1. Simultaneous Multi-Line- Segment Merging for Robot Mapping using Mean Shift Clustering Rolf Lakaemper Temple University, Philadelphia,PA,USA

2. Goal: segment based maps from 2D laser range scans

3. Motivation: 1)The segment based approach captures structural information 2) Segment post processing is fast 3) The segment based approach is memory efficient

4. From point maps to segment maps - Two different ways: 1)Create segment map from a global map (point based) Example: Hough transform or Split and Merge EM (Latecki/Sobel/Lakaemper, PAMI 2009)

5. Or, second: 1)detect segments in single scans (simpler, see e.g. Amigone/Gasparini IROS08) 2)Superimpose (pose- corrected) single scans 3)Cluster & merge segments This talk

6. Remark: Technique is applicable for all mapping algorithms that result in corrected poses of single scans NOT restricted to segment based maps

7. Clustering using Mean Shift

8. Mean Shift (Fukunaga/Hostetler 1975) gradient descent procedure to find multiple modes of density distributions. Iteratively shifts data points to their mean in a certain neighborhood. Mean shift: Δm = m(x) - x data points converging to the same mode belong to one cluster.

9. Main property: except for the definition of the neighborhood (i.e. kernel K), Mean Shift is parameter free. Sensitive to kernel definition In our case, domain knowledge is available to determine the kernel K for robust operation Mean Shift Δm is in the gradient direction of the density estimate q(x) = Σ p K(p − x) Mean Shift is steepest gradient ascent to the modes of the density distribution of P (with K) without explicit computation of the density.

10. Mean Shift for Segment Clustering Transform segment map to center-direction joint space α x,y x y α

11. 3d space: we omit segment length Assumption: length does not vary too much => split segments if too long

12. Use Mean Shift in two phases: Phase 1: detection of locally common directions Phase 2: Clustering by collinearity Splitting into 2 phases makes the approach more robust. For ‘simple’ data sets, the phases can be combined (I'll explain later)

13. Symmetric Gauss Kernel: x,y: we do not assume any expected directions a priori, we do not prefer collinearity to the weaker condition of parallelism. This is the main difference between the first and second phase (which uses an anisotropic kernel) x,y α

14. ... we do not assume any expected directions a priori, we do not prefer collinearity to the weaker condition of parallelism. = This prevents us from making a LOCAL, single segment direction cluster decision

15. Symmetric Gauss Kernel: σ is related to scale h defines spatial-angular relation

16. Result of first phase:

17. Phase 2: Clustering by collinearity aims at sub-clustering each phase 1-cluster using the directional information Cluster direction = average direction of cluster members Elongated (in cluster direction) anisotropic kernel Goal: merge approx. collinear segments Phase 2 is 2 dimensional clustering! (x,y space only)

18. Clustering by collinearity Single clusterSub - clustered Kernel With Covariance Matrix (b,c similar, straightforward)

19. Result of second phase:

20. The single phase approach: - Applicable if data set is 'simple' (low intra cluster direction deviation in first phase) - In first (and only) phase, use kernel with a,b,c defined LOCALLY by i-th segment direction (not by average direction), to determine K_i - Each segment has different kernel - Less robust

21. Segment Merging Merge segments of each cluster to a single representative segment.

22. Results

23. Hallway a)Points b)Segments c)Superimposed segments d)Merged segments

24. Hallway a)Superimposed segments b)Merged segments c)Cleaned version (short segments deleted) 59245 points to 255 segments

25. Texas

26. Freiburg 082er

27. NIST Maze

28. Conclusion and remarks: global segment map was built by superimposing local segment maps Clustering detects a) segments of same direction, b) collinear segments Merging reduces numbers of segments Alert! Segments are only hypotheses of point sets and have to be enjoyed with care – but we can always return to points and use segments to augment the data set

29. Thanks!