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71
Iterative point matching for registration of freeform curves and surfaces
, 1994
"... A heuristic method has been developed for registering two sets of 3D curves obtained by using an edgebased stereo system, or two dense 3D maps obtained by using a correlationbased stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in ma ..."
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Cited by 608 (7 self)
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A heuristic method has been developed for registering two sets of 3D curves obtained by using an edgebased stereo system, or two dense 3D maps obtained by using a correlationbased stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in many practical applications, some a priori knowledge exists which considerably simplifies the problem. In visual navigation, for example, the motion between successive positions is usually approximately known. From this initial estimate, our algorithm computes observer motion with very good precision, which is required for environment modeling (e.g., building a Digital Elevation Map). Objects are represented by a set of 3D points, which are considered as the samples of a surface. No constraint is imposed on the form of the objects. The proposed algorithm is based on iteratively matching points in one set to the closest points in the other. A statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance and disappearance, which allows us to do subsetsubset matching. A leastsquares technique is used to estimate 3D motion from the point correspondences, which reduces the average distance between points in the two sets. Both synthetic and real data have been used to test the algorithm, and the results show that it is efficient and robust, and yields an accurate motion estimate.
Deformable models in medical image analysis: A survey
 Medical Image Analysis
, 1996
"... This article surveys deformable models, a promising and vigorously researched computerassisted medical image analysis technique. Among modelbased techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They hav ..."
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Cited by 540 (7 self)
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This article surveys deformable models, a promising and vigorously researched computerassisted medical image analysis technique. Among modelbased techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They have proven to be effective in segmenting, matching, and tracking anatomic structures by exploiting (bottomup) constraints derived from the image data together with (topdown) a priori knowledge about the location, size, and shape of these structures. Deformable models are capable of accommodating the significant variability of biological structures over time and across different individuals. Furthermore, they support highly intuitive interaction mechanisms that, when necessary, allow medical scientists and practitioners to bring their expertise to bear on the modelbased image interpretation task. This article reviews the rapidly expanding body of work on the development and application of deformable models to problems of fundamental importance in medical image analysis, includingsegmentation, shape representation, matching, and motion tracking.
A Survey of Medical Image Registration
, 1998
"... The purpose of this chapter is to present a survey of recent publications concerning medical image registration techniques. These publications will be classified according to a model based on nine salient criteria, the main dichotomy of which is extrinsic versus intrinsic methods The statistics of t ..."
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Cited by 503 (5 self)
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The purpose of this chapter is to present a survey of recent publications concerning medical image registration techniques. These publications will be classified according to a model based on nine salient criteria, the main dichotomy of which is extrinsic versus intrinsic methods The statistics of the classification show definite trends in the evolving registration techniques, which will be discussed. At this moment, the bulk of interesting intrinsic methods is either based on segmented points or surfaces, or on techniques endeavoring to use the full information content of the images involved. Keywords: registration, matching Received May 25, 1997
Estimating The Tensor Of Curvature Of A Surface From A Polyhedral Approximation
, 1995
"... Estimating principal curvatures and principal directions of a surface from a polyhedral approximation with a large number of small faces, such as those produced by isosurface construction algorithms, has become a basic step in many computer vision algorithms. Particularly in those targeted at medic ..."
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Cited by 215 (5 self)
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Estimating principal curvatures and principal directions of a surface from a polyhedral approximation with a large number of small faces, such as those produced by isosurface construction algorithms, has become a basic step in many computer vision algorithms. Particularly in those targeted at medical applications. In this paper we describe a method to estimate the tensor of curvature of a surface at the vertices of a polyhedral approximation. Principal curvatures and principal directions are obtained by computing in closed form the eigenvalues and eigenvectors of certain # # # symmetric matrices defined by integral formulas, and closely related to the matrix representation of the tensor of curvature. The resulting algorithm is linear, both in time and in space, as a function of the number of vertices and faces of the polyhedral surface. 1
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 145 (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.
RANSACbased DARCES: A New Approach for Fast Automatic Registration of Partially Overlapping Range Images
"... Registration of two partiallyoverlapping range images taken from different views is an important task in 3D computer vision. In general, if there is no initial knowledge about the poses of these two views, the information used for solving the 3D registration problem is mainly the 3D shape of the co ..."
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Cited by 101 (5 self)
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Registration of two partiallyoverlapping range images taken from different views is an important task in 3D computer vision. In general, if there is no initial knowledge about the poses of these two views, the information used for solving the 3D registration problem is mainly the 3D shape of the common parts of the two partiallyoverlapping data sets.
Least squares 3D surface and curve matching
 ISPRS Journal of Photogrammetry and Remote Sensing
, 2005
"... The automatic coregistration of point clouds, representing 3D surfaces, is a relevant problem in 3D modeling. This multiple registration problem can be defined as a surface matching task. We treat it as least squares matching of overlapping surfaces. The surface may have been digitized/sampled poin ..."
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Cited by 85 (17 self)
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The automatic coregistration of point clouds, representing 3D surfaces, is a relevant problem in 3D modeling. This multiple registration problem can be defined as a surface matching task. We treat it as least squares matching of overlapping surfaces. The surface may have been digitized/sampled point by point using a laser scanner device, a photogrammetric method or other surface measurement techniques. Our proposed method estimates the transformation parameters of one or more 3D search surfaces with respect to a 3D template surface, using the Generalized GaussMarkoff model, minimizing the sum of squares of the Euclidean distances between the surfaces. This formulation gives the opportunity of matching arbitrarily oriented 3D surface patches. It fully considers 3D geometry. Besides the mathematical model and execution aspects we address the further extensions of the basic model. We also show how this method can be used for curve matching in 3D space and matching of curves to surfaces. Some practical examples based on the registration of closerange laser scanner and photogrammetric point clouds are presented for the demonstration of the method. This surface matching technique is a generalization of the least squares image matching concept and offers high flexibility for any kind of 3D surface correspondence problem, as well as statistical tools for the analysis of the quality of final matching results.
Tracking Points on Deformable Objects Using Curvature Information
 IN PROCEEDINGS OF THE SECOND EUROPEAN CONFERENCE ON COMPUTER VISION
, 1992
"... The objective of this paper is to present a significant improvement to the approach of Duncan et al. [1, 8] to analyze the deformations of curves in sequences of 2D images. This approach is based on the paradigm that high curvature points usually possess an anatomical meaning, and are therefore good ..."
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Cited by 85 (13 self)
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The objective of this paper is to present a significant improvement to the approach of Duncan et al. [1, 8] to analyze the deformations of curves in sequences of 2D images. This approach is based on the paradigm that high curvature points usually possess an anatomical meaning, and are therefore good landmarks to guide the matching process, especially in the absence of a reliable physical or deformable geometric model of the observed structures. As Duncan's
A Review of Deformable Surfaces: Topology, Geometry and Deformation
 Image and Vision Computing
, 2001
"... Deformable models have raised much interest and found various applications in the fields of computer vision and medical imaging. They provide an extensible framework to reconstruct shapes. Deformable surfaces, in particular, are used to represent 3D objects. They have been used for pattern recogniti ..."
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Cited by 67 (9 self)
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Deformable models have raised much interest and found various applications in the fields of computer vision and medical imaging. They provide an extensible framework to reconstruct shapes. Deformable surfaces, in particular, are used to represent 3D objects. They have been used for pattern recognition [35,2], computer animation [100], geometric modelling [59], simulation [28], boundary tracking [11], image segmentation [69,67,91,5,45], etc. In this paper we propose a survey on deformable surfaces. Many surface representation have been proposed to meet different 3D reconstruction problem requirements. We classify the main representations proposed in the literature and we study the influence of the representation on the model evolution behavior, revealing some similarities between different approaches.
LandmarkBased Registration Using Features Identified Through Differential Geometry
 HANDBOOK OF MEDICAL IMAGING PROCESSING AND ANALYSIS. I. BANKMAN EDITOR. ACADEMIC PRESS. 2000.
, 2000
"... Registration of 3D medical images consists in computing the “best” transformation between two acquisitions, or equivalently, determines the point to point correspondence between the images. Registration algorithms are usually based either on features extracted from the image (featurebased approache ..."
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Cited by 44 (7 self)
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Registration of 3D medical images consists in computing the “best” transformation between two acquisitions, or equivalently, determines the point to point correspondence between the images. Registration algorithms are usually based either on features extracted from the image (featurebased approaches) or on the optimization of a similarity measure of the images intensities (intensitybased or iconic approaches). Another classification criterion is the type of transformation sought (e.g. rigid or nonrigid). In this chapter, we concentrate on featurebased approaches for rigid registration, similar approaches for nonrigid registration being reported in another set of publication [35, 36]. We show how to reduce the dimension of the registration problem by first extracting a surface from the 3D image, then landmark curves on this surface and possibly landmark points on these curves. This concept proved its efficiency through many applications in medical image analysis as we will see in the sequel. This work has been for a long time a central investigation topic of the Epidaure team [2] and we can only reflect here on a small part of the research done in this area. We present in the first section the notions of crest lines and extremal points and how these differential geometry features can be extracted from 3D images. In Section 2, we focus on the different rigid registration algorithms that we used to register such features. The last section analyzes the possible errors in this registration scheme and demonstrates that a very accurate registration could be achieved.