The University of Edinburgh -
Division of Informatics
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Research Paper #685

Title:Lack-of-Fit Detection Using the Run-Distribution Test
Authors:Fitzgibbon,AW; Fisher,RB
Date:Feb 1994
Presented:In the proceedings of the European Conference on Computer Vision, 1994
Abstract:In this paper, we are concerned with the problem of deciding whether a fitted model accurately describes the data to which it has been fitted. We have developed an effective method of testing the lack-of-fit of a parametric model to data, with applications to the computer vision problems of robust estimation, model selection, and curve and surface segmentation. The benefits of this technique are high sensitivity (large response to small outliers) and very low dependence on the noise distribution of the input data. Our test is now to the computer vision community in several ways: - We look at the distribution of the residual errors, rather than basing statistics directly on their values. - We assume a broad enough class of distributions as to be essentially distribution independent. - The test requires no knowledge of the sensor noise level, and its response is essentially independent of that level. We present results of experiments that compare the test with the standard x2 statistic, and the median absolute deviation (MAD) measure used in robust estimation. The experiments are designed to represent typical vision tasks, namely feature tracking, robust fitting, and segmentation. We show that our test is comparable to the MAD and chi-square, but is cheaper than the MAD, and requires no knowledge of the noise level.

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