Hausdorff distance

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Bulgare Sci. , 1993 ). For a survey about similarity measures and shape matching refer to [3]. Introduction. where. Therefore, Hausdorff distance can be used as a measure to determine the degree of resemblance between two objects ( Huttenlocher et al. Distances between pairs are calculated using a Euclidean metric. The feasibility of our method is verified by both simulation and implementation on omni-directional vehicles. First, the distances from the reference surface to the test surface are measured, and then the distances from the test surface to the reference surface are measured. When r is very small, N ( r) grows polynomially with 1/ r. In other words, it is the greatest of all the distances from a point in one set to the closest point in the other set. We introduce its quadratic relaxation over a convex polytope whose solutions provably deliver the Gromov--Hausdorff distance. Mar 3, 2015 · The Hausdorff distance (HD) between two point sets is a commonly used dissimilarity measure for comparing point sets and image segmentations. Three of these distances, namely the city block, chessboard and Euclidean distances are the most popular in pattern recognition and image processing applications. ResourceFunction [ "DiscreteHausdorffDistance"] [ set1, set2] returns the Hausdorff distance between two sets, which is the maximum distance you need to travel from a point in one set to reach a point in the other. In this work, a novel, parallel and locality-oriented Hausdorff distance implementation is proposed. Robust variants. The metric used is based on an approximation of the Hausdorff distance, which has been appropriately implemented in order to reduce unnecessary computation and memory usage. e. It identifies the point that is farthest from any point of B, and measures the distance Sep 18, 2015 · The Yau-Hausdorff distance is then defined in terms of H 1 (A,B): (5) where P x (A θ) is an one-dimensional point set representing the projection of A on the x-axis after being rotated counterclockwise by θ. • A moving window is utilized for the recursive calculation to advance sensitivity and reduce computation. If Z is a nonempty subfamily of M. Edge images are less affected by illumination variations. We will say that vertices x and y correspond to each other if d(x;y) = d HX;Y. 0 License . Modified 5 years, 8 months ago. 5132, that is larger than the value provided by the composite method. Felix Hausdorff (/ ˈ h aʊ s d ɔːr f / HOWS-dorf, / ˈ h aʊ z d ɔːr f / HOWZ-dorf; November 8, 1868 – January 26, 1942) was a German mathematician, pseudonym Paul Mongré (à mon gré (Fr. (eds) Hausdorff Approximations. (1990). May 12, 2023 · We introduce a Hausdorff distance-based cost for Hungarian matching, which more accurately quantifies the discrepancy between predictions and ground truths. In this paper, a new fault location method based on traveling wave differential current with Hausdorff distance and cubic spline interpolation is proposed. We evaluate our method with three datasets designed to locate people's heads, pupil centers and plant centers. #. These measures can be used to match two sets of edge points extracted from any two objects. Hausdorff Distance. Except as otherwise noted, the content of this page is licensed under the Creative Commons Attribution 4. 2 Hausdorff fraction W e Þ x a minimum acceptable distance k. The directed Hausdorff distance from A to 13, h(A. The Fréchet distance in this example is actually about half the horizontal length of the figure, because the point on f f can only move forwards while the point on g g goes back and forth between the left and right extremes. However, there are many examples of non-Hausdorff topological spaces, the simplest of which is the trivial topological space consisting of a set X with at least two points and just X and the empty set as the open sets We would like to show you a description here but the site won’t allow us. Sendov, B. （兩個有相同閉包的子集的豪斯多夫距離是零）。. Feb 1, 2006 · The Hausdorff distance associated to each class is parameterized by a vector of weights and the best solution for this vector of weights provided by the clustering method is also presented in this paper. The algorithms are polynomial in the Jan 1, 2003 · Hausdorff distance is a max–min distance that measures the extent to which two images are similar or different to one another based on their edge maps. Ask Question Asked 5 years, 8 months ago. Jan 21, 2021 · Average Hausdorff distance is a widely used performance measure to calculate the distance between two point sets. Go to the Dictionary of Algorithms and Felix Hausdorff (1868 -1942) devised a metric function between subsets of a metric space. The proposed method does not require one to "guess" the maximum number of objects in the image, and has no notion of bounding boxes, region proposals, or sliding windows. Jan 7, 2008 · Hausdorff clustering. The function h (A,B) is called the directed Hausdorff `distance' from A to B (this function is not symmetric and thus is not a true distance). A straightforward, naive algorithm computes the Hausdorff distance between two point sets A and B âˆ— Corresponding author. This distance between 2-dimensional sets is important in image processing in which the sets are pixelized objects residing in a grid of M x N pixels or cells. According to Benoit Mandelbrot, "A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension . In section 9. S. RandomState seed. 46 (10) 21-24. First, the forward and reverse traveling waves at both ends of the VSC based DC lines are extracted, the Karenbauer transform is used to decouple the positive and negative electrodes to Suffers from same robustness problems as classical Hausdorff distance. Input array. import matplotlib. We then generalize the developments for the Hausdorff distance between two set-valued integrals obtained by applying a parametric family of linear maps to different $\ell_p$ unit norm balls, and then taking the Sep 25, 2023 · The Hausdorff distance measure can be calculated using the formula below: Let , are CIFHSs then Hausdorff distance measures will discussed as 4. The dendrograms are scrutinized and their features confronted. squareform (X[, force, checks]) Convert a vector-form distance vector to a square-form distance matrix, and vice-versa. Title: Comparing images using the Hausdorff distance - Pattern Analysis and Mac hine Intelligence, IEEE Transactions on Author: IEEE Created Date In this paper, we present a trajectory clustering algorithm CTHD (clustering of trajectory based on hausdorff distance). distance. The dendrograms are scrutinized and their features compared. Sendov 1993 "Integral Hausdorff distance" C. Mémoli RegionHausdorffDistance is also known as Hausdorff metric and Pompeiu – Hausdorff distance. Oct 17, 2019 · The recently proposed graph Relative Hausdorff (RH) distance ( Simpson et al. The conventional Hausdorff distance is calculated by using only individual point and each point is equally weighted. directed_hausdorff# scipy. In medical image segmentation, it is used to compare ground truth images with segmentations allowing their ranking. The Hausdorff linkage relies of firm Feb 9, 2021 · Abstract. We identified, however, The notion of the Hausdorff distance was introduced by Felix Hausdorff in 1914 . Mathematics and Its Applications, vol 50. 12 (1) 31-65. These curves allow us to consider a Nov 1, 2011 · 1. with respect to the topology generated by D [5]. random. According to Berger [2], Gromov ﬁrst introduced the F. The (3D) Yau-Hausdorff distance can be used in particular to measure the similarity/dissimilarity of two proteins of any size and does not need aligning and superimposing two structures. 1 we give the definition of Hausdorff distance in the set of all bounded functions in a given interval and we consider some of its properties. Keywords Gromov–Hausdorff distance · Metric geometry · Curvature sets 1 Introduction The Gromov–Hausdorff distance is a useful tool for studying topological properties of families of metric spaces. Google Scholar [10] Bl. : +49 3083875159. scipy. Apr 24, 2014 at 19:12. 4. then we will use the following notation: The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. D(X, Y) is called the Hausdorff distance between sets X. The Hausdorff distance is a metric used to measure the similarity or dissimilarity between two sets of points in a metric space. Sep 1, 2023 · These estimates upper bound the Hausdorff distance or its expectation, depending on whether the linear map is arbitrary or random. 2868) and reaches it in 500 iterations. There are many applications that benefit from an efficient computation of the Hausdorff distance, including shape matching [1], mesh simplification [2], geometric approximation [3], and penetration depth calculation for physically based animation [4]. De nition 6. We explain what is Hausdorff distance, an give an algorithm for computing it in linear time for convex polygons. 這給予 M 的所有子集組成的集一個偽度量。. Acad. 2015) is a promising measure for quantifying similarity between graphs via their degree distributions. Given two sets of points and , the Hausdorff distance is defined as. However, edge images do not carry the overall facial appearance. Feb 12, 2021 · : Computes the Hausdorff distance from point_set_a to point_set_b. We mention what is often a more useful formulation of the Gromov-Hausdor distance. Oct 28, 2008 · A clustering algorithm based on the Hausdorff distance is analyzed and compared to the single, complete, and average linkage algorithms. Aug 6, 2002 · The purpose of object matching is to decide the similarity between two objects. Aug 5, 2013 · Many mathematicians have obtained results in the theory of approximation of functions with respect to the Hausdorff distance – the results are collected in the book of Bl. A very natural distance measure for comparing shapes and patterns is the Hausdorff distance. ハウスドルフ距離. Especially when very large point sets are compared using the HD, for example when evaluating magnetic resonance volume segmentations, or when the underlying applications are based on time critical tasks, like motion detection, then the computational Jul 25, 2023 · The Gromov--Hausdorff distance measures the difference in shape between compact metric spaces and poses a notoriously difficult problem in combinatorial optimization. /3), can then be thought of as he radius of the smallest closed disk which anbe drawn about each point ofA such that each disk contains t least one point ofB. Existing Hausdorff distance-based measures for face recognition are defined between edge images of faces. The Hausdorff distance is a measure of the largest Sep 4, 2021 · We propose two algorithms to approximate the Hausdorff distance between two sets of the Euclidean space $$\\mathbb {R}^{m}$$ R m , whenever such sets can be described as the image of continuous functions defined in suitable domains. Moreover, we note that a static denoising approach hampers the training of rotated DETR, particularly when the detector's predictions surpass the quality of noised ground truths. 12 In a Hausdorff calculation, the minimum distance is measured twice. A map f : X !Y (not necessarily continuous) between metric spaces is called an -GHA (for \Gromov-Hausdor approximation") if jd Y(f(x 1);f(x 2)) d X(x 1;x 2)j< for all x 1;x 2 2X, and Y is in the -neighborhood of f(X). Sendov 1996 "Mathematical modeling of real-world images" Constr. We propose Hausdorff distance as a 3D aperture metric for the rough-walled 3D rock fracture. We can de ne a new distance In mathematics, Hausdorff measure is a generalization of the traditional notions of area and volume to non-integer dimensions, specifically fractals and their Hausdorff dimensions. Find the Hausdorff distance between two sets of elements. Hausdorff space. This distance measures how far two compact metric spaces are from being isometric. ハウスドルフ距離は1914年に出版されたフェリックス・ハウスドルフの著書集合論基礎に現れている。. Although popular, its main weakness is computing power consumption, being one of the slowest set distances. Note: Adapted from [AS98, page 437]. 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. The optimality guarantee is enabled by the fact that the search space of our approach is not Dec 1, 2010 · The Hausdorff distance has also been used in the design of sampling density for smooth surface approximation using discrete triangular meshes reconstructed from sample points on the surface [6]. Secondly, a least-squares fitting method fits the extracted contour Jan 1, 2015 · The subgradient method produces the following value for the minimum point of the Hausdorff distance xËœ = (âˆ’0. The three clustering procedures are applied to a toy example and to the time series of financial data. D is a pseudometric on M and it is a complete metric on Moreover, Afc forms a closed subspace of Mc Mc. Hausdorff Distance Image Comparison. Approx. W e pick Tö to minimize this score. Miscellaneous examples Apr 30, 2004 · Sendov 1990 Hausdorff approximations (Kluwer, Dordrecht) Crossref Google Scholar [9] Bl. The Gromov–Hausdorff distance was introduced by David Edwards in 1975, and it was later rediscovered and generalized by Mikhail Gromov in 1981. Consider the number N ( r) of balls of radius at most r required to cover X completely. Set the norm used to compute the Hausdorff value between two shapes. Sep 8, 2018 · A way to prove that Hausdorff distance is complete. Max intuitively worse but sum also bad. The Hausdorff linkage relies on firm mathematical grounds and turns out to be very effective Jun 23, 2022 · These estimates upper bound the Hausdorff distance or its expectation, depending on whether the linear map is arbitrary or random. Tel. The Hausdorff distance is the maximum distance between any point on the first set and its nearest point on the second set, and vice-versa. Contrary to the notion of shortest distance, which collapses under situations of complex geometrical structures, HD considers relative position and A similar argument confirms that any metric space, in which open sets are induced by a distance function, is a Hausdorff space. The operation works on a 1-to-1 row-wise manner: The Geoseries (elementwise) or geometric object to find the distance to. Results show that when compared to similar tools, a significant gain in both memory and Hausdorff Distance Image Comparison. In these calculations the Hausdorff distance is evaluated at the level d(A,B + {xËœ}) = 0. directed_hausdorff (u, v, seed = 0) [source] # Compute the directed Hausdorff distance between two 2-D arrays. Compute the directed Hausdorff distance between two N-D arrays. Compute the directed Hausdorff distance between two 2-D arrays. Similarly, machine learning-based image segmentation methods aim at reducing a global The Hausdorff distance (HD) between two point sets is a commonly used dissimilarity measure for comparing point sets and image segmentations. v (O,N) array_like Dec 17, 2004 · Hausdorff distance. Trimmed: sum the K smallest distances (same as Hausdorff but sum rather than largest of K) Truncated: truncate individual distances before summing. Next the similarity between trajectories is measured by their respective Hausdorff distances. Jun 1, 2021 · 1. Based on experiments on synthetic images containing various levels of noise, the authors determined that one of Cite this chapter. – user856. In this paper, we present novel loss functions for training convolutional neural network (CNN)-based segmentation methods with the goal of reducing HD directly. To verify its plausibility, we construct a fracture model from a 3D scanned crystalline rock sample. Apr 22, 2014 · 1. If True, automatically aligns GeoSeries based on their indices. 1 Hausdorff hamming distance measure. A clustering algorithm based on the Hausdorff distance is introduced and compared to the single and complete linkage. 2. The Hausdorff distance measures how different two regions are from each other. In this article we develop algorithms for computing the Hausdorff distance in a very general case in which geometric objects are represented by finite collections of k-dimensional simplices in d-dimensional space. Two objects A and B in a black and white image are identical iff the Hausdorff distance between them is 0. It measures the distance between the set of coordinates of the difference between The Hausdorff Distance (HD) is widely used in evaluating medical image segmentation methods. The four clustering procedures are applied to a toy example and to the time series of financial data. The Yau-Hausdorff distance D defined above possesses the following properties: Hausdorff distance to the work of Boutin and Kemper, and Olver. In this paper, we employ the Euclidean distance. @Rahul Yes, you are right, I forgot to mention that it is actually the weak Pytorch-Hausdorff-Distance. 0218,âˆ’0. While the exact value of the Gromov–Hausdorff distance is rarely useful to know, the resulting topology has found many applications. The distance between points p and q is taken to Dec 1, 2011 · In previous Hausdorff distance (HD) measures, points are treated as same importance, or weight different points that calculated from gray domain. ) = "according to my taste"), who is considered to be one of the founders of modern topology and who contributed significantly to set theory, descriptive set theory, measure theory, and functional Compute distance between each pair of the two collections of inputs. Such algorithms are derived from the main results of the paper, which are based on the so called $$\\alpha$$ α -dense curves. Dec 1, 2015 · Hausdorff distance measures the distance between two sets in a metric space. First, the acquired potato image is resized, translated, segmented, and filtered to obtain the potato contour information. , in time O(ab). W e accept itif sH Tö is less than some threshold value, s0. Input array with M points in N dimensions. In the CTHD, the trajectory is firstly described by a sequence of flow vectors and partitioned into a set of sub-trajectory. spatial. In: Beer, G. 1 One-sided Hausdorff distance F or each T , the Hausdorf f scor e, sH T , is m axi dT i. The graphical representations of DNA sequences conserve all sequence information and the Yau-Hausdorff distance is mathematically proved as a true metric. Dec 8, 2023 · This paper is concerned with the Gromov–Hausdorff stability of global attractors for the 3D Navier–Stokes equations with damping under variations of the domain, which describes the complexity of the dynamics of the motion of a fluid flow. A schematic showing the Hausdorff Distance between points sets Xand Y. . The Gromov-Hausdor distance between two graphs X and Y is d GH(X;Y) = inf i:X,!Z;j:Y ,!Z d H(i(X);j(Y)): The Gromov-Hausdor distance between X and Y is de ned Jul 22, 2011 · Related work The Hausdorff distance is one of the most studied similarity measures. In topology and related branches of mathematics, a Hausdorff space ( / ˈhaʊsdɔːrf / HOWSS-dorf, / ˈhaʊzdɔːrf / HOWZ-dorf [1] ), separated space or T2 space is a topological space where, for any two distinct points, there exist neighbourhoods of each that are disjoint from each other. Comparison with the commonly used vertical aperture reveals significant advantages in imaging of the possible aperture bottlenecks present in Gromov–Hausdorff distance How far and how near are some figures under the Gromov–Hausdorff distance. This is pytorch implementation of Hausdorff Distance for 2D image binary segmentation. We apply structural similarity to study function similarity and perform phylogenetic analysis on several datasets. We then generalize the developments for the Hausdorff distance between two set-valued integrals obtained by applying a parametric family of linear maps to different $\ell _{p}$ unit norm balls, and then taking the Hausdorff distance (HD) is an useful measurement to determine the extent to which one shape is similar to another, which is one of the most important problems in pattern recognition, computer vision and image analysis. The proposed method has no notion of bounding boxes, region proposals, or sliding windows. The Hausdorff distance is the largest distance consisting of any point in self with the nearest point in other. Viewed 619 times 2 $\begingroup$ I have Apr 1, 2005 · The classical Hausdorff distance. Feb 1, 2007 · New partial Hausdorff distance-based measure ( H pv) for comparing faces. Especially when very large point sets are compared using the HD, for example when evaluating magnetic resonance volume segmentations, or when the underlying a … This paper proposes an efficient method to estimate the distance between discrete 3D surfaces represented by triangular 3D meshes. The distance between two points a and b is defined as d ( a, b) = ∥ a − b ∥. 数学においてハウスドルフ距離（英: Hausdorff distance ）とは距離空間の部分空間同士の隔たりを測る量の一種である。. Definition: A measure of the resemblance of two (fixed) sets of geometric points P and Q, defined as H (P,Q)=max {max a∈ P min b∈ Q d (a,b), max a∈ Q min b∈ P d (a,b)} where d (·,·) is the distance metric, usually the Euclidean distance . It can be L1 or L2 norm. Feb 22, 2023 · Feb 22, 2023. 6 is a good value to compare shapes. Hausdorff in 1914 (see ); one of his most important results is as follows: The space of closed subsets of a compact set is also compact (P. More This method sets the rank proportion (or fractional value) that establish the Kth ranked value of the partial Hausdorff distance. Thus, this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. By definition, two sets are within Hausdorff distance r from each other iff any point of one set is within distance r from some point of the other set. However, the existing segmentation methods do not attempt to reduce HD directly. 0 License , and code samples are licensed under the Apache 2. May 19, 2023 · Hausdorff distance is a representation of the difference in the boundary between GT and prediction as a distance. Given two curves C 1 and C 2, their Hausdorff distance is defined as (1) D H (C 1, C 2) = max {max p ∈ C 1 min q ∈ C 2 ‖ p − q ‖, max q ∈ C May 16, 2023 · Hi everyone, I am facing problem while evaluating my model using the three metrics: 1-compute_hausdorff_distance 2-compute_average_surface_distance 3-MeanIoU This is my result, it looks wrong =(inf scipy. Many early works focused on the Hausdorff distance for finite point sets. Parameters: u (M,N) array_like. 2938,âˆ’0. The Hausdorff distance (HD) is an important algorithm to measure the similarity of two geometric objects because it is defined as MAX-MIN distance between two point sets and it has the ability to determine the degree of resemblance between two point sets without defining the correlation between points. For a set of a points and a set of b points in any fixed dimension, the Hausdorff distance can be computed by checking all pairs, i. 設 X 和 Y 是 Hausdorff distance (GH) versus Hausdorff distance un-der the action of Euclidean isometries (EH). Oct 25, 2020 · In this video, I'll give a bit of motivation, introduce the delta expansion of a set and then give the distance formula for sets and talk through some of the properties of Hausdorff distance Undergraduate tutorial on Hausdorff distance. zeros(shape 非閉子集間的豪斯多夫距離可以定義為它們的閉包的豪斯多夫距離。. ただし A ~ is the set A dilated by a disk ofradius c. In this paper, a new weighting function of HD based on the eigenface from edge domain, which reflects the discriminative properties of face edge images effectively, is proposed for face recognition. Then, we (1) show they are comparable in a precise sense that is not the linear behaviour one would expect and (2) ex-plain the source of this phenomenon via explicit con-structions. This paper introduces 24 possible distance measures based on the Hausdorff distance between two point sets. and Y. Urysohn arrived independently at this theorem in 1921–1922, see ). Efficient algorithms for computing the Hausdorff distance between all possible relative positions of a binary image and a model are This example shows how to calculate the Hausdorff distance between two sets of points. R. The gradient orientation of each point is ignored, which limits the performance of Hausdorff distance in the image registration. Sep 18, 2015 · The Yau-Hausdorff method can be used for measuring the similarity of DNA sequences based on two important tools: the Yau-Hausdorff distance and graphical representation of DNA sequences. Default is 0, a random shuffling of u and v that guarantees reproducibility. The implementation is made for batch-wise inference. Jul 31, 2022 · An ellipse-fitting-based Hausdorff distance and intersection over union (IoU) method for identifying irregular potatoes is proposed to solve the problem. Inspired by the Hausdorff metric from topology ( Hausdorff 1914 ), RH distance was devised to capture degree distribution closeness at all scales, and hence is well Jun 3, 2016 · It was introduced by F. The algorithm was proposed by Atallah (1983), and is illustrated with an interactive applet. Crossref Google Scholar [11] Bl. It identifies the point that is farthest from any point of B, and measures the distance Jun 20, 2018 · This loss function is a modification of the average Hausdorff distance between two unordered sets of points. More formally, let there be a space X with a metric function d. RegionHausdorffDistance is the greatest of all distances from a point in one region to the closest point in the other region. At the present time, the Hausdorff metric is widely used in both abstract and applied areas of mathematics including nonsmooth analysis (see, for example, [2, 3]), optimization theory (see, for example, [2, 4]) and calculus of variations (see, for example, []). directed_hausdorff. The Gromov–Hausdorff stability accounts for the Gromov–Hausdorff distance between two global attractors which may lie in disjoint phase spaces, as Oct 19, 2012 · The Hausdorff distance is a well-known distance measure between two data sets. Contributed by: Sjoerd Smit. It is well known that. The Gromov–Hausdorff distance between compact spaces X and Y is the infimum of the Hausdorff distance over all metric spaces Z that contain X and Y as subspaces. Apr 1, 2023 · An internal short circuit fault detection method for electric vehicle battery by calculating Hausdorff distance is proposed. ¶. directed_hausdorff (u, v[, seed]) Compute the directed Hausdorff distance between two 2-D arrays. Sendov (1979). Local numpy. Experimentally had been shown that 0. We identified, however, ranking errors of average Hausdorff distance m … Jun 26, 2021 · The Hausdorff distance, commonly used in a range of computer vision and image processing tasks, may be regarded as an ideal choice to compute relatively more accurate distances between objects. 在歐幾里得幾何常用一個類似概念，稱為在等距同構下的豪斯多夫距離。. of all these distances, the Hausdor distance between X and Y is the longest distance. Oct 14, 1997 · The Hausdorff distance between A and B will be taken as h(A,B)=da(A)+dA(B). F or each T ,Hausdorf ffraction scor e,sH F T is cardinality sH F T Sep 1, 2021 · Hausdorff distance (HD) is a popular similarity metric used in the comparison of images or 3D volumes. Jan 8, 2013 · Public Member Functions. Remark 2. This loss function is a modification of the Average Hausdorff Distance between two unordered sets of points. 4 Distance measur es 4. Finally, (3) by conveniently modifying the May 12, 2023 · We introduce a Hausdorff distance-based cost for Hungarian matching, which more accurately quantifies the discrepancy between predictions and ground truths. pyplot as plt import numpy as np from skimage import metrics shape = (60, 60) image = np. In the allocation step, the individuals are assigned to the classes according to their (minimum) adaptive Hausdorff distance to the prototypes. Apr 18, 2015 · The concept of distance between sets was introduced and studied in [] by Hausdorff. The Hausdorff distance is a useful measure of the similarity between geometric objects. Figure 1. " [1] Presented here is a list of fractals, ordered by increasing Hausdorff dimension, to illustrate what it means for a fractal to have a low or a high dimension. Aug 29, 2022 · The Hausdorff distance is adopted in the reward function for measuring the distance between the current and target topology. the target image by minimizing such global loss functions as the sum of squared difference of image intensities or the mutual information [12], [13]. Here ϱ are the elements of ℧ which is a universal set, “n” represents the number of elements of universal sets and “m” represents the number of attributes. The Hausdorff distance is the longest distance you can be forced to travel by an adversary who chooses a point in one of the two sets, from where you then must travel to the other set. Contribute to gogoymh/Pytorch-Hausdorff-Distance development by creating an account on GitHub. ws tr ip bt ep xj ka ab dt jo