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Summary: Journal of Mathematical Imaging and Vision 11, 195205 (1999)
c 1999 Kluwer Academic Publishers. Manufactured in The Netherlands.
Reliable Location and Regression Estimates with Application
to Range Image Segmentation
M. BACCAR, L.A. GEE AND M.A. ABIDI
University of Tennessee at Knoxville, Department of Electrical & Computer Engineering, Knoxville, TN, USA
Abstract. Range images provide important sources of information in many three-dimensional robot vision prob-
lems such as navigation and object recognition. Many physical factors, however, introduce noise to the discrete
measurements in range images, identifying the need to reassess the error distribution in samples taken from real
range images. This paper suggests the use of the L p norms to yield reliable estimates of location and regression
coefficients. This particular approach is compared against two commonly used approaches: Equally Weighted Least
Squares, which minimizes the L2 norm; and the Chebychev approximation, which minimizes the L1 norm. The
problem is a weighted least squares case where the weights are derived from the chosen parameter, p, and its ability
to yield a variety of location estimates spanning from the sample mean to the sample median. These two estimates
have a wide application in image processing that includes noise removal. This paper will show the problems as-
sociated with these two techniques, and suggest experimental solutions to minimize them. A specific operating
range is determined in which the L p norms perform well and a regression module is used in conjunction with a
region-growing segmentation algorithm to provide a reliable partition of range images.
Keywords: mean and median estimates, L p norms, robustness, efficiency, image segmentation
1. Introduction
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