Abstract
We tackle the problem of perspective 3D-reconstruction of Lambertian surfaces through photometric stereo, in the presence of outliers to Lambert’s law, depth discontinuities, and unknown spatially-varying lightings. To this purpose, we introduce a robust \(L^1\)-TV variational formulation of the recovery problem where the shape itself is the main unknown, which naturally enforces integrability and permits to avoid integrating the normal field.
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References
Alldrin, N.G., Mallick, S.P., Kriegman, D.J.: Resolving the generalized bas-relief ambiguity by entropy minimization. In: CVPR (2007)
Basri, R., Jacobs, D., Kemelmacher, I.: Photometric stereo with general, unknown lighting. IJCV 72(3), 239–257 (2007)
Bresson, X., Chan, T.: Fast dual minimization of the vectorial total variation norm and applications to color image processing. IPI 2(4), 455–484 (2008)
Chambolle, A.: An algorithm for total variation minimization and applications. JMIV 20(1–2), 89–97 (2004)
Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. JMIV 40(1), 120–145 (2011)
Durou, J.-D., Aujol, J.-F., Courteille, F.: Integrating the normal field of a surface in the presence of discontinuities. In: Cremers, D., Boykov, Y., Blake, A., Schmidt, F.R. (eds.) EMMCVPR 2009. LNCS, vol. 5681, pp. 261–273. Springer, Heidelberg (2009)
Georghiades, A.: Incorporating the torrance and sparrow model of reflectance in uncalibrated photometric stereo. In: ICCV (2003)
Goldluecke, B., Strekalovskiy, E., Cremers, D.: The natural vectorial total variation which arises from geometric measure theory. SIIMS 5(2), 537–563 (2012)
Goldstein, T., Osher, S.: The Split Bregman method for L1-regularized problems. SIIMS 2(2), 323–343 (2009)
Ikehata, S., Wipf, D., Matsushita, Y., Aizawa, K.: Robust photometric stereo using sparse regression. In: CVPR (2012)
Mecca, R., Tankus, A., Wetzler, A., Bruckstein, A.M.: A direct differential approach to photometric stereo with perspective wiewing. SIIMS 7(2), 579–612 (2014)
Mumford, D.: Bayesian rationale for the variational formulation. In: Geometry-Driven Diffusion in Computer Vision, pp. 135–146 (1994)
Osher, S., Burger, M., Goldfarb, D., Xu, J., Yin, W.: An iterative regularization method for total variation-based image restoration. MMS 4(2), 460–489 (2005)
Papadhimitri, T., Favaro, P.: A new perspective on uncalibrated photometric stereo. In: CVPR (2013)
Quéau, Y., Lauze, F., Durou, J.D.: Solving uncalibrated photometric stereo using total variation. To appear in JMIV (2015)
Simchony, T., Chellappa, R., Shao, M.: Direct analytical methods for solving Poisson equations in computer vision problems. PAMI 12(5), 435–446 (1990)
Woodham, R.J.: Photometric method for determining surface orientation from multiple images. Optical Engineering 19(1), 139–144 (1980)
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Quéau, Y., Lauze, F., Durou, JD. (2015). A \(L^1\)-TV Algorithm for Robust Perspective Photometric Stereo with Spatially-Varying Lightings. In: Aujol, JF., Nikolova, M., Papadakis, N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2015. Lecture Notes in Computer Science(), vol 9087. Springer, Cham. https://doi.org/10.1007/978-3-319-18461-6_40
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DOI: https://doi.org/10.1007/978-3-319-18461-6_40
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