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32
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 603 (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...
Hierarchic Voronoi Skeletons
, 1995
"... Robust and timeefficient skeletonization of a (planar) shape, which is connectivity preserving and based on Euclidean metrics, can be achieved by first regularizing the Voronoi diagram (VD) of a shape's boundary points, i.e., by removal of noisesensitive parts of the tessellation and then by ..."
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Cited by 154 (3 self)
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Robust and timeefficient skeletonization of a (planar) shape, which is connectivity preserving and based on Euclidean metrics, can be achieved by first regularizing the Voronoi diagram (VD) of a shape's boundary points, i.e., by removal of noisesensitive parts of the tessellation and then by establishing a hierarchic organization of skeleton constituents. Each component of the VD is attributed with a measure of prominence which exhibits the expected invariance under geometric transformations and noise. The second processing step, a hierarchic clustering of skeleton branches, leads to a multiresolution representation of the skeleton, termed skeleton pyramid.
Matching 3D Anatomical Surfaces with NonRigid Deformations using OctreeSplines
 International Journal of Computer Vision
, 1996
"... Abstract. This paper presents a new method for determining the minimal nonrigid deformation between two 3D surfaces, such as those which describe anatomical structures in 3D medical images. Although we match surfaces, we represent the deformation as a volumetric transformation. Our method perform ..."
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Cited by 148 (2 self)
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Abstract. This paper presents a new method for determining the minimal nonrigid deformation between two 3D surfaces, such as those which describe anatomical structures in 3D medical images. Although we match surfaces, we represent the deformation as a volumetric transformation. Our method performs a least squares minimization of the distance between the two surfaces of interest. To quickly and accurately compute distances between points on the two surfaces, we use a precomputed distance map represented using an octree spline whose resolution increases near the surface. To quickly and robustly compute the deformation, we use a second octree spline to model the deformation function. The coarsest level of the deformation encodes the global (e.g., affine) transformation between the two surfaces, while finer levels encode smooth local displacements which bring the two surfaces into closer registration. We present experimental results on both synthetic and real 3D surfaces. 1.
Automatic Target Recognition by Matching Oriented Edge Pixels
 IEEE Transactions on Image Processing
, 1997
"... This paper describes techniques to perform efficient and accurate target recognition in difficult domains. In order to accurately model small, irregularly shaped targets, the target objects and images are represented by their edge maps, with a local orientation associated with each edge pixel. Three ..."
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Cited by 124 (5 self)
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This paper describes techniques to perform efficient and accurate target recognition in difficult domains. In order to accurately model small, irregularly shaped targets, the target objects and images are represented by their edge maps, with a local orientation associated with each edge pixel. Threedimensional objects are modeled by a set of twodimensional views of the object. Translation, rotation, and scaling of the views are allowed to approximate full threedimensional motion of the object. A version of the Hausdorff measure that incorporates both location and orientation information is used to determine which positions of each object model are reported as possible target locations. These positions are determined efficiently through the examination of a hierarchical cell decomposition of the transformation space. This allows large volumes of the space to be pruned quickly. Additional techniques are used to decrease the computation time required by the method when matching is perfo...
Evaluation of 14 nonlinear deformation algorithms applied to human brain MRI registration
 NEUROIMAGE 46 (2009) 786–802
, 2009
"... ..."
2D Euclidean distance transform algorithms: A comparative survey
 ACM COMPUTING SURVEYS
, 2008
"... The distance transform (DT) is a general operator forming the basis of many methods in computer vision and geometry, with great potential for practical applications. However, all the optimal algorithms for the computation of the exact Euclidean DT (EDT) were proposed only since the 1990s. In this wo ..."
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Cited by 59 (4 self)
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The distance transform (DT) is a general operator forming the basis of many methods in computer vision and geometry, with great potential for practical applications. However, all the optimal algorithms for the computation of the exact Euclidean DT (EDT) were proposed only since the 1990s. In this work, stateoftheart sequential 2D EDT algorithms are reviewed and compared, in an effort to reach more solid conclusions regarding their differences in speed and their exactness. Six of the best algorithms were fully implemented and compared in practice.
How qualitative spatial reasoning can improve strategy game AIs
 IEEE Intelligent Systems
, 2001
"... Spatial reasoning is a major source of difficulties for strategy game AIs. We conjecture that qualitative spatial reasoning techniques can help overcome these difficulties. We briefly review the relevant qualitative reasoning ideas, and outline four potential advantages of our approach. We desc ..."
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Cited by 39 (3 self)
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Spatial reasoning is a major source of difficulties for strategy game AIs. We conjecture that qualitative spatial reasoning techniques can help overcome these difficulties. We briefly review the relevant qualitative reasoning ideas, and outline four potential advantages of our approach. We describe two explorations in progress: How visual routines can be used to quickly compute qualitative spatial descriptions for war games, and how qualitative descriptions can help in pathfinding. Introduction Creating good strategy game AIs is hard. Spatial reasoning is a major source of difficulties: Terrain is of vital importance in war games, and geography is key in Civilizationstyle empire/trading games. Since today's strategy AI's are tightly bound to the underlying game world simulation, it is hard to start their development before the game world is up and running, and harder still to reuse the algorithms and representations in a new game, unless the underlying engine is extremely s...
An Image Processing System for Driver Assistance
, 1998
"... Systems for automated image analysis are useful for a variety of tasks and their importance is still growing due to technological advances and an increase of social acceptance. Especially in the field of driver assistance systems the progress in science has reached a level of high performance. Fully ..."
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Cited by 30 (8 self)
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Systems for automated image analysis are useful for a variety of tasks and their importance is still growing due to technological advances and an increase of social acceptance. Especially in the field of driver assistance systems the progress in science has reached a level of high performance. Fully or partly autonomously guided vehicles, particularly for roadbased tra#c, pose high demands on the development of reliable algorithms due to the conditions imposed by natural environments. At the Institut fur Neuroinformatik methods for analyzing driving relevant scenes by computer vision are developed in cooperation with several partners from the automobile industry. We introduce a system which extracts the important information from an image taken by a CCD camera installed at the rear view mirror in a car. The approach consists of a sequential and a parallel sensor and information processing. Three main tasks namely the initial segmentation (object detection), the object tracking and the object classification are realized by integration in the sequential branch and by fusion in the parallel branch. The main gain of this approach is given by the integrative coupling of di#erent algorithms providing partly redundant information.
Optical Character Recognition for Typeset Mathematics
 Proc. of Int'l Symp. on Symbolic and Algebraic Computation, (ACM Press) (ISSAC94
, 1994
"... There is a wealth of mathematical knowledge that could be potentially very useful in many computational applications, but is not available in electronic form. This knowledge comes in the form of mechanically typeset books and journals going back more than a hundred years. Besides these older sources ..."
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Cited by 19 (3 self)
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There is a wealth of mathematical knowledge that could be potentially very useful in many computational applications, but is not available in electronic form. This knowledge comes in the form of mechanically typeset books and journals going back more than a hundred years. Besides these older sources, there are a great many current publications, filled with useful mathematical information, which are difficult if not impossible to obtain in electronic form. What we would like to do is extract character information from these documents, which could then be passed to higherlevel parsing routines for further extraction of mathematical content (or any other useful 2dimensional semantic content). Unfortunately, current commercial OCR (optical character recognition) software packages are quite unable to handle mathematical formulas, since their algorithms at all levels use heuristics developed for other document styles 1 . We are concerned with the development of OCR methods that are able...