1. Multi-model Estimation with J-linkage Jeongkyun Lee

2. How do we find parameters of a model that contains outliers?  Application in vision: geometric figure fitting, planar surface detection, motion segmentation, etc. Motivation 2

3.  Least Squares  Least Median of Squares (LMedS)  Random Sample Consensus (RANSAC)  M-SAC  MLESAC  PROSAC  Etc. Single-model Estimation 3

4. Least Squares 4  Calculate parameters of model function  Overdetermined data set  Minimized sum of squared residuals with a matrix form,

5. Least Squares 5 With outliersWithout outliers

6.  Iterative method  Non-deterministic  Robust fitting in the presence of outliers  Simple algorithm RANSAC 6  M. A. Fischler, R. C. Bolles. Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography. Comm. of the ACM, Vol 24, pp 381-395, 1981. Algorithm

7. RANSAC 7

8.  Residual histogram analysis (RHA)  Sequential RANSAC  Multi-RANSAC  J-linkage  Kernel fitting (KF)  Mean-shift (MS)  Etc. Multi-model Estimation 8

9.  Fit multiple structures simultaneously  Require no initial parameters: # of models, model parameters Multi-model Estimation with J-Linkage 9 Algorithm Given N points, 1.Generate M model hypothesis (Random sampling) 2.Build a N x M matrix, comprised of Preference Sets of points 3.J-linkage clustering

10. 10 Multi-model Estimation with J-Linkage Preference Set

11. 11 Multi-model Estimation with J-Linkage

12.  J-linkage Clustering –Starting from all singletons –Each sweep of the algorithm merges the two clusters with the smallest distance 12 Multi-model Estimation with J-Linkage Measure the degree of overlap of the two sets and ranges from 0 (identical sets) to 1 (disjoint sets)

13.  J-linkage Clustering 13 Multi-model Estimation with J-Linkage Algorithm Assumption One-to-one matching between a point and a model

14.  Example 14 Multi-model Estimation with J-Linkage 1 2 3 4

15.  Results 15 Multi-model Estimation with J-Linkage

16.  Results 16 Multi-model Estimation with J-Linkage

17.  Results 17 Multi-model Estimation with J-Linkage

18.  Results 18 Multi-model Estimation with J-Linkage

19.  Other Results 1 19 Multi-model Estimation with J-Linkage David F. Fouhey, “Multi-model Estimation in the Presence of Outliers”

20.  Other Results 1 20 Multi-model Estimation with J-Linkage David F. Fouhey, “Multi-model Estimation in the Presence of Outliers”

21.  Other Results 2 21 Multi-model Estimation with J-Linkage Hanzi Wang, “Robust Multi-Structure Fitting”, A tutorial in ACCV 2012.

22.  Other Results 2 22 Multi-model Estimation with J-Linkage Hanzi Wang, “Robust Multi-Structure Fitting”, A tutorial in ACCV 2012.

23. Reference 23  David F. Fouhey, “Multi-model Estimation in the Presence of Outliers”  Stefano Branco, “RANSAC/MLESAC, Estimating parameters of models with outliers”  Hanzi Wang, “Robust Multi-Structure Fitting”, A tutorial in ACCV 2012.

24. 24 Thank you!

25. Appendix 25

26. Appendix 26