[PDF] Autocalibration and the absolute quadric | Semantic Scholar (2024)

The theory and a practical algorithm for the autocalibration of a moving projective camera, from m ≥ 5 views of a planar scene, which generalizes Hartley's method for the internal calibration of a rotating camera to allow camera translation and to provide 3D as well as calibration information.

It is shown how the ALQ turns out to be particularly suitable to address the Euclidean autocalibration of a set of cameras with square pixels and otherwise varying intrinsic parameters, providing new linear and non-linear algorithms for this problem.

The aim of autocalibration is to compute the internal parameters, starting from weakly calibrated cameras, to recover metric properties of camera and/or scene, i.e., to compute a Euclidean reconstruction.

It is shown in this paper that in certain common situations this supplementary information supplemented by known values of the camera's internal parameters or scene constraints may not resolve ambiguities or stabilize the algorithms.

This work proposes an algorithm that only requires 5 cameras (the theoretical minimum), thus halving the number of cameras required by previous algorithms based on the same constraint, and introduces the six-line conic variety (SLCV), consisting in the set of planes intersecting six given lines of 3D space in points of a conic.

Imposing chirality constraints to limit the search for the plane at infinity to a 3-dimensional cubic region of parameter space is imposed and it is shown that this dense search allows one to avoid areas of local minima effectively and find global minima of the cost function.

An optimized linear factorization method for recovering both the 3D geometry of a scene and the camera parameters from multiple uncalibrated images is presented and is able to enforce an accurate Euclidean reconstruction.

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A reconstruction method that allows to vary the focal length and is resistant to noise, and in which case also reconstruction from a moving rig becomes possible even for pure translation.

This work presents a new unified representation which will be useful when dealing with multiple views in the case of uncalibrated cameras, and shows how a special decomposition of a set of two or three general projection matrices, called canonic, enables us to build geometric descriptions for a system of cameras which are invariant with respect to a given group of transformations.

There is no epipolar structure since all images are taken from the same point in space and determination of point matches is considerably easier than for images taken with a moving camera, since problems of occlusion or change of aspect or illumination do not occur.

This paper studies the geometry of perspective projection into multiple images and the matching constraints that this induces between the images, and encodes exactly the information needed for reconstruction: the location of the joint image in the space of combined image coordinates.

The geometry of multi image perspective projection and the matching constraints that this induces on image measurements are studied and their complex algebraic interdependency is captured by quadratic structural simplicity constraints on the Grassmannian.

This paper addresses the problem of self-calibration and metric reconstruction from one unknown motion of an uncalibrated stereo rig and finds that redundancy of the information contained in a sequence of stereo images makes this method more robust than using a sequences of monocular images.

The self-calibration technique described in this article is the generalization to a large number of images of the algorithm developped by Luong and Faugeras based on the Kruppa equations.

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