Defect Detection using Nonparametric Regression

Halim, Siana (2012) Defect Detection using Nonparametric Regression. In: 8th World Congress in Probability in Statistics, 07-07-2012 - , Istanbul - Turki.

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Abstract

To compare signals, we first model them as nonparametric regression setup, we then wish to test either those signals are significantly the same against they are significantly different. To perform a test, first we need to measure the distance between two nonparametric regression and use this distance as test statistic for testing the null hypothesis. Typically, the distribution of test statistic under the hypothesis null is not known. This problem can be handled by deriving the asymptotic approximation for unknown distribution that holds for sample size infinitely. However, this approach practically cannot be applied in signal, since the structure of the data is frequently too complicated. We then used bootstrap tests, we move from our original data to the bootstrap world of pseudo data vector or resample. We apply this method to image processing for detecting defect on the texture. We model the images as 2D Gasser-Mueller Kernel Density with rotational-ellipsoidal support function, to estimate the regression function. Moreover, we let the errors correlated in their neighborhoods. We use standardized the modification of the Mallows distance between these two estimates, to test the hypothesis and construct spatial bootstrap to get the distribution of the test statistic. The spatial bootstrap is needed to preserve the bound of a pixel to its neighborhood.

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