Self-calibration from image derivatives

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Abstract
This study investigates the problem of estimating the calibration parameters from image motion fields induced by a rigidly moving camera with unknown calibration parameters, where the image formation is modeled with a linear pinhole-camera model. The equations obtained show the flow to be clearly 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 are linearly related to the flow, and from these parameters the calibration can be determined. However, as for discrete motion, in the general case it is not possible, to decouple image measurements from two frames only into their translational and rotational component. 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 a full calibration at least four successive image frames are necessary with the 3D-rotation changing between the measurements. The geometric analysis gives rise to a direct self-calibration method that avoids computation of optical flow or point correspondences and uses only normal flow measurements. In this technique the direction of translation is estimated employing in a novel way smoothness constraints. Then the calibration parameters are estimated from the rotational components of several flow fields using Levenberg-Marquardt parameter estimation, iterative in the calibration parameters only. The technique proposed does not require calibration objects in the scene or special camera motions and it also avoids the computation of exact correspondence. This makes it suitable for the calibration of active vision systems which have to acquire knowledge about their intrinsic parameters while they perform other tasks, or as a tool for analyzing image sequences in large video databases.

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