Results 1  10
of
26
Accurate NonIterative O(n) Solution to the PnP Problem
, 2007
"... We propose a noniterative solution to the PnP problem—the estimation of the pose of a calibrated camera from n 3Dto2D point correspondences—whose computational complexity grows linearly with n. This is in contrast to stateoftheart methods that are O(n 5) or even O(n 8), without being more accu ..."
Abstract

Cited by 31 (4 self)
 Add to MetaCart
We propose a noniterative solution to the PnP problem—the estimation of the pose of a calibrated camera from n 3Dto2D point correspondences—whose computational complexity grows linearly with n. This is in contrast to stateoftheart methods that are O(n 5) or even O(n 8), without being more accurate. Our method is applicable for all n ≥ 4 and handles properly both planar and nonplanar configurations. Our central idea is to express the n 3D points as a weighted sum of four virtual control points. The problem then reduces to estimating the coordinates of these control points in the camera referential, which can be done in O(n) time by expressing these coordinates as weighted sum of the eigenvectors of a 12 × 12 matrix and solving a small constant number of quadratic equations to pick the right weights. The advantages of our method are demonstrated by thorough testing on both synthetic and realdata.
EPnP: An Accurate O(n) Solution to the PnP Problem
 INT J COMPUT VIS
, 2008
"... We propose a noniterative solution to the PnP problem—the estimation of the pose of a calibrated camera from n 3Dto2D point correspondences—whose computational complexity grows linearly with n. This is in contrast to stateoftheart methods that are O(n 5) or even O(n 8), without being more ac ..."
Abstract

Cited by 27 (0 self)
 Add to MetaCart
We propose a noniterative solution to the PnP problem—the estimation of the pose of a calibrated camera from n 3Dto2D point correspondences—whose computational complexity grows linearly with n. This is in contrast to stateoftheart methods that are O(n 5) or even O(n 8), without being more accurate. Our method is applicable for all n ≥ 4 and handles properly both planar and nonplanar configurations. Our central idea is to express the n 3D points as a weighted sum of four virtual control points. The problem then reduces to estimating the coordinates of these control points in the camera referential, which can be done in O(n) time by expressing these coordinates as weighted sum of the eigenvectors of a 12 × 12 matrix and solving a small constant number of quadratic equations to pick the right weights. Furthermore, if maximal precision is required, the output of the closedform solution can be used to initialize a GaussNewton scheme, which improves accuracy with negligible amount of additional time. The advantages of our method are demonstrated by thorough testing on both synthetic and realdata.
Pose Estimation with Radial Distortion and Unknown Focal Length
 Proc. Conference on Computer Vision and Pattern Recognition (CVPR’09
, 2009
"... This paper presents a solution to the problem of pose estimation in the presence of heavy radial distortion and a potentially large number of outliers. The main contribution is an algorithm that solves for radial distortion, focal length and camera pose using a minimal set of four point corresponden ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
This paper presents a solution to the problem of pose estimation in the presence of heavy radial distortion and a potentially large number of outliers. The main contribution is an algorithm that solves for radial distortion, focal length and camera pose using a minimal set of four point correspondences between 3D world points and image points. We use a RANSAC loop to find a set of inliers and an initial estimate for bundle adjustment. Unlike previous approaches where one starts out by assuming a linear projection model, our minimal solver allows us to handle large radial distortions already at the RANSAC stage. We demonstrate that with the inclusion of radial distortion in an early stage of the process, a broader variety of cameras can be handled than was previously possible. In the experiments, no calibration whatsoever is applied to the camera. Instead we assume square pixels, zero skew and centered principal point. Although these assumptions are not strictly true, we show that good results are still obtained and by that conclude that the proposed method is applicable to uncalibrated photographs. 1.
Direct Solution of Modulus Constraints
"... The modulus constraint is a constraint on the position of the plane at infinity (1 ) which applies to the problem of selfcalibration in the case of constant internals. For any pair of cameras which are known to have the same internal parameters, the classical modulus constraint is the vanishing of ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
The modulus constraint is a constraint on the position of the plane at infinity (1 ) which applies to the problem of selfcalibration in the case of constant internals. For any pair of cameras which are known to have the same internal parameters, the classical modulus constraint is the vanishing of a certain quartic polynomial whose coefficients are determinedfrom the cameras. Given a projective threeview reconstruction, it is of practical interest to recover the plane at infinity by solving for the threeparameters of 1 . Geometrically this is the problem of intersecting three quartic surfaces in projective space, so one should expect to get 64 solutions. It is not clear how to carry out the process in practice because continuation methods are slow and nonlinear optimization may producealocal minimum. This paper presents a new derivation of the classical constraints, and additionally shows how to derive novel cubic constraints which exist for any triple of views. For three views, it is shown how to use the new constraint to classify the 64=4\Theta 4 \Theta 4 classical solutions into one spurious (namely the trifocal plane), 21 feasible and 2 \Theta 21 which must berejectedon physical grounds. The ambiguity is thus reducedfrom 64 to 21. A numerical algorithm is given to compute all 21 feasible solutions.
A Variational Approach to Problems in Calibration of Multiple Cameras
 Proc. IEEE Conf. Computer Vision and Pattern Recognition
, 2004
"... This paper addresses the problem of calibrating camera parameters using variational methods. One problem addressed in this paper is the severe lens distortion in wide angle/inexpensive camera lenses. The camera distortion effects lead to inaccurate 3D reconstructions and geometrical measurements if ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
This paper addresses the problem of calibrating camera parameters using variational methods. One problem addressed in this paper is the severe lens distortion in wide angle/inexpensive camera lenses. The camera distortion effects lead to inaccurate 3D reconstructions and geometrical measurements if not accounted for. A second problem is the color calibration problem caused by variations in camera responses which results in different color measurements and affects the algorithms that depend on these measurements. We present multiview stereo techniques based on variational ideas to address these calibration problems. To reduce computational complexity of such algorithms, we utilize a prior knowledge on the calibration object which is used in the process, and evolve the pose, orientation, and scale parameters of such a 3D model object. We derive the evolution equations for the distortion coefficients, the color calibration parameters of the cameras, and present experimental results which demonstrate their potential use. 1.
A Custom Computing Framework for Orientation and Photogrammetry
 MIT EECS
, 2000
"... There is great demand today for realtime computer vision systems, with applications including image enhancement, target detection and surveillance, autonomous navigation, and scene reconstruction. These operations generally require extensive computing power; when multiple conventional processors an ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
There is great demand today for realtime computer vision systems, with applications including image enhancement, target detection and surveillance, autonomous navigation, and scene reconstruction. These operations generally require extensive computing power; when multiple conventional processors and custom gate arrays are inappropriate, due to either excessive cost or risk, a class of devices known as FieldProgrammable Gate Arrays (FPGAs) can be employed. FPGAs offer the flexibility of a programmable solution and nearly the performance of a custom gate array. When implementing a custom algorithm in an FPGA, one must be more efficient than with a gate array technology. By tailoring the algorithms, architectures, and precisions, the gate count of an algorithm may be sufficiently reduced to fit into an FPGA. The challenge is to perform this customization of the algorithm, while still maintaining the required performance. The techniques required to perform algorithmic optimization for FPGAs are scattered across many fields; what is currently lacking is a framework for utilizing all these well known and developing techniques. The purpose of this thesis is to develop
Egomotion using assorted features
 In IEEE computer society conference on computer vision and pattern recognition (CVPR
, 2010
"... We describe a novel and robust minimal solver for performing online visual odometry with a stereo rig. The proposed method can compute the underlying camera motion given any arbitrary, mixed combination of point and line correspondences across two stereo views. This facilitates a hybrid visual odome ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
We describe a novel and robust minimal solver for performing online visual odometry with a stereo rig. The proposed method can compute the underlying camera motion given any arbitrary, mixed combination of point and line correspondences across two stereo views. This facilitates a hybrid visual odometry pipeline that is enhanced by welllocalized and reliablytracked line features while retaining the wellknown advantages of point features. Utilizing trifocal tensor geometry and quaternion representation of rotation matrices, we develop a polynomial system from which camera motion parameters can be robustly extracted in the presence of noise. We show how the more popular approach of using direct linear/subspace techniques fail in this regard and demonstrate improved performance using our formulation with extensive experiments and comparisons against the 3point and linesfm algorithms. 1.
Minimal projective reconstruction for combinations of points and lines in three views
 In Proceedings of the British Machine Vision Conference
, 2002
"... In this article we address the problem of projective reconstruction of structure and motion given only image data. In particular we investigate three novel minimal combinations of points and lines over three views, and give complete solutions and reconstruction methods for two of these cases: “four ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
In this article we address the problem of projective reconstruction of structure and motion given only image data. In particular we investigate three novel minimal combinations of points and lines over three views, and give complete solutions and reconstruction methods for two of these cases: “four points and three lines in three views”, and “two points and six lines in three views”. We show that in general there are three and seven solutions respectively to these cases. The reconstruction methods are tested on real and simulated data. We also give tentative results for the case of nine lines in correspondence over three views, where experiments indicate that there may be up to 36 complex solutions. 1
Numerical Methods for Geometric Vision: From Minimal to Large Scale Problems
"... This thesis presents a number of results and algorithms for the numerical solution of problems in geometric computer vision. Estimation of scene structure and camera motion using only image data has been one of the central themes of research in photogrammetry, geodesy and computer vision. It has imp ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
This thesis presents a number of results and algorithms for the numerical solution of problems in geometric computer vision. Estimation of scene structure and camera motion using only image data has been one of the central themes of research in photogrammetry, geodesy and computer vision. It has important applications for robotics, autonomous vehicles, cartography, architecture, the movie industry, photography etc. Images inherently provide ambiguous and uncertain data about the world. Hence, geometric computer vision turns out to be as much about statistics as about geometry. Basically we consider two types of problems: Minimal problems where the number of constraints exactly matches the number of unknowns and large scale problems which need to be addressed using e cient optimization algorithms. Solvers for minimal problems are used heavily during preprocessing to eliminate outliers in uncertain data. Such problems are usually solved by nding the zeros of a system of polynomial equations.