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2-D robust recursive least squares lattice algorithm for defect inspection of textile products

In this paper, a 2-D robust recursive least squares lattice algorithm is introduced and is applied to defect detection problem in textured images. The algorithm combines concepts of 1-D robust regression with the recursive least squares lattice algorithm. The philosophy of using different optimization functions that results in weighted least-squares solutions in the theory of 1-D robust regression is extended to 2-D. With this approach, whatever probability distribution of the estimation error may be, small weights are assigned to the outliers in that distribution so that the least squares algorithm will be less sensitive to the outliers. The results obtained are compared with those of conventional recursive least squares lattice algorithm. The performance evaluation, in terms of defect detection rate, demonstrates the importance of the proposed algorithm in reducing the effect of the outliers that generally correspond to false alarms in classification of textures as defective or nondefective.