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Lines and free line segments tangent to arbitrary threedimensional convex polyhedra
 SIAM Journal on Computing
, 2006
"... SUE WHITESIDES∗ ∗ Abstract. Motivated by visibility problems in three dimensions, we investigate the complexity and construction of the set of tangent lines in a scene of threedimensional polyhedra. We prove that the set of lines tangent to four possibly intersecting convex polyhedra in R 3 with a ..."
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Cited by 24 (15 self)
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SUE WHITESIDES∗ ∗ Abstract. Motivated by visibility problems in three dimensions, we investigate the complexity and construction of the set of tangent lines in a scene of threedimensional polyhedra. We prove that the set of lines tangent to four possibly intersecting convex polyhedra in R 3 with a
On the Number of Maximal Free Line Segments Tangent to Arbitrary Threedimensional Convex Polyhedra
, 2005
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Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme
Three dimensional manifolds, Kleinian groups and hyperbolic geometry
 BULL. AMER. MATH. SOC
, 1982
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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 659 (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.
Fitting Parameterized ThreeDimensional Models to Images
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1991
"... Modelbased recognition and motion tracking depends upon the ability to solve for projection and model parameters that will best fit a 3D model to matching 2D image features. This paper extends current methods of parameter solving to handle objects with arbitrary curved surfaces and with any nu ..."
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Cited by 358 (8 self)
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Modelbased recognition and motion tracking depends upon the ability to solve for projection and model parameters that will best fit a 3D model to matching 2D image features. This paper extends current methods of parameter solving to handle objects with arbitrary curved surfaces and with any
Lines tangent to four triangles in threedimensional space
 PROC. 16TH CANAD. CONF. COMPUT. GEOM
, 2005
"... We investigate the lines tangent to four triangles in R³. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangents, and at most 156 if the triangles are disjoint. In addition, if the triangles are in (algebraic) general position, th ..."
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Cited by 6 (1 self)
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We investigate the lines tangent to four triangles in R³. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangents, and at most 156 if the triangles are disjoint. In addition, if the triangles are in (algebraic) general position
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 543 (11 self)
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of graphs in twodimensional manifolds. This structure represents simultaneously an embedding, its dual, and its mirror image. Furthermore, just two operators are sufficient for building and modifying arbitrary diagrams.
Light Field Rendering
, 1996
"... A number of techniques have been proposed for flying through scenes by redisplaying previously rendered or digitized views. Techniques have also been proposed for interpolating between views by warping input images, using depth information or correspondences between multiple images. In this paper, w ..."
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Cited by 1354 (22 self)
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, we describe a simple and robust method for generating new views from arbitrary camera positions without depth information or feature matching, simply by combining and resampling the available images. The key to this technique lies in interpreting the input images as 2D slices of a 4D function
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 540 (5 self)
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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
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