Fuzzy Frankot-Chellappa Method for Surface Normal Integration
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Sep 21, 2024
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Abstract
In this paper, we propose the Fuzzy formulation of the classic Frankot-Chellappa method by which surfaces can be reconstructed using normal vectors. In the Fuzzy formulation, the surface normal vectors may be uncertain or ambiguous. The underlying model yields a Fuzzy Poisson partial differential equation, where it is imperative to give meaningful representations of Fuzzy derivatives. The solution of the resulting Fuzzy model is approached numerically. To this end, a fuzzy formulation for the discrete sine transform method is explored, which results in a fast, accurate and robust method for surface reconstruction. In experiments we consider specifically the robustness with respect to noisy surface normal vectors.
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Hajighasemi, S., & Breuß, M.
(2024).
Fuzzy Frankot-Chellappa Method for Surface Normal Integration.
Proceedings Of The Conference Algoritmy, , 245 - 254.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/2183/1046
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References
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[2] T. Allahviranloo, Difference methods for fuzzy partial differential equations, Comput. Methods Appl. Math., 2(3) (2006), pp. 233–242.
[3] M. Bähr, M. Breuß, An Improved Eikonal Method for Surface Normal Integration, Proceeding of the 37th German Conference on Pattern Recognition. Aachen, Germany (2015).
[4] M. Bähr, M. Breuß, Y. Queau, A.S. Boroujerdi J.D. Durou, LU-Fast and accurate surface normal integration on non-rectangular domains, Comput. Vis. Media., 3 (2017), pp. 107–129.
[5] J.D. Durou, J.F. Aujol, F. Courteille, Integrating the normal field of a surface in the presence of discontinuities, Energy Minimization Methods Comput. Vis. Pattern Recogn., 5681 (2009), pp. 261–273.
[6] D. Dubois, H. Prade, Operations on fuzzy numbers, International Journal of Systems Science., 9(6) (1978), pp. 613–626.
[7] R.T. Frankot, R. Chellappa, A method for enforcing integrability in shape from shading algorithms, IEEE Trans. Pattern Anal. Mach. Intell., 10(4) (1988), pp. 576–593.
[8] R. Ghasemi Moghaddam, T. Allahviranloo, On the fuzzy Poisson equation, Fuzzy Sets Syst., 347 (2018), pp. 105–128.
[9] M. Harker, P. O’ Leary, Least squares surface reconstruction from measured gradient fields, In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition., (2008).
[10] B.K.P. Horn, Robot Vision, McGraw-Hill Book, (1986)
[11] Y. Queau, J-D. Durou, J-F. Aujol, Normal Integration: A survey, J Math Imaging Vis., 60 (2018), pp. 576–593.
[12] I. Perfilieva, Fuzzy transforms: Theory and applications, Fuzzy Sets Syst., 157 (2006), pp. 993–1023.
[13] I. Perfilieva, P. Valášek, Fuzzy Transforms in Removing Noise, in Computational Intelligence, Theory and Applications, International Conference 8th Fuzzy Days, Dortmund, Germany, (2004).
[14] T. Simchony, R.T. Frankot, Direct analytical methods for solving poisson equations in computer vision problems, IEEE Trans. Pattern Anal. Mach. Intell., 12(5) (1990), pp. 435–446.