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91
SelfCalibration from Image Triplets
, 1996
"... We describe a method for determining affine and metric calibration of a camera with unchanging internal parameters undergoing planar motion. It is shown that affine calibration is recovered uniquely, and metric calibration up to a two fold ambiguity. The novel ..."
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Cited by 105 (18 self)
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We describe a method for determining affine and metric calibration of a camera with unchanging internal parameters undergoing planar motion. It is shown that affine calibration is recovered uniquely, and metric calibration up to a two fold ambiguity. The novel
Metric Calibration of a Stereo Rig
 In Proc. IEEE Workshop on Representation of Visual Scenes
, 1995
"... We describe a method to determine affine and metric calibration for a stereo rig. The method does not involve the use of calibration objects or special motions, but simply a single general motion of the rig with fixed parameters (i.e. camera parameters and relative orientation of the camera pair). T ..."
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Cited by 80 (10 self)
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We describe a method to determine affine and metric calibration for a stereo rig. The method does not involve the use of calibration objects or special motions, but simply a single general motion of the rig with fixed parameters (i.e. camera parameters and relative orientation of the camera pair). The novel aspects of this work are: first, relating the distinguished objects of Euclidean geometry to fixed entities of a Euclidean transformation matrix; second, showing that these fixed entities are accessible from the conjugate Euclidean transformation arising from the projective transformation of the structure under a motion of the fixed stereo rig; third, a robust and automatic implementation of the method. Results are included of affine and metric calibration and structure recovery using images of real scenes. 1 Introduction It is known that from two uncalibrated views, 3D structure can be recovered modulo a projectivity of 3space [5, 8]. Furthermore, given three or more views acquir...
On Geometric Assembly Planning
, 1992
"... This dissertation addresses the problem of generating feasible assembly sequences for a mechanical product from a geometric model of the product. An operation specifies a motion to bring two subassemblies together to make a larger subassembly. An assembly sequence is a sequence of operations that co ..."
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Cited by 71 (12 self)
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This dissertation addresses the problem of generating feasible assembly sequences for a mechanical product from a geometric model of the product. An operation specifies a motion to bring two subassemblies together to make a larger subassembly. An assembly sequence is a sequence of operations that construct the product from the individual parts. I introduce the nondirectional blocking graph, a succinct characterization of the blocking relationships between parts in an assembly. I describe efficient algorithms to identify removable subassemblies by constructing and analyzing the NDBG. For an assembly A of n parts and m partpart contacts equivalent to k contact points, a subassembly that can translate a small distance from the rest of A can be identified in O(mk 2 ) time. When rotations are allowed as well, the time bound is O(mk 5 ). Both algorithms are extended to find connected subassemblies in the same time bounds. All free subassemblies can be identified in outputdependent ...
On Computing FourFinger Equilibrium and ForceClosure Grasps of Polyhedral Objects
 International Journal of Robotics Research
, 1996
"... : This paper addresses the problem of computing stable grasps of threedimensional polyhedral objects. We consider the case of a hand equipped with four hard fingers and assume point contact with friction. We prove new necessary and sufficient conditions for equilibrium and force closure, and presen ..."
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Cited by 61 (6 self)
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: This paper addresses the problem of computing stable grasps of threedimensional polyhedral objects. We consider the case of a hand equipped with four hard fingers and assume point contact with friction. We prove new necessary and sufficient conditions for equilibrium and force closure, and present a geometric characterization of all possible types of fourfinger equilibrium grasps. We then focus on concurrent grasps, for which the lines of action of the four contact forces all intersect in a point. In this case, the equilibrium conditions are linear in the unknown grasp parameters, which reduces the problem of computing the stable grasp regions in configuration space to the problem of constructing the eightdimensional projection of an elevendimensional polytope. We present two projection methods: the first one uses a simple Gaussian elimination approach, while the second one relies on a novel outputsensitive contourtracking algorithm. Finally, we use linear optimization within t...
Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components
, 2001
"... In engineering and applied mathematics, polynomial systems arise whose solution sets contain components of different dimensions and multiplicities. In this article we present algorithms, based on homotopy continuation, that compute much of the geometric information contained in the primary decomposi ..."
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Cited by 56 (26 self)
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In engineering and applied mathematics, polynomial systems arise whose solution sets contain components of different dimensions and multiplicities. In this article we present algorithms, based on homotopy continuation, that compute much of the geometric information contained in the primary decomposition of the solution set. In particular, ignoring multiplicities, our algorithms lay out the decomposition of the set of solutions into irreducible components, by finding, at each dimension, generic points on each component. As byproducts, the computation also determines the degree of each component and an upper bound on itsmultiplicity. The bound issharp (i.e., equal to one) for reduced components. The algorithms make essential use of generic projection and interpolation, and can, if desired, describe each irreducible component precisely as the common zeroesof a finite number of polynomials.
3D motion estimation, understanding and prediction from noisy image sequences
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 1987
"... AbstractThis paper presents an approach to understanding general 3D motion of a rigid body from image sequences. Based on dynamics, a locally constant angular momentum (LCAM) model is introduced. The model is local in the sense that it is applied to a limited number of image frames at a time. Spec ..."
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Cited by 39 (2 self)
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AbstractThis paper presents an approach to understanding general 3D motion of a rigid body from image sequences. Based on dynamics, a locally constant angular momentum (LCAM) model is introduced. The model is local in the sense that it is applied to a limited number of image frames at a time. Specifically, the model constrains the motion, over a local frame subsequence, to be a superposition of precession and translation. Thus, the instantaneous rotation axis of the object is allowed to change through the subsequence. The trajectory of the rotation center is approximated by a vector polynomial. The parameters of the model evolve in time so that they can adapt to long term changes in motion characteristics. The nature and parameters of short term motion can be estimated continuously with the goal of understanding motion through the image sequence. The estimation algorithm presented in this paper is linear, i.e., the algorithm consists of solving simultaneous linear equations. Based on the assumption that the motion is smooth, object positions and motion in the near future can be predicted, and short missing subsequences can be recovered. Noise smoothing is achieved by overdetermination and a leastsquares criterion. The framework is flexible in the sense that it allows both overdetermination in number of feature points and the number of image frames. The number of frames from which the model is derived can be varied according to the complexity of motion and the noise level so as to obtain stable and good estimates of parameters over the entire image sequence. Simulation results are given for noisy synthetic data and images taken of a model airplane. Index TermsComputer vision, dynamic model, image sequence analysis, motion, motion estimation, motion prediction, motion understanding. I.
Affine Calibration of Mobile Vehicles
 EuropeChina workshop on Geometrical Modelling and Invariants for Computer Vision
, 1995
"... this paper we describe a method for achieving affine calibration for a fixed stereo rig on an AGV using constraints that arise naturally during motion  namely, that translation is in a plane perpendicular to the rotation axis. We describe and compare two approaches which employ these constraints: f ..."
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Cited by 38 (10 self)
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this paper we describe a method for achieving affine calibration for a fixed stereo rig on an AGV using constraints that arise naturally during motion  namely, that translation is in a plane perpendicular to the rotation axis. We describe and compare two approaches which employ these constraints: first, by recovering structure modulo a projectivity, and thence the plane at infinity; second, by using only image measurements based on the fundamental matrix (i.e. no structure recovery). The methods require no knowledge of the translation or angle of rotation. All processing  point correspondence based on corners, computation of the fundamental matrix, 3D structure recovery, affine calibration  is robust and automatic.
Smoothness analysis of subdivision schemes by proximity
 Constr. Approx
, 2006
"... Abstract. Linear curve subdivision schemes may be perturbed in various ways, e.g. by modifying them such as to work in a manifold, surface, or group. The analysis of such perturbed and often nonlinear schemes “T ” is based on their proximity to the linear schemes “S ” which they are derived from. Th ..."
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Cited by 33 (9 self)
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Abstract. Linear curve subdivision schemes may be perturbed in various ways, e.g. by modifying them such as to work in a manifold, surface, or group. The analysis of such perturbed and often nonlinear schemes “T ” is based on their proximity to the linear schemes “S ” which they are derived from. This paper considers two aspects of this problem: One is to find proximity inequalities which together with C k smoothness of S imply C k smoothness of T. The other is to verify these proximity inequalities for several ways to construct the nonlinear scheme T analogous to the linear scheme S. The first question is treated for general k, whereas the second one is treated only in the case k = 2. The main result of the paper is that convergent geodesic / projection / Lie group analogues of a certain class of factorizable linear schemes have C 2 limit curves. 1.