Reliable Location and Regression Estimates with Application to Range Image Segmentation

Range images provide important sources of information in many three-dimensional robot vision problems 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 Lp 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 associated with these two techniques, and suggest experimental solutions to minimize them. A specific operating range is determined in which the Lp 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.