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Between Shapes, Using the Hausdorff Distance
International Symposium on Algorithms and Computation, 2020Given two shapes $A$ and $B$ in the plane with Hausdorff distance $1$, is there a shape $S$ with Hausdorff distance $1/2$ to and from $A$ and $B$? The answer is always yes, and depending on convexity of $A$ and/or $B$, $S$ may be convex, connected, or ...
M. V. Kreveld +4 more
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Hausdorff distance for target detection
2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353), 2003The paper presents a system for target detection in static images based on the Hausdorff distance. The Hausdorff distance can determine the degree of resemblance between an image and a model. As such, the proposed system uses this distance as a cost function for the template matching task.
GASTALDO, PAOLO, ZUNINO, RODOLFO
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On the Hausdorff dimensions of distance sets
Mathematika, 1985The distance set of a subset E of \(R^ n\) is \(D(E)=\{| x- y|:x,y\in E\}.\) If E is analytic (i.e. Suslin), the author uses Fourier transform to derive the following lower bound for the Hausdorff dimension of \(E\): \[ \dim D(E)\geq \min \{1,(\dim E)-(n-1)/2\}. \] Moreover, \(D(E)\) has positive Lebesgue measure if \(\dim E>(n+1)/2\).
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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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Hausdorff dimension and distance sets
Israel Journal of Mathematics, 1994The author uses a brilliant refinement of Fourier restriction phenomena to spheres to improve results on difference sets \(D(A)= \{| x- y|; x,y\in A\}\) for Souslin sets \(A\) in \(\mathbb{R}^ n\) due to Falconer. For example, if \(A\subset \mathbb{R}^ 2\) and the Hausdorff dimension \(\dim A> {13\over 9}\) (instead of \({3\over 2}\) as in Falconer's ...
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Page similarity and the Hausdorff distance
7th International Conference on Image Processing and its Applications, 1999The VideoWriter is a real-time system that uses digitized images from a computer-controlled video camera to find the location of pages on a desktop. Once an image of a page is extracted, the system must determine if the page has been previously stored. We investigate the use of the Hausdorff distance metric to compare two-level versions of page images.
Charles Robertson, John Robinson
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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 for Iris Recognition
2007 IEEE 22nd International Symposium on Intelligent Control, 2007Iris is a promising biometric due to its high reliability and stability. In this paper, a novel iris recognition technique based on Hausdorff distance is proposed. A modified partial Hausdorff distance (a dissimilarity measure) is computed directly between the normalized iris images for comparison and no feature is extracted explicitly.
Y.H.K. Wong, N. Sudha
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Hausdorff distance and convexity
2017The goal of this thesis is to discuss the Hausdorff Distance and prove that the metric space SX , which is the set of compact subsets of X = R n with the hausdorff distance is a complete metric space. In the first part, we discuss open r-neighborhoods and convexity.
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