Reconstruction of isometrically deformable flat surfaces in 3D from multiple camera images

This paper deals with the reconstruction of smooth, flexible, isometrically embedded flat surfaces in 3D, such as a sheet of paper or a flag waving in the wind, from a set of 2D projected observations such as camera images. To solve the problem, a set of matched features of the waving object at different poses is needed, which are then applied to the reconstruction algorithm here described. The complete algorithm consists of 2 phases, the first obtaining an initial approximation from local features, the second uses this result to iterate a global cost function, trying to achieve a better estimate. To validate the algorithm, synthetic data with noise is generated, reconstructed and compared to ground truth data. Also, a second experiment consisting of real images of a sheet of paper is shown.

[1]  C Tomasi,et al.  Shape and motion from image streams: a factorization method. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Pascal Fua,et al.  Local deformation models for monocular 3D shape recovery , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[3]  Levent Tunçel,et al.  Optimization algorithms on matrix manifolds , 2009, Math. Comput..

[4]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[5]  Jack Dongarra,et al.  Templates for the Solution of Algebraic Eigenvalue Problems , 2000, Software, environments, tools.

[6]  Takeo Kanade,et al.  Shape and motion from image streams under orthography: a factorization method , 1992, International Journal of Computer Vision.

[7]  Pedro M. Q. Aguiar,et al.  Factorization with missing data for 3D structure recovery , 2002, 2002 IEEE Workshop on Multimedia Signal Processing..

[8]  John M. Lee.  Riemannian Manifolds: An Introduction to Curvature , 1997 .

[9]  Eric O. Postma,et al.  Dimensionality Reduction: A Comparative Review , 2008 .

[10]  Adrien Bartoli,et al.  Maximizing the Predictivity of Smooth Deformable Image Warps through Cross-Validation , 2008, Journal of Mathematical Imaging and Vision.

[11]  Vincent Lepetit,et al.  Closed-Form Solution to Non-rigid 3D Surface Registration , 2008, ECCV.