Abstract
High resolution reconstruction of 3D surfaces from images remains an active area of research since most of the methods in use are based on practical assumptions that limit their applicability. Furthermore, an additional complication in all active illumination 3D reconstruction methods is the presence of shadows, whose presence cause loss of information in the image data. We present an approach for the reconstruction of surfaces via Photometric Stereo, based on the perspective formulation of the Shape from Shading problem, solved via partial differential equations. Unlike many photometric stereo solvers that use computationally costly variational methods or a two-step approach, we use a novel, well-posed, differential formulation of the problem that enables us to solve a first order partial differential equation directly via an alternating directions raster scanning scheme. The resulting formulation enables surface computation for very large images and allows reconstruction in the presence of shadows.
This research was partly supported by European Community’s FP7- ERC program, grant agreement no. 267414 and by Broadcom foundation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Wu, C., Narasimhan, S.G., Jaramaz, B.: A multi-image shape-from-shading framework for near-lighting perspective endoscopes. IJCV, 211–228 (2009)
Deguchi, K., Okatani, T.: Shape reconstruction from an endoscope image shape-from-shading technique for a point light source at the projection center. In: Workshop on MMBIA, pp. 290–298. IEEE Computer Society (1996)
Yeung, S.Y., Tsui, H.T., Yim, A.: Global shape from shading for an endoscope image. In: Taylor, C., Colchester, A. (eds.) MICCAI 1999. LNCS, vol. 1679, pp. 318–327. Springer, Heidelberg (1999)
Hernández, C., Vogiatzis, G., Cipolla, R.: Shadows in three-source photometric stereo. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part I. LNCS, vol. 5302, pp. 290–303. Springer, Heidelberg (2008)
Onn, R., Bruckstein, A.M.: Integrability Disambiguates Surface Recovery in Two-Image Photometric Stereo. IJCV 5, 105–113 (1990)
Lee, S., Brady, M.: Integrating stereo and photometric stereo to monitor the development of glaucoma. Image and Vision Computing 9, 39–44 (1991)
Mecca, R.: Uniqueness for shape from shading via photometric stereo technique. In: ICIP, pp. 2933–2936 (2011)
Mecca, R., Falcone, M.: Uniqueness and approximation of a photometric shape-from-shading model. Accepted to SIAM Journal on Imaging Sciences (2012)
Mecca, R., Tankus, A., Bruckstein, A.M.: Two-Image Perspective Photometric Stereo Using Shape-from-Shading. In: Lee, K.M., Matsushita, Y., Rehg, J.M., Hu, Z. (eds.) ACCV 2012, Part IV. LNCS, vol. 7727, pp. 110–121. Springer, Heidelberg (2013)
Kimmel, R., Yavneh, I.: An algebraic multigrid approach for image analysis. SIAM Journal on Scientific Computing 24, 1218–1231 (2003)
Tankus, A., Kiryati, N.: Photometric stereo under perspective projection. In: ICCV, pp. 611–616 (2005)
Kimmel, R., Bruckstein, A.M.: Tracking level sets by level sets: A method for solving the shape from shading problem. CVIU 62, 47–58 (1995)
Horn, B.K.P., Brooks, M.J.: Shape from Shading. The MIT Press (1989)
Prados, E., Faugeras, O.D.: Shape from shading: A well-posed problem? In: CVPR, vol. 2, pp. 870–877. IEEE Computer Society (2005)
Tankus, A., Sochen, N.A., Yeshurun, Y.: Shape-from-shading under perspective projection. IJCV 63, 21–43 (2005)
R.Mecca, Tankus, A., Bruckstein, A.: Two-image perspective photometric stereo: Analytical and numerical analysis of a new differential model. Technical report, Technion - Israel Institute of Technology, Computer Science Department (2013)
Danielsson, P.E.: Euclidean distance mapping. Computer Graphics And image Processing 14, 227–248 (1980)
Qian, J., Zhang, Y.T., Zhao, H.K.: Fast sweeping methods for eikonal equations on triangular meshes. SIAM J. Numer. Anal. 45, 83–107 (2007)
Weber, O., Devir, Y.S., Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Parallel algorithms for approximation of distance maps on parametric surfaces. ACM Trans. Graph. 27, 104:1–104:16 (2008)
Chacon, A., Vladimirsky, A.: Fast two-scale methods for eikonal equations. SIAM J. Scientific Computing 34 (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mecca, R., Rosman, G., Kimmel, R., Bruckstein, A.M. (2013). Perspective Photometric Stereo with Shadows. In: Kuijper, A., Bredies, K., Pock, T., Bischof, H. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2013. Lecture Notes in Computer Science, vol 7893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38267-3_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-38267-3_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38266-6
Online ISBN: 978-3-642-38267-3
eBook Packages: Computer ScienceComputer Science (R0)