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Matching geometric objects with respect to their Hausdorff distance is a well investigated problem in computational geometry with various application areas. The variant investigated in this paper is motivated by the problem of det...
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Matching geometric objects with respect to their Hausdorff distance is a well investigated problem in computational geometry with various application areas. The variant investigated in this paper is motivated by the problem of determining a matching (in this context also called registration) for neurosurgical operations. The task is: given a sequence P of weighted point sets (anatomic landmarks measured from a patient), a second sequence Q of corresponding point sets (defined in a 3D model of the patient) and a transformation class T, compute the transformations t ∈ T that minimize the weighted directed Hausdorff distance of t(P) to Q. The weighted Hausdorff distance, as introduced in this paper, takes the weights of the point sets into account. For this application, a weight reflects the precision with which a landmark can be measured. We present an exact solution for translations in the plane, a simple 2-approximation as well as a FPTAS for translations in arbitrary dimension and a constant factor approximation for rigid motions in the plane or in R~3.
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In this paper, a new weighted Hausdorff distance measure is proposed for face localization. The weighting function in the new Hausdorff distance measure has large values at important locations, in which the values are proportional...
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In this paper, a new weighted Hausdorff distance measure is proposed for face localization. The weighting function in the new Hausdorff distance measure has large values at important locations, in which the values are proportional to the frequency of edge points appearing. Thus, the weighting function can reflect the common properties of face edge maps effectively. When comparing the edge maps of the face model and that of a candidate face region in face localization, the weighted Hausdorff distance incorporates information about the location of important edge points so that the face can be localized more accurately. Experimental results show the new weighted Hausdorff distance measure achieves accurate face localization.
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With the emergence of digital libraries, more and more documents are stored and transmitted through the Internet in the format of compressed images. It is of significant meaning to develop a system which is capable of retrieving d...
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With the emergence of digital libraries, more and more documents are stored and transmitted through the Internet in the format of compressed images. It is of significant meaning to develop a system which is capable of retrieving documents from these compressed document images. Aiming at the popular compression standard-CCITT Group 4 which is widely used for compressing document images, we present an approach to retrieve the documents from CCITT Group 4 compressed document images in this paper. The black and white changing elements are extracted directly from the compressed document images to act as the feature pixels, and the connected components are detected simultaneously. Then the word boxes are bounded based on the merging of the connected components. Weighted Hausdorff distance is proposed to assign all of the word objects from both the query document and the document from database to corresponding classes by an unsupervised classifier, whereas the possible stop words are excluded. Document vectors are built by the occurrence frequency of the word object classes, and the pair-wise similarity of two document images is represented by the scalar product of the document vectors. Nine groups of articles pertaining to different domains are used to test the validity of the presented approach. Preliminary experimental results with the document images captured from students' theses show that the proposed approach has achieved a promising performance. (C) 2002 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved. [References: 20]
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In this note we prove that the Hausdorff distance between compact sets and the Kantorovich distance between measures, provide an adequate setting for the convergence of Muckenhoupt weights. The results which we prove on compact me...
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In this note we prove that the Hausdorff distance between compact sets and the Kantorovich distance between measures, provide an adequate setting for the convergence of Muckenhoupt weights. The results which we prove on compact metric spaces with finite metric dimension can be applied to classical fractals.
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In this paper we have introduced the notion of distance between two single valued neutrosophic sets and studied its properties. We have also defined several similarity measures between them and investigated their characteristics. ...
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In this paper we have introduced the notion of distance between two single valued neutrosophic sets and studied its properties. We have also defined several similarity measures between them and investigated their characteristics. A measure of entropy of a single valued neutrosophic set has also been introduced.
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An approach to searching for user-specified words in imaged Chinese documents, without the requirements of layout analysis and OCR processing of the entire documents, is proposed in this paper. A small number of Chinese characters...
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An approach to searching for user-specified words in imaged Chinese documents, without the requirements of layout analysis and OCR processing of the entire documents, is proposed in this paper. A small number of Chinese characters that cannot be successfully bounded using connected component analysis due to larger gaps between elements within the characters are blacklisted. A suitable character that is not included in the blacklist is chosen from the user-specified word as the initial character to search for a matching candidate in the document. Once a matched candidate is found, the adjacent characters in the horizontal and vertical directions are examined for matching with other corresponding characters in the user-specified word, subject to the constraints of alignment (either horizontal or vertical direction) and size similarity. A weighted Hausdorff distance is proposed for the character matching. Experimental results show that the present method can effectively search the user-specified Chinese words from the document images with the format of either horizontal or vertical text lines, or both appearing on the same image.
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The aim of this note is to study "saturation" of the Chi and weighted Erlang cumulative distribution functions M(t) = 1 - 1/(Γ(k/2))Γ(k/2,t~2/2) M_1(t) = 1 - 1/Γ(λ+θ)Γ(λ+θ,t/β), respectively, to the horizontal asymptote w...
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The aim of this note is to study "saturation" of the Chi and weighted Erlang cumulative distribution functions M(t) = 1 - 1/(Γ(k/2))Γ(k/2,t~2/2) M_1(t) = 1 - 1/Γ(λ+θ)Γ(λ+θ,t/β), respectively, to the horizontal asymptote with respect to Hausdorff distance. We prove upper and lower estimates for the one-sided Hausdorff approximation of the Heaviside step-function h_(t_1) (t) by means of these families. Numerical examples on real datasets (1. "actual data to estimate the number of software residual faults" and 2. "2017 meningitis outbreak data were obtained from Nigeria Centre for Disease Control") using CAS Mathematica, illustrating our results are given.
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In this paper we will consider the possibility of approximating the input function s(t) in the differential model y'(t) = ky(t)s(t); y(t_0) — y_o with the Gupta-Kundu [7] type correction. We prove upper and lower estimates for th...
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In this paper we will consider the possibility of approximating the input function s(t) in the differential model y'(t) = ky(t)s(t); y(t_0) — y_o with the Gupta-Kundu [7] type correction. We prove upper and lower estimates for the onesided Hausdorff approximation of the Heaviside step-function h_(t*) (t) by means of a new logistic family. Numerical examples, illustrating our results are given.
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Theories of random sets and fuzzy random sets are useful concepts which are frequently applied in scientific areas including information science, probability and statistics. In this paper strong limit theorems are derived for rand...
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Theories of random sets and fuzzy random sets are useful concepts which are frequently applied in scientific areas including information science, probability and statistics. In this paper strong limit theorems are derived for random sets and fuzzy random sets with slowly varying weights in separable Banach spaces. Both independent and dependent cases are covered to provide a wide range of applications. (C) 2008 Elsevier Inc. All rights reserved.
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In this article, we propose a new weighted Z-similarity measure between two Z-numbers, which is able to retain the original information provided by experts in linguistic terms. This measure takes care of the directional aspect of ...
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In this article, we propose a new weighted Z-similarity measure between two Z-numbers, which is able to retain the original information provided by experts in linguistic terms. This measure takes care of the directional aspect of reliability of information by leveraging the Hausdorff distance. Probabilistic-approach-based statistical distance measure is used to characterize the internal relationship between two parts of a Z-number. Some properties of the Z-similarity measure are proved. The measure is capable of quantifying the probability of basic events in bow-tie analysis. It is experimentally shown that the Z-similarity measure is able to overcome the lacuna of the available techniques. Sensitivity analysis is done to verify its feasibility and applicability. We further propose another measure, called Z-similarity-based basic event contribution (Z-BEC), to quantify the contribution of basic events to the occurrence of different accidents. The performance of the Z-BEC measure is compared with that of Fussell-Vesely index and Birnbaum's structural index.
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