A flexible new technique for camera calibration
01 Nov 2000-IEEE Transactions on Pattern Analysis and Machine Intelligence (IEEE Computer Society)-Vol. 22, Iss: 11, pp 1330-1334
TL;DR: A flexible technique to easily calibrate a camera that only requires the camera to observe a planar pattern shown at a few (at least two) different orientations is proposed and advances 3D computer vision one more step from laboratory environments to real world use.
Abstract: We propose a flexible technique to easily calibrate a camera. It only requires the camera to observe a planar pattern shown at a few (at least two) different orientations. Either the camera or the planar pattern can be freely moved. The motion need not be known. Radial lens distortion is modeled. The proposed procedure consists of a closed-form solution, followed by a nonlinear refinement based on the maximum likelihood criterion. Both computer simulation and real data have been used to test the proposed technique and very good results have been obtained. Compared with classical techniques which use expensive equipment such as two or three orthogonal planes, the proposed technique is easy to use and flexible. It advances 3D computer vision one more step from laboratory environments to real world use.
Citations
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01 Jan 2001
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Abstract: Downloading the book in this website lists can give you more advantages. It will show you the best book collections and completed collections. So many books can be found in this website. So, this is not only this multiple view geometry in computer vision. However, this book is referred to read because it is an inspiring book to give you more chance to get experiences and also thoughts. This is simple, read the soft file of the book and you get it.
14,282 citations
TL;DR: This paper has designed a stand-alone, flexible C++ implementation that enables the evaluation of individual components and that can easily be extended to include new algorithms.
Abstract: Stereo matching is one of the most active research areas in computer vision. While a large number of algorithms for stereo correspondence have been developed, relatively little work has been done on characterizing their performance. In this paper, we present a taxonomy of dense, two-frame stereo methods designed to assess the different components and design decisions made in individual stereo algorithms. Using this taxonomy, we compare existing stereo methods and present experiments evaluating the performance of many different variants. In order to establish a common software platform and a collection of data sets for easy evaluation, we have designed a stand-alone, flexible C++ implementation that enables the evaluation of individual components and that can be easily extended to include new algorithms. We have also produced several new multiframe stereo data sets with ground truth, and are making both the code and data sets available on the Web.
7,458 citations
Cites background from "A flexible new technique for camera..."
...Recent references on stereo camera calibration and rectification include [130, 70, 131, 52, 39]....
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Book•
30 Sep 2010
TL;DR: Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images and takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene.
Abstract: Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of recipes, this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.
4,146 citations
Cites background from "A flexible new technique for camera..."
...8: Sample calibration patterns: (a) a three-dimensional target from (Quan and Lan 1999); (b) a two-dimensional target from (Zhang 2000)....
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...1: Some examples of geometric alignment and calibration: (a) geometric alignment of 2D images for stitching; (b) a two-dimensional calibration target (Zhang 2000); (c) calibration from vanishing points; (d) scene with easy to find lines and vanishing directions (Criminisi et al....
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...2008), and (c) calibration patterns (Zhang 2000)....
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01 Sep 1999
TL;DR: Compared with classical techniques which use expensive equipment, such as two or three orthogonal planes, the proposed technique is easy to use and flexible, and advances 3D computer vision one step from laboratory environments to real-world use.
Abstract: Proposes a flexible new technique to easily calibrate a camera. It only requires the camera to observe a planar pattern shown at a few (at least two) different orientations. Either the camera or the planar pattern can be freely moved. The motion need not be known. Radial lens distortion is modeled. The proposed procedure consists of a closed-form solution followed by a nonlinear refinement based on the maximum likelihood criterion. Both computer simulation and real data have been used to test the proposed technique, and very good results have been obtained. Compared with classical techniques which use expensive equipment, such as two or three orthogonal planes, the proposed technique is easy to use and flexible. It advances 3D computer vision one step from laboratory environments to real-world use. The corresponding software is available from the author's Web page ( ).
2,661 citations
Cites background from "A flexible new technique for camera..."
...The proof is omitted due to space limitation, and is available from our technical report [24]....
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...Thanks go to Bill Triggs and Gideon Stein for suggesting experiments on model imprecision, which can be found in the technical report [24]....
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...The solution can be found in our technical report [24]....
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Book•
05 Mar 2004
TL;DR: Bringing together all aspects of mobile robotics into one volume, Introduction to Autonomous Mobile Robots can serve as a textbook or a working tool for beginning practitioners.
Abstract: Mobile robots range from the Mars Pathfinder mission's teleoperated Sojourner to the cleaning robots in the Paris Metro. This text offers students and other interested readers an introduction to the fundamentals of mobile robotics, spanning the mechanical, motor, sensory, perceptual, and cognitive layers the field comprises. The text focuses on mobility itself, offering an overview of the mechanisms that allow a mobile robot to move through a real world environment to perform its tasks, including locomotion, sensing, localization, and motion planning. It synthesizes material from such fields as kinematics, control theory, signal analysis, computer vision, information theory, artificial intelligence, and probability theory. The book presents the techniques and technology that enable mobility in a series of interacting modules. Each chapter treats a different aspect of mobility, as the book moves from low-level to high-level details. It covers all aspects of mobile robotics, including software and hardware design considerations, related technologies, and algorithmic techniques.] This second edition has been revised and updated throughout, with 130 pages of new material on such topics as locomotion, perception, localization, and planning and navigation. Problem sets have been added at the end of each chapter. Bringing together all aspects of mobile robotics into one volume, Introduction to Autonomous Mobile Robots can serve as a textbook or a working tool for beginning practitioners.
2,414 citations
Cites methods from "A flexible new technique for camera..."
...For further discussion of calibration and to download and use a standard calibration program, see [158]....
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References
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TL;DR: Under the assumption of the radial distortion model, this paper presents a computationally efficient method for explicitly correcting the distortion of image coordinates in frame buffer without involving the computation of camera position and orientation.
Abstract: By implicit camera calibration, we mean the process of calibrating a camera without explicitly computing its physical parameters. Implicit calibration can be used for both three-dimensional (3-D) measurement and generation of image coordinates. In this paper, we present a new implicit model based on the generalized projective mappings between the image plane and two calibration planes. The back-projection and projection processes are modelled separately to ease the computation of distorted image coordinates from known world points. A set of constraints of perspectivity is derived to relate the transformation parameters of the two calibration planes. Under the assumption of the radial distortion model, we present a computationally efficient method for explicitly correcting the distortion of image coordinates in frame buffer without involving the computation of camera position and orientation. By combining with any linear calibration techniques, this method makes explicit the camera physical parameters. Extensive experimental comparison of our methods with the classic photogrammetric method and Tsai's (1986) method in the aspects of 3-D measurement (both absolute and relative errors), the prediction of image coordinates, and the effect of the number of calibration points, is made using real images from 15 different depth values. >
350 citations
"A flexible new technique for camera..." refers background in this paper
...It has also been found that any more elaborated modeling not only would not help (negligible when compared with sensor quantization), but also would cause numerical instability [23, 25]....
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...Based on the reports in the literature [2, 23, 25], it is likely that the distortion function is totally dominated by the radial components, and especially dominated by the first term....
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...We have [2, 25] x̆ = x + x[k1(x + y2) + k2(x + y2)2] y̆ = y + y[k1(x + y2) + k2(x + y2)2] , where k1 and k2 are the coefficients of the radial distortion....
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13 Mar 1984
TL;DR: A new and simple analytical technique is presented that accomplishes the inverse problem of computing the camera location and orientation from the transformation matrix rather easily and has considerable applications for motion tracking.
Abstract: The relationship between the three-dimensional coordinates of a point and the corresponding two-dimensional coordinates of its image, as seen by a camera, can be expressed in terms of a 3 by 4 matrix using the homogeneous coordinate system. This matrix is known more generally as the transformation matrix and can be determined experimentaily by measuring the image coordinates of six or more known paoints in space. Such a transformation can also be derived analytically from knowledge of the camera position, orientation, focal length and scaling and translation parameters in the image plane. However, the inverse problem of computing the camera location and orientation from the transformation matrix involves solution of simultaneous nonlinear equations in several variables and is considered difficult. In this paper we present a new and simple analytical technique that accomplishes this inversion rather easily. This technique works very well in practice and has considerable applications for motion tracking.
303 citations
"A flexible new technique for camera..." refers background in this paper
...See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/3193178...
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Journal Article•
TL;DR: In this article, a method of self calibration applicable to non-metric cameras is presented and discussed in connection with various other calibration approaches, including radial symmetric and decentering lens distortions, affinity, and non-perpendicularity of axes.
Abstract: In this paper a method of self calibration applicable to non-metric cameras is presented and discussed in connection with various other calibration approaches The method is extremely general and includes radial symmetric and decentering lens distortions, affinity, and non-perpendicularity of axes Although it provides interior orientation parameters for each photograph separately, the minimum control requirement remains at two horizontal and three vertical control points
296 citations
"A flexible new technique for camera..." refers background in this paper
...The reader is referred to [20, 2, 4, 26] for more elaborated models....
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...Much work has been done, starting in the photogrammetry community (see [2, 4] to cite a few), and more recently in computer vision ([9, 8, 23, 7, 26, 24, 17, 6] to cite a few)....
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04 Jan 1998
TL;DR: It is shown that the uncertainty on the focal length estimation leads to an Euclidean calibration up to a quasi anisotropic homothety whereas the error on the principal point can often be interpreted as a translation.
Abstract: For many practical applications it is important to relax the self-calibration conditions to allow for changing internal camera parameters (e.g. zooming/focusing...). Classical techniques failed for such conditions. We present the available constraints that allow us to right a projective calibration to a Euclidean one. Meanwhile, we found that the estimations of the internal parameters were rather inaccurate. We discuss theoretically this difficulty and above all the resulting effect on the 3D reconstruction. In fact, we show that the uncertainty on the focal length estimation leads to an Euclidean calibration up to a quasi anisotropic homothety whereas the error on the principal point can often be interpreted as a translation. Hopefully, the calibration we come up with, is quite acceptable for reconstruction of models.
268 citations
"A flexible new technique for camera..." refers background in this paper
...See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/3193178...
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20 Jun 1995
TL;DR: A simple and accurate method for internal camera calibration based on tracking image features through a sequence of images while the camera undergoes pure rotation that can be used both for laboratory calibration and for self calibration in autonomous robots.
Abstract: Describes a simple and accurate method for internal camera calibration based on tracking image features through a sequence of images while the camera undergoes pure rotation. A special calibration object is not required and the method can therefore be used both for laboratory calibration and for self calibration in autonomous robots. Experimental results with real images show that focal length and aspect ratio can be found to within 0.15 percent, and lens distortion error can be reduced to a fraction of a pixel. The location of the principal point and the location of the center of radial distortion can each be found to within a few pixels. We perform a simple analysis to show to what extent the various technical details affect the accuracy of the results. We show that having pure rotation is important if the features are derived from objects close to the camera. In the basic method accurate angle measurement is important. The need to accurately measure the angles can be eliminated by rotating the camera through a complete circle while taking an overlapping sequence of images and using the constraint that the sum of the angles must equal 960 degrees. >
196 citations
"A flexible new technique for camera..." refers background in this paper
...See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/3193178...
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