Self-Calibration from Image Sequences This thesis develops new algorithms to obtain the calibration parameters of a camera using only information contained in an image sequence, with the objective of using the camera calibration to compute a Euclidean reconstruction. This problem is known as selfcalibration. The motivation for this work is to allow the Euclidean reconstruction of a scene using only a pre-recorded image sequence where no information is available on the camera or the objects in the scene. The approach used is to utilise known motion constraints, which are common for cameras mounted on mobile vehicles or robotic arms, to simplify the algebraic complexity of the self-calibration problem. The algorithms are designed to be easily extendible to use multiple images rather than the minimum number of three required for self-calibration. The uncertainty of the parameters are also computed to give a measure of confidence in the camera calibration. The first method uses a pure camera translation to allow the problem to be stratified by

We investigate the motions that lead to ambiguous Euclidean scene reconstructions under several common calibration constraints, giving a complete description of such critical motions for: (i) internally calibrated orthographic and perspective cameras; (ii) in two images, for cameras with unknown focal lengths, either different or equal. One aim of the work was to evaluate the potential of modern algebraic geometry tools for rigorously proving properties of vision algorithms, so we use idealtheoretic calculations as well as classical algebra and geometry. We also present numerical experiments showing the effects of near-critical configurations for the varying and fixed focal length methods.

Zoom lenses appear to fit very naturally into the framework of active vision --- controlling a zoom lens allows an adjustment of the image, enabling either an analysis of a wide scene or a close look at a region or object of particular interest. However, their integration into vision systems is not without difficulty since zoom interacts insidiously with both low and high level processes. This thesis concerns developing and analyzing algorithms that function in spite of zoom; algorithms for visual tracking, camera calibration and Euclidean reconstruction. An approach grounded in visual geometry is adopted, motivated by the notion that the geometric descriptions of point (corner) and line (straight edge) features are zoom-invariant.

Using zoom lenses in a computer vision system affects many aspects of the processing in the path from image formation to structure recovery. This thesis is concerned with understanding and addressing the particular issues which arise when wishing to control zoom in an active vision system — one able to fixate upon and track objects in the scene. The optical properties of zoom lenses interact with the imaging process in a number of ways. The first part of this work begins by confirming that the pinhole camera model is nonetheless valid for the cameras to be used. Then, using geometric arguments, it is shown how zoom-varying lens distortion adversely affects camera auto-calibration techniques which rely on purely rotational motion. Whilst pin-cushion distortion is tolerable, it is shown that barrelling distortion causes algorithm failure. The breakdown point is predicted, then verified using synthetic experiments. Suggestions for automatic recovery of the distortion parameters are given. The lowest level of the visual processing involves detecting and matching image features before robust segmentation and motion estimation. Achieving robustness comes at high computational cost, and the second part of this work addresses some of the theoretical and computational issues in Torr and Zisserman’s

A new approach to self-calibration and Euclidean reconstruction from image sequences is presented. The key idea is to start with the affine camera model as a first approximation to obtain affine 3D structure. It is then upgraded to Euclidean structure and finally, refined by applying the full perspective camera model. All steps in this procedure are described in detail and well-motivated. The method is robust and it also provides an estimate of the accuracy of the estimated parameters. The proposed method makes no assumption about the scene nor the camera motion. The only assumption required is that the camera has zero skew, which is a minimal condition in order to self-calibrate the camera and obtain a Euclidean reconstruction of the scene and the camera motion. However, if other information is available about the camera, for example constant intrinsic parameters, it can and should be incorporated to constrain the reconstruction. Experiments on both synthetic and real data are present...

The modulus constraint is a constraint on the position of the plane at infinity (1 ) which applies to the problem of self-calibration 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 three-view 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 non-linear 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.

We present an autocalibration algorithm for upgrading a projective reconstruction to a metric reconstruction by estimating the absolute dual quadric. The algorithm enforces the rank degeneracy and the positive semidefiniteness of the dual quadric as part of the estimation procedure, rather than as a post-processing step. Furthermore, the method allows the user, if he or she so desires, to enforce conditions on the plane at infinity so that the reconstruction satisfies the chirality constraints. The algorithm works by constructing low degree polynomial optimization problems, which are solved to their global optimum using a series of convex linear matrix inequality relaxations. The algorithm is fast, stable, robust and has time complexity independent of the number of views. We show extensive results on synthetic as well as real datasets to validate our algorithm. 1.

This study investigates the problem of estimating camera calibration parameters from image motion fields induced by a rigidly moving camera with unknown parameters, where the image formation is modeled with a linear pinhole-camera model. The equations obtained show the flow to be separated into a component due to the translation and the calibration parameters and a component due to the rotation and the calibration parameters. A set of parameters encoding the latter component is linearly related to the flow, and from these parameters the calibration can be determined. However, as for discrete motion, in general it is not possible to decouple image measurements obtained from only two frames into translational and rotational components. Geometrically, the ambiguity takes the form of a part of the rotational component being parallel to the translational component, and thus the scene can be reconstructed only up to a projective transformation. In general, for full calibration at least four ...

This paper introduces a new, stratified approach for the metric self calibration of a camera with fixed internal parameters. The method works by intersecting modulus-constraint manifolds, which are a specific type of screw-transform manifold. Through the addition of a single scalar parameter, a 2-dimensional modulus-constraint manifold can become a 3-dimensional Kruppa-constraint manifold allowing for direct self calibration from disjoint pairs of views. In this way, we demonstrate that screw-transform manifolds represent a single, unified approach to performing both stratified and direct self calibration. This paper also shows how to generate the screw-transform manifold arising from turntable (i.e., pairwise-planar) motion and discusses some important considerations for creating a working algorithm from these ideas.

In this paper, we describe an algorithm for generating three dimensional models of human faces from uncalibrated images. Input images are taken by a camera generally with a small rotation around a single axis which may cause degenerate solutions during auto-calibration. We describe a solution to this problem by a priori assumptions on the camera. To generate a specific person 's head, a generic human head model is deformed according to the 3D coordinates of points obtained by reconstructing the scene using images calibrated with our algorithm. The deformation process is based on a physical based massless spring model and it requires local re-triangulation in the areas with high curvatures. This is achieved by locally applying Delaunay triangulation method. However, there may occur degeneracies in Delaunay triangulation such as encroaching of edges. We describe an algorithm for removing the degeneracies during triangulation by modifying the definition of the Delaunay cavity. This algorithm has also the e#ect of preserving the curvature in the face area. We have compared the models generated with our algorithm with the models obtained using cyberscanners. The RMS geometric error in these comparisons are less than 1.8x10E-2.