Statistical decision methods in the presence of linear nuisance parameters and despite imaging system heteroscedastic noise: Application to wheel surface inspection

This paper proposes a novel method for fully automatic anomaly detection on objects inspected using an imaging system. In order to address the inspection of a wide range of objects and to allow the detection of any anomaly, an original adaptive linear parametric model is proposed; The great flexibility of this adaptive model offers highest accuracy for a wide range of complex surfaces while preserving detection of small defects. In addition, because the proposed original model remains linear it allows the application of the hypothesis testing theory to design a test whose statistical performances are analytically known. Another important novelty of this paper is that it takes into account the specific heteroscedastic noise of imaging systems. Indeed, in such systems, the noise level depends on the pixels' intensity which should be carefully taken into account for providing the proposed test with statistical properties. The proposed detection method is then applied for wheels surface inspection using an imaging system. Due to the nature of the wheels, the different elements are analyzed separately. Numerical results on a large set of real images show both the accuracy of the proposed adaptive model and the sharpness of the ensuing statistical test.