Specular Surface Recovery from Reflections of a Planar Pattern Undergoing an Unknown Pure Translation

This paper addresses the problem of specular surface recovery, and proposes a novel solution based on observing the reflections of a translating planar pattern. Previous works have demonstrated that a specular surface can be recovered from the reflections of two calibrated planar patterns. In this paper, however, only one reference planar pattern is assumed to have been calibrated against a fixed camera observing the specular surface. Instead of introducing and calibrating a second pattern, the reference pattern is allowed to undergo an unknown pure translation, and a closed form solution is derived for recovering such a motion. Unlike previous methods which estimate the shape by directly triangulating the visual rays and reflection rays, a novel method based on computing the projections of the visual rays on the translating pattern is introduced. This produces a depth range for each pixel which also provides a measure of the accuracy of the estimation. The proposed approach enables a simple auto-calibration of the translating pattern, and data redundancy resulting from the translating pattern can improve both the robustness and accuracy of the shape estimation. Experimental results on both synthetic and real data are presented to demonstrate the effectiveness of the proposed approach.