Abstract
In this paper a 2D Leap Frog Algorithm is applied to solve the so-called noisy Photometric Stereo problem. In 3-source Photometric Stereo (noiseless or noisy) an ideal unknown Lambertian surface is illuminated from distant light-source directions (their directions are assumed to be linearly independent). The subsequent goal, given three images is to reconstruct the illuminated object’s shape. Ultimately, in the presence of noise, this problem leads to a highly non-linear optimization task with the corresponding cost function having a large number of independent variables. One method to solve it is 2D Leap Frog Algorithm. During reconstruction, problem that commonly arises, renders the outliers generated in the retrieved shape. In this paper we implement 2D Leap Frog. In particular we focus on choosing snapshot size and on invoking two algorithms that can remove outliers from reconstructed shape. Performance of extended 2D Leap Frog is illustrated by examples chosen especially to demonstrate how this solution is applicable in computer vision. Remarkably, this optimization scheme can also be used for an arbitrary optimization problem depending on large number of variables.
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Atanassov, R., Bose, P., Couture, M.: Algorithms for optimal outlier removal. School of Computer Science, Carleton University, Ottawa
Chauvenet, W.: A Manual of Spherical and Practical Astronomy, 5th edn. Lippincott, Philadelphia (1960)
Horn, B.: Robot Vision. McGraw-Hill, New York (1986)
Horn, B., Brooks, M.: Shape from Shading. The MIT Press (1989)
Maruya, M., Nemoto, K., Takashima, Y.: Texture based 3D shape reconstruction from multiple stereo images. In: Proceedings of 11th IAPR International Pattern Recognition Conference A: Computer Vision and Applications, vol. I, pp. 137–140 (1992)
Noakes, L., Kozera, R.: A 2D Leap Frog algorithm for optimal surface reconstruction. In: Proc. SPIE 1999, Vision Geometry VII–3811, pp. 352–364 (1999)
Noakes, L., Kozera, R.: Denoising Images: Non-linear Leap-Frog for Shape and Light-Source Recovery. In: Asano, T., Klette, R., Ronse, C. (eds.) Geometry, Morphology, and Computational Imaging. LNCS, vol. 2616, pp. 419–436. Springer, Heidelberg (2003)
Kozera, R.: Existence and uniqueness in photometric stereo. Applied Mathematics and Computation 44(1), 1–104 (1991)
Noakes, L., Kozera, R.: Nonlinearities and noise reduction in 3-Source Photometric Stereo. Journal of Mathematical Imaging and Vision 18(II), 119–127 (2003)
Noakes, L., Kozera, R., Klette, R.: The Lawn-Mowing Algorithm for noisy gradient vector. In: Proc. SPIE 1999, Vision Geometry VIII-3811, pp. 305–316 (1999)
Zubrzycki, S.: Lectures in Probability Theory and Mathematical Statistics. American Elsevier Pub., New York (1972)
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Kozera, R., Tchórzewski, J. (2012). Outlier Removal in 2D Leap Frog Algorithm. In: Cortesi, A., Chaki, N., Saeed, K., Wierzchoń, S. (eds) Computer Information Systems and Industrial Management. CISIM 2012. Lecture Notes in Computer Science, vol 7564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33260-9_12
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DOI: https://doi.org/10.1007/978-3-642-33260-9_12
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