Three-dimensional curve reconstruction from multiple images

1. Three-dimensional curve reconstruction from multiple images Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong

2. Outline Introduction Problem formulation Curve reconstruction Experimental results Conclusions

3. Introduction Unlike most existing methods, our approach does not require any other additional information of the image features or calibration of cameras. Since this is a point-based curve reconstruction approach , the problem of missing and/or partially occluded curves is readily handled using methods that are already established for occluded points.

4. Outline Introduction Problem formulation Curve reconstruction Experimental results Conclusions

5. Problem Formulation

6. Problem Formulation • The 2D reprojection error measured can be defined as

7. Outline Introduction Problem formulation Curve reconstruction Experimental results Conclusions

8. Curve Reconstruction

9. Curve Reconstruction Introducing (5) into (3)

10. Curve Reconstruction To avoid the non-linearity in the function,we can introducing the inverse depth =

11. Curve Reconstruction We may incorporate constraint 7(b) into the cost function (7) by means of a penalty term with a penalty factor γ.

12. Curve Reconstruction We use a three-step process to obtain a good initial guess for iterative algorithm. (1) 2D representative point selection. (2) initial point correspondences establishment 1. Affine-invariant points detection 2. Affine-invariant segments matching 3. Matching section extension 4. Similarity score computation (3) initial 3D reconstruction

13. Curve Reconstruction Point-based curve reconstruction algorithm

14. Curve Reconstruction

15. Outline • Introduction • Problem formulation • Curve reconstruction • Experimental results • Conclusions

16. Experimental Result Synthetic Images

17. Experimental Result Tissue Box • Jar

18. Experimental Result Mug • Dell Box

19. Outline Introduction Problem formulation Curve reconstruction Experimental results Conclusions

20. Conclusions In this paper, we propose a new approach for reconstructing 3D curves from a sequence of images taken by uncalibrated cameras. It is capable of constructing both planar curves and non-planar curves, and it readily handles cases where not all curves are visible or some curves are partially occluded.