEEE, 2006. http://dx.doi.org/10.1109/fpt.2006.270387.

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