Linear self-calibration of a rotating and zooming camera

Abstract

A linear self-calibration method is given for computing the calibration of a stationary but rotating camera. The internal parameters of the camera are allowed to vary from image to image, allowing for zooming (change of focal length) and possible variation of the principal point of the camera. In order for calibration to be possible some constraints must be placed on the calibration of each image. The method works under the minimal assumption of zeroskew (rectangular pixels), or the more restrictive but reasonable conditions of square pixels, known pixel aspect ratio, and known principal point. Being linea6 the algorithm is extremely rapid, and avoids the convergence problems characteristic of iterative algorithms.

Multi-view geometry of 1D radial cameras and its application to omnidirectional camera calibration

“…As with perspective cameras [11,5], pure rotation turns out to be particularly well suited for self-calibration of central omnidirectional cameras. In particular, we present an automatic approach that recovers the accurate non-parametric distortion curve relating image radius to angle of incoming rays.…”

Camera calibration and the search for infinity

“…A method for computing the calibration of a rotating and zooming camera was given in [2] and is summarized here. The method given there relies on the fact that images obtained by such a camera are related by image-to-image homographies, otherwise known as 2D projective transformations.…”

“…The advantage of these methods is that more robust, simpler and often linear methods are available for self-calibration in this case, both for unchanging ( [4]) and changing ( [1,2]) internal parameters. The theme of this paper is that these simple methods are applicable to the case of cameras undergoing general motion, once the plane at infinity has been determined.…”

Self-calibration with Partially Known Rotations

“…If the rotation axes are known (Figure 1: "known axes · known £ angles"), we start with the formulation in equation (6). The angles « i are replaced by k i ¬ i , and the values k are the new optimization parameters (5 · r parameters in total):…”

“…On the other hand, in many practical situations, additional knowledge is available, which can be used to increase the robustness of self-calibration. De Agapito, Hayman and Reid [6] exploit a priori knowledge on the intrinsic parameters by using a MAP estimator. In this paper, we focus on rotation knowledge.…”