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Camera pose and calibration from 4 or 5 known 3D points
 In Proc. 7th Int. Conf. on Computer Vision
, 1999
"... We describe two direct quasilinear methods for camera pose (absolute orientation) and calibration from a single image of 4 or 5 known 3D points. They generalize the 6 point ‘Direct Linear Transform ’ method by incorporating partial prior camera knowledge, while still allowing some unknown calibratio ..."
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Cited by 30 (0 self)
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We describe two direct quasilinear methods for camera pose (absolute orientation) and calibration from a single image of 4 or 5 known 3D points. They generalize the 6 point ‘Direct Linear Transform ’ method by incorporating partial prior camera knowledge, while still allowing some unknown calibration parameters to be recovered. Only linear algebra is required, the solution is unique in nondegenerate cases, and additional points can be included for improved stability. Both methods fail for coplanar points, but we give an experimental eigendecomposition based one that handles both planar and nonplanar cases. Our methods use recent polynomial solving technology, and we give a brief summary of this. One of our aims was to try to understand the numerical behaviour of modern polynomial solvers on some relatively simple test cases, with a view to other vision applications.
Routines for Relative Pose of Two Calibrated Cameras from 5
 Points, Technical Report, http://www.inrialpes.fr/movi/people/Triggs INRIA
, 2000
"... This report describes a library of C routines for finding the relative pose of two calibrated perspective cameras given the images of five unknown 3D points. The relative pose is the translational and rotational displacement between the two camera frames, also called camera motion and relative orien ..."
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Cited by 12 (1 self)
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This report describes a library of C routines for finding the relative pose of two calibrated perspective cameras given the images of five unknown 3D points. The relative pose is the translational and rotational displacement between the two camera frames, also called camera motion and relative orientation.
Gröbner bases and wavelet design
, 2000
"... In this paper, we detail the use of symbolic methods in order to solve some advanced design problems arising in signal processing. Our interest lies especially in the construction of wavelet filters for which the usual spectral factorization approach (used for example to construct the wellknown Dau ..."
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In this paper, we detail the use of symbolic methods in order to solve some advanced design problems arising in signal processing. Our interest lies especially in the construction of wavelet filters for which the usual spectral factorization approach (used for example to construct the wellknown Daubechies filters) is not applicable. In these problems, we show how the design equations can be written as multivariate polynomial systems of equations and accordingly how Gröbner algorithms offer an effective way to obtain solutions in some of these cases.
AN ALGEBRAIC APPROACH TO BLIND IDENTIFICATION OF COMMUNICATION CHANNELS
"... In this paper, a new algorithm for the blind identification of SISO communication channels is introduced. Based on methods from computational algebraic geometry, the approach achieves a full description of the solution space and thus avoids the local minima issue of adaptive algorithms. Furthermore, ..."
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In this paper, a new algorithm for the blind identification of SISO communication channels is introduced. Based on methods from computational algebraic geometry, the approach achieves a full description of the solution space and thus avoids the local minima issue of adaptive algorithms. Furthermore, unlike most symbolic methods, the computational cost is kept low by a split of the problem into two stages. First, a symbolic precomputation is done offline, once for all, to get a more convenient parametric representation of the problem. The solutions of the problem are then easily obtained from this representation by solving a single univariate polynomial equation.
Membres du jury M. JeanPierre Verjus président
, 2010
"... pour obtenir le grade de Docteur en sciences ..."
Allocation and Interface Synthesis Algorithms for ComponentBased Design
, 2000
"... Since 1965, the size of transistors has been halved and their speed of operation has been doubled, every 18 to 24 months, a phenomenon known as Moore’s Law. This has allowed rapid increases in the amount of circuitry that can be included on a single die. However, as the availability of hardware real ..."
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Since 1965, the size of transistors has been halved and their speed of operation has been doubled, every 18 to 24 months, a phenomenon known as Moore’s Law. This has allowed rapid increases in the amount of circuitry that can be included on a single die. However, as the availability of hardware real estate escalates at an exponential rate, the complexity involved in creating circuitry that utilizes that real estate grows at an exponential, or higher, rate. Componentbased design methodologies promise to reduce the complexity of this task and the time required to design integrated circuits by raising the level of abstraction at which circuitry is specified, synthesized, verified, or physically implemented. This thesis develops algorithms for synthesizing integrated circuits by mapping highlevel specifications onto existing components. To perform this task, wordlevel polynomial representations are introduced as a mechanism for canonically and compactly representing the functionality of complex components. Polynomial representations can be applied to a broad range of circuits, including combinational, sequential, and datapath dominated circuits. They provide the basis for efficiently comparing the functionality of a circuit
A LINEAR ALGEBRA APPROACH TO SYSTEMS OF POLYNOMIAL EQUATIONS WITH APPLICATION TO DIGITAL COMMUNICATIONS
"... We introduce in this paper a new algebraic approach to some problems arising in signal processing and communications that can be described as or reduced to systems of multivariate quadratic polynomial equations. Based on methods from computational algebraic geometry, the approach achieves a full d ..."
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We introduce in this paper a new algebraic approach to some problems arising in signal processing and communications that can be described as or reduced to systems of multivariate quadratic polynomial equations. Based on methods from computational algebraic geometry, the approach achieves a full description of the solution space and thus avoids the local minima issue of adaptive algorithms. Furthermore, unlike most symbolic methods, the computational cost is kept low by a split of the problem into two stages. First, a symbolic precomputation is done offline once for all, to get a more convenient parametric tracematrix representation of the problem using normal forms. The solutions of the problem are then easily obtained from this representation by solving a single univariate polynomial equation. This approach is quite general and can be applied to a wide variety of problems: SISO channel identification of PSK modulations but also filter design and possibly MIMO blind source separation by deflation. 1.