Robust Regression for Data with Multiple Structures
Haifeng Chen(1) Peter Meer(1) and David Tyler(2)
(1)Department of Electrical and Computer Engineering
(2)Department of Statistics
Rutgers University, Piscataway, NJ 08854, USA
In many vision problems (e.g., stereo, motion)
multiple structures can occur in the data,
in which case several instances of the same model
need to be recovered from a single data set. However,
once the measurement noise becomes significantly large
relative to the separation between the structures,
the robust statistical methods commonly used in the vision community
tend to fail. In this paper, we
show that all these techniques are special cases of
the general class of M-estimators with auxiliary scale, and
explain their failure in the presence
of noisy multiple structures. To be able to cope with data containing
multiple structures the techniques innate to vision (Hough and RANSAC)
should be combined with the robust methods customary in statistics.
The implications of our analysis are illustrated by introducing
a simple procedure for 2D multistructured data
problematic for all known current techniques.
2001 Computer Vision and Pattern Recognition Conference,
Kauai, Hawaii, December 2001, vol. I, 1069-1075.
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