Focal length calibration from two views: method and analysis of singular cases

Sturm, Peter; Cheng, Zhanwen; Chen, P. C. Y.; Poo, A.N.

doi:10.1016/j.cviu.2004.11.002

Cited by 36 publications

(24 citation statements)

References 18 publications

(36 reference statements)

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“…Their reported results were not perfect. We believe that this is because of a generic degeneracy: whenever the two mirrors are arranged in a rotationally symmetric position with respect to the camera's optical axis, the two virtual cameras (the real camera reflected in the two mirrors) are in a degenerate relative pose for focal length computation [474]. In situations close to this, results may be expected to be inaccurate.…”

Section: Self-calibration From Image Matchesmentioning

confidence: 93%

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Camera Models and Fundamental Concepts Used in Geometric Computer Vision

Sturm

2010

FNT in Computer Graphics and Vision

153

122

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A printed and bound version is available at a special discount price of US35 from Now Publishers. This can be obtained by entering the promotional code CGV006023 on https://www.nowpublishers.com/bookorder.aspx?doi=0600000023&product=CGVInternational audienceThis survey is mainly motivated by the increased availability and use of panoramic image acquisition devices, in computer vision and various of its applications. Different technologies and different computational models thereof exist and algorithms and theoretical studies for geometric computer vision ("structure-from-motion") are often re-developed without highlighting common underlying principles. One of the goals of this survey is to give an overview of image acquisition methods used in computer vision and especially, of the vast number of camera models that have been proposed and investigated over the years, where we try to point out similarities between different models. Results on epipolar and multi-view geometry for different camera models are reviewed as well as various calibration and self-calibration approaches, with an emphasis on non-perspective cameras. We finally describe what we consider are fundamental building blocks for geometric computer vision or structure-from-motion: epipolar geometry, pose and motion estimation, 3D scene modeling, and bundle adjustment. The main goal here is to highlight the main principles of these, which are independent of specific camera models

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Section: Self-calibration From Image Matchesmentioning

confidence: 93%

“…From the fundamental matrix between two perspective images, one may estimate up to two intrinsic parameters [206,474]; usually one just computes the focal length. Hence, in many cases it should be possible to obtain a full self-calibration of non-perspective cameras from a single fundamental matrix.…”

Section: Self-calibration From Image Matchesmentioning

confidence: 99%

Camera Models and Fundamental Concepts Used in Geometric Computer Vision

Sturm

2010

FNT in Computer Graphics and Vision

153

122

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“…In this way three different equations can be formulated, one of 3 rd degree and two linear on the square of the common camera constant value. It should be noted that the degrees of the proposed equations are in accordance to the ones suggested by Sturm (2001) and Sturm et al (2005) which are based on the solution of the Kruppa equations through Singular Value Decomposition (SVD).…”

Section: Images With Common Camera Constantmentioning

confidence: 75%

“…An equivalent equation has been presented by Bougnoux (1998) based on the solution of the Kruppa equations, by Kanatani & Matsunaga (2000) based on constraints on the Essential Matrix and by Huang et al (2004) through the absolute dual quadric. Sturm (2001) and Sturm et al (2005) dealt with the case of common camera constant and formulated three different equations (one linear and two quadratic) for its determination. They also demonstrated that a common c may be calculated even when the camera axes are coplanar, as long as they are not parallel or their point of intersection is not equidistant from the two projection centres.…”

Section: Introductionmentioning

confidence: 99%

A Euclidean Formulation of Interior Orientation Costraints Imposed by the Fundamental Matrix

Kalisperakis

Karras

Petsa

2016

ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:Epipolar geometry of a stereopair can be expressed either in 3D, as the relative orientation (i.e. translation and rotation) of two bundles of optical rays in case of calibrated cameras or, in case of unclalibrated cameras, in 2D as the position of the epipoles on the image planes and a projective transformation that maps points in one image to corresponding epipolar lines on the other. The typical coplanarity equation describes the first case; the Fundamental matrix describes the second. It has also been proven in the Computer Vision literature that 2D epipolar geometry imposes two independent constraints on the parameters of camera interior orientation. In this contribution these constraints are expressed directly in 3D Euclidean space by imposing the equality of the dihedral angle of epipolar planes defined by the optical axes of the two cameras or by suitably chosen corresponding epipolar lines. By means of these constraints, new closed form algorithms are proposed for the estimation of a variable or common camera constant value given the fundamental matrix and the principal point position of a stereopair.

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“…This is equivalent to computing the fundamental matrix between the distortion corrected images. From the fundamental matrix we can extract the focal length [21].…”

Section: Central Camerasmentioning

confidence: 99%

A Factorization Based Self-Calibration for Radially Symmetric Cameras

Ramalingam

Sturm

Boyer

2006

Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06)

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The paper proposes a novel approach for planar selfcalibration of radially symmetric cameras. We model these camera images using notions of distortion center and concentric distortion circles around it. The rays corresponding to pixels lying on a single distortion circle form a right circular cone. Each of these cones is associated with two unknowns; optical center and focal length (opening angle). In the central case, we consider all distortion circles to have the same optical center, whereas in the non-central case they have different optical centers lying on the same optical axis. Based on this model we provide a factorization based self-calibration algorithm for planar scenes from dense image matches. Our formulation provides a rich set of constraints to validate the correctness of the distortion center. We also propose possible extensions of this algorithm in terms of non-planar scenes, non-unit aspect ratio and multiview constraints. Experimental results are shown.

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Focal length calibration from two views: method and analysis of singular cases

Cited by 36 publications

References 18 publications

Camera Models and Fundamental Concepts Used in Geometric Computer Vision

Camera Models and Fundamental Concepts Used in Geometric Computer Vision

A Euclidean Formulation of Interior Orientation Costraints Imposed by the Fundamental Matrix

A Factorization Based Self-Calibration for Radially Symmetric Cameras

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