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Comparing Images Using the Hausdorff Distance
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1993
"... 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. Thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. In this paper we provide ef ..."
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Cited by 485 (9 self)
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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. Thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. In this paper we provide efficient algorithms for computing the Hausdorff distance between all possible relative positions of a binary image and a model. We focus primarily on the case in which the model is only allowed to translate with respect to the image. Then we consider how to extend the techniques to rigid motion (translation and rotation). The Hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived. The method is quite tolerant of small position errors as occur with edge detectors and other feature extraction methods. Moreover, we show how the method extends naturally to the problem of comparing a portion of a model against an i...
Geometric Pattern Matching under Euclidean Motion
, 1993
"... Given two planar sets A and B, we examine the problem of determining the smallest " such that there is a Euclidean motion (rotation and translation) of A that brings each member of A within distance " of some member of B. We establish upper bounds on the combinatorial complexity of this su ..."
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Cited by 71 (2 self)
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Given two planar sets A and B, we examine the problem of determining the smallest " such that there is a Euclidean motion (rotation and translation) of A that brings each member of A within distance " of some member of B. We establish upper bounds on the combinatorial complexity of this subproblem in modelbased computer vision, when the sets A and B contain points, line segments, or (filledin) polygons. We also show how to use our methods to substantially improve on existing algorithms for finding the minimum Hausdorff distance under Euclidean motion. 1 Author's address: Department of Computer Science, Cornell University, Ithaca, NY 14853. This work was supported by the Advanced Research Projects Agency of the Department of Defense under ONR Contract N0001492J1989, and by ONR Contract N0001492J1839, NSF Contract IRI9006137, and AFOSR Contract AFOSR910328. 2 Author's address: Department of Computer Science, Johns Hopkins University, Baltimore, MD 21218. This work was suppo...
Application Challenges to Computational Geometry
, 1996
"... With rapid advances in computer hardware and visualization systems, geometric computing is creeping into virtually every corner of science and engineering, from design and manufacturing to astrophysics to molecular biology to fluid dynamics. This report assesses the opportunities and challenges this ..."
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With rapid advances in computer hardware and visualization systems, geometric computing is creeping into virtually every corner of science and engineering, from design and manufacturing to astrophysics to molecular biology to fluid dynamics. This report assesses the opportunities and challenges this presents for the field of computational geometry in the years ahead. Can CG meet the algorithmic needs of practitioners? Should it look to applied areas for new sources of problems? Can CG live up to its potential and become a key player in the vast and diverse world of geometric computing? These are some of the questions addressed in this document. It was prepared by a group of computer scientists, engineers, and mathematicians with extensive experience in geometric computing. This report is intended as a wakeup call rather than an agenda setter. It is hoped it will engage a communitywide discussion on the future of computational geometry. This document is available as Technical Report ...
ModelBased Object Recognition from a Complex Binary Imagery using Genetic Algorithm
"... . This paper describes a technique for modelbased object recognition in a noisy and cluttered environment, by extending the work presented in an earlier study by the authors. In order to accurately model small irregularly shaped objects, the model and the image are represented by their binary e ..."
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. This paper describes a technique for modelbased object recognition in a noisy and cluttered environment, by extending the work presented in an earlier study by the authors. In order to accurately model small irregularly shaped objects, the model and the image are represented by their binary edge maps, rather then approximating them with straight line segments. The problem is then formulated as that of finding the best describing match between a hypothesized object and the image. A special form of template matching is used to deal with the noisy environment, where the templates are generated online by a Genetic Algorithm. For experiments, two complex test images have been considered and the results when compared with standard techniques indicate the scope for further research in this direction. 1 Introduction Finding the best transformation that maps an object model into the image of a scene is a central issue in object recognition. There are several approaches to this ...
This thesis is dedicated to my mother and the greatest influence on my life, Late Mrs.
, 2005
"... I would like to begin by thanking my parents, albeit I understand any amount of gratitude shown to them is woefully inadequate. My father’s unconditional support is largely the reason that this PhD is completed in United States. No words are sufficient to describe my late mother’s contribution to my ..."
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I would like to begin by thanking my parents, albeit I understand any amount of gratitude shown to them is woefully inadequate. My father’s unconditional support is largely the reason that this PhD is completed in United States. No words are sufficient to describe my late mother’s contribution to my life. I owe every bit of my existence to her. This thesis is dedicated to her memory. I have been lucky to receive tremendous affection from several members in my extended family. Their support and encouragement has been instrumental in my overcoming several hurdles in life. I am particularly grateful to my fiance Nimisha and her parents who have kept exemplary patience while I completed my thesis. I am indeed blessed to have them in my life. I am indebted to my advisor, Prof. Brian Evans. Brian has influenced not only my graduate studies, but my whole life. He has instilled in me by example, a strong sense of discipline and integrity, for which I am eternally grateful. Brian is a deeply committed researcher, teacher, and advisor. Observing him for four years has helped me define my own research goals.
On Characteristic Points and Approximate Decision Algorithms for the Minimum Hausdorff Distance
"... We investigate approximate decision algorithms for determining whether the minimum Hausdorff distance between two points sets (or between two sets of nonintersecting line segments) is at most ". An approximate decision algorithm is a standard decision algorithm that answers yes or no except ..."
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We investigate approximate decision algorithms for determining whether the minimum Hausdorff distance between two points sets (or between two sets of nonintersecting line segments) is at most ". An approximate decision algorithm is a standard decision algorithm that answers yes or no except when " is in an indecision interval where the algorithm is allowed to answer don't know. We present algorithms with indecision interval [ffi \Gamma fl; ffi + fl] where ffi is the minimum Hausdorff distance and fl can be chosen by the user. In other words, we can make our algorithm as accurate as desired by choosing an appropriate fl. For two sets of points (or two sets of nonintersecting lines) with respective cardinalities m and n our approximate decision algorithms run in time O(("=fl) 2 (m + n) log(mn)) for Hausdorff distance under translation, and in time O(("=fl) 2 mn log(mn)) for Hausdorff distance under Euclidean motion. 1 Introduction Determining the extent to which two plana...