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32
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 ..."
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Cited by 34 (5 self)
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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 ..."
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Cited by 32 (0 self)
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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 ..."
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Cited by 11 (0 self)
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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 ..."
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Cited by 8 (0 self)
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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 ..."
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Cited by 5 (2 self)
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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.
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 ..."
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Cited by 3 (0 self)
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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
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 ..."
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Cited by 2 (2 self)
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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.
Attentionbased Target Localization using Multiple Instance Learning ⋆
"... Abstract. We propose a novel Multiple Instance Learning (MIL) framework to perform target localization from image sequences. The proposed approach consists of a softmax logistic regression MIL algorithm using log covariance features to automatically learn the model of a target that persists across i ..."
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Cited by 2 (0 self)
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Abstract. We propose a novel Multiple Instance Learning (MIL) framework to perform target localization from image sequences. The proposed approach consists of a softmax logistic regression MIL algorithm using log covariance features to automatically learn the model of a target that persists across input frames. The approach makes no assumptions about the target’s motion model and can be used to learn models for multiple targets present in the scene. The learned target models can also be updated in an online manner. We demonstrate the validity and usefulness of the proposed approach to localize targets in various scenes using commercialgrade surveillance cameras. We also demonstrate its applicability to bootstrap conventional tracking systems and show that automatic initialization using our technique helps to achieve superior performance. 1