Infinite Homography Research Articles

Extensions of Plane-Based Calibration to the Case of Translational Motion in a Robot Vision Setting

In this paper, a technique for calibrating a camera using a planar calibration object with known metric structure, when the camera (or the calibration plane) undergoes pure translational motion, is presented. The study is an extension of the standard formulation of plane-based camera calibration where the translational case is considered as degenerate. We derive a flexible and straightforward way of using different amounts of knowledge of the translational motion for the calibration task. The theory is mainly applicable in a robot vision setting, and the calculation of the hand-eye orientation and the special case of stereo head calibration are also being addressed. Results of experiments on both computer-generated and real image data are presented. The paper covers the most useful instances of applying the technique to a real system and discusses the degenerate cases that needs to be considered. The paper also presents a method for calculating the infinite homography between the two image planes in a stereo head, using the homographies estimated between the calibration plane and the image planes. Its possible usage and usefulness for simultaneous calibration of the two cameras in the stereo head are discussed and illustrated using experiments

Reconstruction of structured scenes from two uncalibrated images

This paper investigates a practical heuristics method for reconstruction of structured scenes from two uncalibrated images. The method is based on an initial estimation of principal homographies from 2D initial point matches that may contain some outliers, and the homographies are refined recursively by incorporating the supporting matches of both points and lines on principal space surfaces. Then epipolar geometry is recovered directly from the refined homographies and cameras are calibrated from three orthogonal vanishing points and the recovered infinite homography. There are several points of novelty. First, a simple homography-guided method for matching line segments between two views is proposed. Second, under the assumption of zero-skew, the cameras are auto-calibrated with all the four intrinsic parameters varying between the two views. The advantages of the method is that it can build more realistic models with minimal human interactions, and it also allows us to reconstruct more visible surfaces on the detected planes than traditional methods which can only reconstruct the overlapping parts, since the homography provides a one-to-one mapping of points and lines between different views. Extensive experiments with real images illustrate the validity and advantages of the proposed method.

The impact of radial distortion on the self-calibration of rotating cameras

Recent methods of automatically calibrating the intrinsic parameters of cameras undergoing pure rotation are based on the infinite homography constraint, and have been found to be sensitive to radial distortion in the imagery. This paper develops a straightforward argument based on geometrical optics to show that increasing pin-cushion radial distortion will produce a gently worsening underestimate of the lens’ focal length, whereas increasing barrel radial distortion will produce a more sharply increasing overestimate followed by failure of the calibration. A second geometrical argument uses the approximation of a barrel-distorted image to a spherical projection to estimate the degree of distortion at which breakdown is likely to occur. The predictions are verified experimentally using data from real scenes with varying degrees of distortion and noise added. The paper also considers four methods of correcting the radial distortion within self-calibration. The first method pre-calibrates the distortion as a function of focal length, but the remainder assume no such prior knowledge. Although these prior-less methods are successful to an extent, everyday scenes are unlikely to provide image feature data of sufficient density and quality to make them fully viable.

Self-Calibration of Rotating and Zooming Cameras

In this paper we describe the theory and practice of self-calibration of cameras which are fixed in location and may freely rotate while changing their internal parameters by zooming. The basis of our approach is to make use of the so-called infinite homography constraint which relates the unknown calibration matrices to the computed inter-image homographies. In order for the calibration to be possible some constraints must be placed on the internal parameters of the camera. We present various self-calibration methods. First an iterative non-linear method is described which is very versatile in terms of the constraints that may be imposed on the camera calibration: each of the camera parameters may be assumed to be known, constant throughout the sequence but unknown, or free to vary. Secondly, we describe a fast linear method which works under the minimal assumption of zero camera skew or the more restrictive conditions of square pixels (zero skew and known aspect ratio) or known principal point. We show experimental results on both synthetic and real image sequences (where ground truth data was available) to assess the accuracy and the stability of the algorithms and to compare the result of applying different constraints on the camera parameters. We also derive an optimal Maximum Likelihood estimator for the calibration and the motion parameters. Prior knowledge about the distribution of the estimated parameters (such as the location of the principal point) may also be incorporated via Maximum a Posteriori estimation. We then identify some near-ambiguities that arise under rotational motions showing that coupled changes of certain parameters are barely observable making them indistinguishable. Finally we study the negative effect of radial distortion in the self-calibration process and point out some possible solutions to it.

Reconstruction Based Recognition of Scenes with Multiple Repeated Components

This paper proposes an invariance based recognition scheme for scenes with multiple repeated components. The scheme considers three component subsets which characterize the scene completely. Each such three component subset is reconstructed using single image based information. We have developed a mathematical framework for the projective reconstruction based on relative affine structure of each such three component building block. This is extended to the case when each of the components is a quadric. A set of projective invariants of three quadrics has also been obtained by us. Although the reconstruction scheme is general and applicable to all multiple repeated components, it requires the computation of infinite homography. The infinite homography and hence the reconstruction scheme are only image computable with the given information in the case of translational repetition. We therefore develop a recognition strategy for the specific case of translationally repeated quadrics. As a recognition strategy for scenes with multiple translationally repeated quadric components, we propose to compute and store invariant values for each such three component subsets. Experiments on real data have shown the applicability of this approach for recognition of aerial images of power plants. The discriminatory power of the invariants and the stability of the recognition results have also been experimentally demonstrated.