Multi-model Estimation with J-linkage Jeongkyun Lee

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

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

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

Least Squares 5 With outliersWithout outliers

 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 , Algorithm

RANSAC 7

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

 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 Multi-model Estimation with J-Linkage Preference Set

11 Multi-model Estimation with J-Linkage

 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)

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

 Example 14 Multi-model Estimation with J-Linkage

 Results 15 Multi-model Estimation with J-Linkage

 Results 16 Multi-model Estimation with J-Linkage

 Results 17 Multi-model Estimation with J-Linkage

 Results 18 Multi-model Estimation with J-Linkage

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

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

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

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

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 Thank you!

Appendix 25

Appendix 26