Template-Based Paper Reconstruction from a Single Image is Well Posed when the Rullings are Parallel

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1) The document presents a method for reconstructing a 3D model of a piece of paper from a single 2D image by using a template, when the paper deformations result in parallel rulings like pages of a book. 2) It shows that under the assumption of parallel rulings, the problem can be reduced to reconstructing 2D points given a pair of 1D cameras, making the problem well-posed. 3) The paper formulates the reconstruction as a functional optimization problem that is solved numerically to recover the 3D shape and pose of the paper. Experimental results demonstrate applications like texture replacement and occlusion handling.

Technologie Business

Template-based Paper Reconstruction from a Single Image is Well Posed when the Rulings are Parallel Pierluigi Taddei , Politecnico di Milano, Milano, Italy [email_address] Adrien Bartoli, LASMEA (CNRS / UBP), Clermont-Ferrand, France [email_address]

The problem at a glance ,[object Object],perspective image paper template internal camera parameters set of point correspondences 3D pose of the piece of paper

Related works ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Related works ,[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Assumpions H W

Is the problem well posed? ,[object Object],[object Object],[object Object],[object Object],Generalized cylinder, well posed Generic isometry, ill posed

Parametrization ,[object Object],[object Object],[object Object],[object Object]

Reduction to a 2D reconstruction using 1D cameras (1) ,[object Object]

Reduction to a 2D reconstruction using 1D cameras (2) ,[object Object],[object Object],[object Object]

Formulating the problem (1) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],Formulating the problem (2)

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Formulating the problem (3)

[object Object],[object Object],[object Object],[object Object],[object Object],Solving the problem

Generatrix plane recovery (1) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Generatrix plane recovery (1) ,[object Object],[object Object],[object Object]

Generatrix plane recovery (2) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Generatrix plane recovery (3) ,[object Object],[object Object],[object Object],[object Object],[object Object]

Experimental results (texture replacement)

Experimental results (handling occlusion)

Conclusion and future works ,[object Object],[object Object],[object Object]

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Template-Based Paper Reconstruction from a Single Image is Well Posed when the Rullings are Parallel

1. Template-based Paper Reconstruction from a Single Image is Well Posed when the Rulings are Parallel Pierluigi Taddei , Politecnico di Milano, Milano, Italy [email_address] Adrien Bartoli, LASMEA (CNRS / UBP), Clermont-Ferrand, France [email_address]

6. a well-posed problem

9. reduction to a 2D problem

10.

11.

12.

13. solving the problem

14.

15.

16.

17.

18. recover the generatrix plane

19.