Résumé: We develop in this paper a new formulation for the calibration and pose estimation of three-layer flat-refractive geometry. We then extend it into the general n-layer case. We show that contrary to state-of-the-art theory, our new forms yield stable solutions under the presence of high levels of noise while improving the accuracy estimates by two orders of magnitude or more. Our closed-form expressions facilitate a direct and linear solution of the pose parameters and need no a priori knowledge. In developing our forms, we provide new insights into the nature of such systems, specifically showing that the effect of refraction on the system is captured by a single surface replacing all layers. By characterizing this surface form, we solve the n-layer problem using a fixed set of parameters, irrespective of the number of layers. Finally, we identify a new configuration in which the camera obtains central-perspective properties. Such configuration contrasts the axial nature of this system and can simplify subsequent processing. Our analyses demonstrate that reaching the levels of accuracies we record requires only simple means, e.g., a single image of a planar target. Hence, further to advancing the theory of flat-refractive geometry, we also provide a viable framework for its application.

Langue: Anglais