@inproceedings{c69fcd5bf6da459da50408b98879623e,
title = "Orthogonal Distance Fitting of Precision Freeform Surfaces Based on L1 Norm",
abstract = "Precision free-form surfaces are widely used in advanced optical and mechanical devices. In order to evaluate the form quality of a free-form surface, it is required to fit the measurement data with the design template and compare the relative deviation between them. A common approach is to minimize the sum of squared differences in the z direction. Its solution is not robust enough and may be biased due to outliers. This paper presents a fitting algorithm which employs the sum of orthogonal distances to evaluate the goodness of fit. The orthogonal projection points are updated simultaneously with the shape and motion parameters. Additionally, the l1 norm is adopted to improve the robustness of the solution. The Monte-Carlo simulation demonstrated that the bias in the fitted intrinsic characteristics of this method is much smaller than the traditional algebraic fitting, whereas the fitted motion parameters have no distinct difference.",
keywords = "free-form surface, coordinate measuring machines",
author = "Xiangchao Zhang and Xiangqian Jiang and Scott, {Paul J.}",
note = "Publisher Copyright: {\textcopyright} 2009 by World Scientific Publishing Co. Pte. Ltd.; International Conference on Advanced Mathematical and Computational Tools in Metrology and Testing : Mathematical Tools for Measurements, AMCTM 2008 ; Conference date: 23-06-2008 Through 25-06-2008",
year = "2009",
month = apr,
day = "1",
doi = "10.1142/9789812839527_0055",
language = "English",
isbn = "9789812839510",
volume = "78",
series = "Advances in Mathematics for Applied Sciences",
publisher = "World Scientific Publishing Co.",
pages = "385--390",
editor = "Franco Pavese and Markus B{\"a}r and Forbes, {Alistair B.} and Linares, {J. M.} and C. Perruchet and Zhang, {N. F.}",
booktitle = "Advanced Mathematical and Computational Tools in Metrology and Testing VIII",
address = "United States",
}