Bias in robust estimation caused by discontinuities and multiplestructures
Stewart, C.V.
Dept. of Comput. Sci., Rensselaer Polytech. Inst., Troy, NY;
This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Aug 1997
Volume: 19,
Issue: 8
On page(s): 818-833
ISSN: 0162-8828
References Cited: 29
CODEN: ITPIDJ
INSPEC Accession Number: 5693723
Digital Object Identifier: 10.1109/34.608280
Current Version Published: 2002-08-06
Abstract
When fitting models to data containing multiple structures, such
as when fitting surface patches to data taken from a neighborhood that
includes a range discontinuity, robust estimators must tolerate both
gross outliers and pseudo outliers. Pseudo outliers are outliers to the
structure of interest, but inliers to a different structure. They differ
from gross outliers because of their coherence. Such data occurs
frequently in computer vision problems, including motion estimation,
model fitting, and range data analysis. The focus in this paper is the
problem of fitting surfaces near discontinuities in range data. To
characterize the performance of least median of the squares, least
trimmed squares, M-estimators, Hough transforms, RANSAC, and MINPRAN on
this type of data, the “pseudo outlier bias” metric is
developed using techniques from the robust statistics literature, and it
is used to study the error in robust fits caused by distributions
modeling various types of discontinuities. The results show each robust
estimator to be biased at small, but substantial, discontinuities. They
also show the circumstances under which different estimators are most
effective. Most importantly, the results imply present estimators should
be used with care, and new estimators should be developed
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