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Few methods have been proposed to measure three-dimensional shapes of transparent objects such as those made of glass and acrylic. In this paper, we propose a novel method for estimating the surface shapes of transparent objects by analyzing the polarization state of the light. Existing methods do not fully consider the reflection, refraction, and transmission of the light occurring inside a transparent object. We employ a polarization raytracing method to compute both the path of the light and its polarization state. Polarization raytracing is a combination of conventional raytracing, which calculates the trajectory of light rays, and Mueller calculus, which calculates the polarization state of the light. First, we set an initial value of the shape of the transparent object. Then, by changing the shape, the method minimizes the difference between the input polarization data and the rendered polarization data calculated by polarization raytracing. Finally, after the iterative computation is converged, the shape of the object is obtained. We also evaluate the method by measuring some real transparent objects.
Polarization, Raytracing, Shape-from-X, Transparency, Mueller calculus

K. Ikeuchi and D. Miyazaki, "Shape Estimation of Transparent Objects by Using Inverse Polarization Ray Tracing," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 29, no. , pp. 2018-2030, 2007.
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