Second-Order Algebraic Surfaces and Two Image Photometric Stereo (original) (raw)
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Application of Computer Algebra to Photometric Stereo with Two Light Sources
Programming and Computer Software, 2018
This paper addresses the problem of reconstructing the shape of an unknown Lambertian surface from its two photometric images obtained by successive illumination of the surface with two different remote light sources. Using computer algebra methods, we investigate the conditions of existence and uniqueness of a solution to a system of algebraic equations that determine the gradient of a function of two variables given by the equation. We also analyze necessary and sufficient conditions for unique determination of a second-order algebraic surface from its two images in the general case. Correctness of the theoretical results obtained is confirmed by simulating photometric images of various surfaces.
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This paper addresses the problem of reconstructing the shape of an unknown Lambertian surface given in the 3D space by a continuously differentiable function. The surface is reconstructed from its photometric images obtained by its successive illumination with three different remote light sources. Using computer algebra methods, we show that the unique solution of the problem, which exists in the domain of all three images, can be continued beyond this domain based on the solutions obtained for any pair of the three images. To disambiguate the reconstruction of the surface from its two images, we compute the corresponding value of the parameter at the boundary of the domain. Soundness of the theoretical results is confirmed by simulating photometric images of various surfaces.
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2008 15th IEEE International Conference on Image Processing, 2008
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An Application of the Photometric Stereo Method
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7' The orientation of patches on the surface of an object can be determined from multiple images taken with different illumination, but from the Sante viewing position. This method. refer red to as photometric stereo, can be implemented using table lookup based on nunwrica l inversion of experimentally determined reflectance maps. Here we concentrate on
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This paper presents a new multi-light source photometric stereo system for reconstructing images of various characteristics of non-Lambertian rough surfaces with widely varying texture and specularity. Compared to the traditional three-light photometric stereo method, extra lights are employed using a hierarchical selection strategy to eliminate the effects of shadows and specularities, and to make the system more robust. We also show that six lights is the minimum needed in order to apply photometric stereo to the entire visible surface of any convex object. Experiments on synthetic and real scenes demonstrate that the proposed method can extract surface reflectance and orientation effectively, even in the presence of strong shadows and highlights. Hence, the method offers advantages in the recovery of dichromatic surfaces possessing rough texture or deeply relieved topographic features, with applications in reverse engineering and industrial surface inspection. Experimental results are presented in the paper. Published by Elsevier B.V.