Using simplified meshes for crude registration of two partially overlapping range images

1. Using simplified meshes for crude registration of two partially overlapping range images Mercedes R.G.Márquez Wu Shin-Ting State University of Matogrosso do Sul State University of Campinas- Brazil

2. Topics • Registration Problem • Related Works • Our Proposal • 4.1 QSLIM Method • 4.2. Structures for Matching • 4.3. Local Matching • 4.4. Filtering matches • 5. Results

3. Problem • Find the rigid transformation T which aligns two partially overlapped range images I1, I2, I1 I2

4. Registration Principle • If correct correspondences (pi,qi ), are known,then the solution of equations system , by least squares method is the transformation T.

5. Traditional ICP (Iterative Closest Point) • Assume closest points correspond to each other, compute the best transform and iterate to find alignment • Converges if starting position (T0) is “close enough“

6. Getting T0 (Crude Registration) • It can be obtained in manual form.

7. Getting T0 (Crude Registration) • In automatic form : • Intrinsic Properties Matching . • Generating transformation T for each set of correspondences • Discarding false transformations

8. Topics • Registration Problem • Related Works • Our Proposal • 4.1 QSLIM Method • 4.2. Structures for Matching • 4.3. Local Matching • 4.4. Filtering matches • 5. Results

9. Related Works • Spin Images Matching (SIM) • - Spin-images (2D histograms) generated from dense sampling (only distances are considered) • - Spin-images matching.

10. Related Works • RANSAC based DARCES • A structure is determined in image I1 and exhaustively searched in image I2. Complete (dense) sampling is used.

11. Related Works • Intrinsic Curve Matching (ICM) • - Curves with zero mean gaussian curvature. • - Smallest distance between each curve pair is compared for matching

12. Related Works • Methods use complete sampling for extracting correspondences. • Questions : • How can we select more efficiently the correspondences ? • How can we discard the false matches efficiently ?

13. Topics • Registration Problem • Related Works • Our Proposal • 4.1 QSLIM Method • 4.2. Structures for Matching • 4.3. Local Matching • 4.4. Filtering matches • 5. Results

14. Our Proposal • We propose to reduce the size of data sets by simplifying the range images into meshes with fewer elements. • Conjecture  A simplified mesh that preserves the global geometric characteristic of the original data suffices for a coarse registration.

15. Topics • Registration Problem • Related Works • Our Proposal • 4.1 QSLIM Method • 4.2. Structures for Matching • 4.3. Local Matching • 4.4. Filtering matches • 5. Results

16. QSLIM Method • It is a method based in edge contraction and quadric error concept. Quadric error of a point v is given by sum of squared distances to adjacent faces. The substitute point of the edge contraction is determined by quadric error minimization process – optimal contraction.

17. Topics • Registration Problem • Related Works • Our Proposal • 4.1 QSLIM Method • 4.2. Structures for Matching • 4.3. Local Matching • 4.4. Filtering matches • 5. Results

18. Structures for matching We construct a spatial structure for matching. It is from simplified mesh and consists of a vertex and three adjacent vertices. It is more discriminative than planar structure !!! It possesses two intrinsic properties : distance and curvature (given by angles between edges and approximate normal vector in V)

19. Topics • Registration Problem • Related Works • Our Proposal • 4.1 QSLIM Method • 4.2. Structures for Matching • 4.3. Local Matching • 4.4. Filtering matches • 5. Results

20. Local Matching QSLIM guarantees than geometric characteristics are similarly represented but does not ensure the existence of a corresponding vertex in corresponding mesh. For ensuring success in matching we add in mesh M2 the 4-neighbors of each vertex.

21. Local Matching The search procedure is similar to DARCES. When distances are similar, we still compare solid angle of spatial structure (curvature) !!!.

22. Topics • Registration Problem • Related Works • Our Proposal • 4.1 QSLIM Method • 4.2. Structures for Matching • 4.3. Local Matching • 4.4. Filtering matches • 5. Results

23. Filtering Matches - Neighborhood Test: We evaluate the errors in the neighborhood of vertex V (generator of structure) - Visibility Test: • If 50% of faces of 1-neighborhood of V (transformed by T) are not visible from view direction of image I2, T is discarded.

24. Topics • Registration Problem • Related Works • Our Proposal • 4.1 QSLIM Method • 4.2. Structures for Matching • 4.3. Local Matching • 4.4. Filtering matches • 5. Results

25. Results Images with same characteristics that those used by Planitz et.al. Curvature variation low Edges and apexes Curvature variation high (reasonable) Symmetry

26. Results- Efficiency in data reduction Data Reduction Percentage  99,5%

27. Results – Efficiency in Correspondences reduction Angel Dragon Hub Club Banana Dino machine Correspondences Reduction  90,4%

28. Results – Efficiencyin falses local matches reduction Angel Dragon Hub Club Banana Dino machine Falses matches reduction 89,9%

29. Results

30. Results

31. Results – ICP Convergence Angel Dragon Hub Club Banana Dino machine ICP Convergence (in average) 6