Improved shape from shading without initial information

Abstract

The number of constraints imposed on the surface, the light source, the camera model and in particular the initial information makes shape from shading (SFS) very difficult for real applications. There are a considerable number of approaches which require an initial data about the 3D object such as boundary conditions (BC). However, it is difficult to obtain these information for each point of the object Edge in the image, thus the application of these approaches is limited. This paper shows an improvement of the Global View method proposed by Zhu and Shi [1]. The main improvement is that we make the resolution done automatically without any additional information on the 3D object. The method involves four steps. The first step is to determine the singular curves and the relationship between them. In the second step, we generate the global graph, determine the sub-graphs, and determine the partial and global configuration. The proposed method to determine the convexity and the concavity of the singular curves is applied in the third step. Finally, we apply the Fast-Marching method to reconstruct the 3D object. Our approach is successfully tested on some synthetic and real images. Also, the obtained results are compared and discussed with some previous methods.

Keywords

shape from shading / SFS / image formation equation / level-set / graphs theory / 3D reconstruction

References

[1] Zhu Q, Shi J. Shape from shading: Recognizing the mountains through a global view. In: Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 2006, 1839–1846

[2] Leng B, Xiong Z, Fu X. A 3D shape retrieval framework for 3D smart cities, Frontiers of Computer Science, 2010, 4(3): 394–404

[3] Bai X, Bai S, Zhu Z, LateckiL J. 3D shape matching via two layer coding. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015, 37(12): 2361–2373

[4] Zhang Z, Tan T, Huang K, Wang Y. Three-dimensional deformablemodel- based localization and recognition of road vehicles. IEEE Transactions on Image Processing, 2012, 21(1): 1–13

[5] Huang X Z, Sun X, Ren Z, Tong X, Guo B N, Zhou K. Irradiance regression for efficient final gathering in global illumination. Frontiers of Computer Science, 2015, 9(3): 456–465

[6] Horn B K P. Obtaining shape from shading information. The Psychology of Computer Vision, 1975: 115–155

[7] Durou J D, Falcone M, Sagona M. Numerical methods for shape fromshading: a new survey with benchmarks. Computer Vision and Image Understanding, 2008, 109(1): 22–43

[8] Abada L, Aouat S. Shape from shading with and without boundary conditions. In: Chen L M, Kapoor S, Bhatia R, <Eds/>. Intelligent Systems for Science and Information. Springer International Publishing, 2014: 369–387

[9] Bruss A R. The eikonal equation: Some results applicable to computer vision. Journal of Mathematical Physics, 1982, 23(5): 890–896

[10] Rouy E, Tourin A. A viscosity solutions approach to shape-from shading. SIAM Journal on Numerical Analysis, 1992, 29(3): 867–884

[11] Prados E, Faugeras O. Shape from shading: a well-posed problem? In: Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 2005, 870–877

[12] Prados E, Faugeras O. “Perspective shape from shading” and viscosity solutions. In: Proceedings of the 9th IEEE International Conference on Computer Vision. 2003, 826–831

[13] Prados E, Faugeras O. A generic and provably convergent shape-fromshading method for orthographic and pinhole cameras. International Journal of Computer Vision, 2005, 65(1-2): 97–125

[14] Camilli F, Prados E. Shape-from-Shading with discontinuous image brightness. Applied Numerical Mathematics, 2006, 56(9): 1225–1237

[15] Ragheb H, Hancock E R. Darboux smoothing for shape-from-shading. Pattern Recognition Letters, 2003, 24(1): 579–595

[16] Abada L, Aouat S. Solving the perspective shape from shading problem using a new integration method. In: Proceedings of Science and Information Conference. 2013, 416–422

[17] Chang J Y, Lee K M, Lee S U. Shape from shading using graph cuts. Pattern Recognition, 2008, 41(12): 3749–3757

[18] Lei Y, Bo T. Perspective SFS 3-D shape reconstruction algorithm with hybrid reflectance model. In: Proceedings of the 2011 International Conference on Computer Science and Network Technology. 2011, 1764–1767

[19] Xiong Y, Chakrabarti A, Basri R, Gortler S J, Jacobs D W, Zickler T. From shading to local shape. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015, 37(1): 67–79

[20] Kuroe Y, Kawakami H. Versatile neural network method for recovering shape from shading by model inclusive learning. In: Proceedings of the 2011 International Joint Conference on Neural Networks. 2011, 3194–3199

[21] Chen Z M, Cao J Z, Huang J Q. A novel 3D reconstruction algorithm based on hybrid immune particle swarm optimization. In: Proceedings of the 29th IEEE Chinese Control Conference. 2010, 5228–5231

[22] Wang G, Liu S, Han J, Zhang X. A novel shape from shading algorithm for non-Lambertian surfaces. In: Proceedings of the 3rd International Conference on Measuring Technology and Mechatronics Automation. 2011, 222–225.

[23] Oren M, Nayar S K. Generalization of the Lambertian model and implications for machine vision. International Journal of Computer Vision, 1995, 14(3): 227–251

[24] Garro V, Giachetti A. Scale space graph representation and kernel matching for non rigid and textured 3D shape retrieval. IEEE Transactions on Pattern Analysis and Machine Intelligence, doi:10.1109/TPAMI.2015.2477823, 2015

[25] Mehrdad V, Ebrahimnezhad H. 3D object retrieval based on histogram of local orientation using one-shot score support vector machine. Frontiers of Computer Science, 2015, 9(6): 990–1005

[26] Guo Y, Bennamoun M, Sohel F, et al. 3D object recognition in cluttered scenes with local surface features: a survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2014, 36(11): 2270–2287

[27] Lee M, Choi C H. Fast facial shape recovery from a single image with general, unknown lighting by using tensor representation. Pattern Recognition, 2011, 44(7): 1487–1496

[28] Jiang D L, Hu Y X, Yan S C, Zhang L, Zhang H J, Gao W. Efficient 3D reconstruction for face recognition. Pattern Recognition, 38(6): 787–798

[29] Song Z, Chung R. Nonstructured light-based sensing for 3D reconstruction. Pattern Recognition, 2010, 43(10): 3560–3571

[30] Abada L, Aouat S. Tabusearch to solve the shape from shading ambiguity. International Journal on Artificial Intelligence Tools,

[31] Guo Y W, Peng Q S, Hu G F, Wang J. Smooth feature line detection for meshes. Journal of Zhejiang University SCIENCE A, 2005, 6(5): 460–468

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg