Decomposition of transformation matrices for robot vision

Ganapathy, Sriram

doi:10.1109/robot.1984.1087163

Cited by 185 publications

(59 citation statements)

References 5 publications

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“…(4), the PTM M can only be determined up to a non-zero scale factor, that is, ifM is a valid solution of (4), then for any non-zero scale a, aM is also a valid solution. The scalar a is irrelevant to the task although it may have an effect on the numerical accuracy of the PTM.…”

Section: The Conventional Linear Least Squares Approachmentioning

confidence: 99%

“…A popular camera calibration paradigm achieves camera calibration by first computing the so-called perspective transformation matrix (PTM) [3], and then decomposing the matrix into intrinsic and extrinsic camera parameters [4]. This class of algorithms usually assumes a pinhole camera model, with no lens distortion, and provides a closed-form solution.…”

Section: Introductionmentioning

confidence: 99%

“…The second step in a PTM-based camera calibration algorithm is to derive camera parameters from the estimated PTM [4][5][6]. Closed-form solutions have been presented by Faugeras and Toscani [5][6], and Puget and Skordas [7] among many others.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Computing The Perspective Transformation Matrix and Camera Parameters

Tan¹,

Sullivan²,

Baker³

1993

Procedings of the British Machine Vision Conference 1993

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A popular camera calibration paradigm achieves camera calibration by first computing the so-called perspective transformation matrix (PTM) [3], and then decomposing the matrix into intrinsic and extrinsic camera parameters [4]. This class of algorithms usually assumes a pinhole camera model, with no lens distortion, and provides a closed-form solution. Two recent variants are due to Faugeras and Toscani [5][6], and Puget and Skordas [7].The PTM relates the 3D world coordinates of points to their 2D image coordinates. It is common practice to seek many such correspondences, so that the PTM is strongly overconstrained. The solution has then conventionally been computed by the standard linear least squares (LLS) technique by setting one of the matrix elements to unity [8]. In their recent papers [5][6], Faugeras and Toscani argue that arbitrarily setting one of the matrix elements to unity causes the t. This work was carried out as part of the ESPRIT project P2152 (VIEWS).

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Section: The Conventional Linear Least Squares Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Computing The Perspective Transformation Matrix and Camera Parameters

Tan¹,

Sullivan²,

Baker³

1993

Procedings of the British Machine Vision Conference 1993

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“…The cameras' intrinsic parameters (focal length, point of intersection of the optical axis with the image plane, scaling factors) are assumed to be known before initialisation begins. They were found using [8]. No knowledge of the translation and rotation between the two cameras need be provided as input to the system.…”

Section: System Initialisationmentioning

confidence: 99%

Prediction of stereo disparity using optical flow

Beardsley¹,

Brady²,

Murray³

1990

Procedings of the British Machine Vision Conference 1990

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One of the fundamental tasks in an autonomous vehicle navigation system is to create a model of the scene around the vehicle. This model, possibly in combination with a predefined map of the environment, provides the basis for obstacle avoidance and route planning. As in most areas of AI, the choice of representation for the model is a key issue [1]. In vehicle navigation, a 3D representation of a scene is often used i.e. points in the scene are represented by 3D position (see, for instance, [2,3,4]). In contrast to this approach, we intend to investigate the possibility of carrying out navigation without explicit 3D information, using quantities which are more directly related to image plane measurements yet which still encode the information required for the navigation task.This idea is undeveloped at the moment. However, it has provided the motivation for the work described here. The purpose of the work is to carry out temporal and stereo correspondence matching in an integrated way. It is certainly true that this integration can be carried out effectively in 3D-based systems [5], but the method in this paper performs the integration without reference to explicit 3D information. The overall approach was suggested by [6], and the main features of the integration are listed below. The current system is limited to straight translational motion in a static scene.• Temporal correspondence matching is used to support the stereo correspondence matching. This approach was adopted for two reasons. Firstly, the the combination of rate of image capture and typical vehicle speed is such that corners are only displaced by small amounts in consecutive images in a sequence so only a small search area is required for temporal matching -in contrast, the search area during stereo matching is along an epipolar line so matching ambiguities are more likely to arise. Secondly, the corner detector used [7] is sensitive to change in viewpoint. This affects the 'corner strength' attribute which is generated to characterise a corner, and hence affects the matching processes. Temporal matching is less affected than stereo matching because the change in viewpoint between two consecutive frames of a sequence is much smaller than the change in viewpoint between the left and right cameras.• Two attributes are used for corner comparison during stereo matching -corner strength and a motion-based attribute.• Stereo matches found in one stereo pair are 'cascaded' forwards to initiate matching in the next stereo pair in the sequence.• Finally, the main subject of the paper is a method by which the optical flow at a corner is used to predict its stereo disparity. Given this prediction, the search area for stereo matching is confined around a point instead of along an epipolar line. Section 1 describes system initialisation, section 2 the basic concepts underlying the main processing, section 3 the main processing itself, and section 4 the results.

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“…It is proved that the P5P problem could have two solutions [11]. For n ≥ 6, the PnP problem has one solution and can be solved with the DLT method [4].…”

Section: Introductionmentioning

confidence: 99%

On the Probability of the Number of Solutions for the P4P Problem

Gao

2006

J Math Imaging Vis

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This paper studies the multi-solution phenomenon for the perspective four point (P4P) problem from geometric and algebraic aspects. We give a pure geometric proof that the P4P problem could have up to five solutions. We also give a clear picture on how these five solutions could be realized. We prove that with probability one, the P4P problem has a unique solution which can be represented by a set of rational functions in the parameters. The simulant experiments show that to solve the P4P problem with the rational functions is stable and accurate.

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Decomposition of transformation matrices for robot vision

Cited by 185 publications

References 5 publications

On Computing The Perspective Transformation Matrix and Camera Parameters

On Computing The Perspective Transformation Matrix and Camera Parameters

Prediction of stereo disparity using optical flow

On the Probability of the Number of Solutions for the P4P Problem

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