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Strategies to detect non-linear similarities by means of correlation methods



Fernando Puente León
Michael Heizmann


Intelligent Robots and Computer Vision XX: Algorithms, Techniques, and Active Vision, D.P. Casasent (ed.), Proceedings of SPIE, Vol. 4572, 2001.



Correlation methods represent a well-known and reliable approach to detect similarities between images, signal patterns, and stochastic processes. However, by means of the cross-correlation function only linear similarities are registered. Unfortunately, often it is not possible to avoid non-linearities in the characteristics of the sensors used or, as in image processing, in the interaction between illumination and the scene to be captured. Thus, in such cases correlation methods may yield poor results. In this paper, we describe alternative strategies to enhance the performance of correlation methods even when the statistical connection between the signals is non-linear. To reduce the impact of non-linearities on the signals to be analyzed, a preprocessing is performed in which certain properties affecting first-order statistics are manipulated. This step impresses the same histogram to the signals to be compared, so that typically higher correlation coefficients are obtained as compared to if no preprocessing methods were used. The performance of our approach is demonstrated with two different tasks. First, a preprocessing strategy is proposed for signals obtained from train-based sensors to enable an identification of rail switches. Finally, a method for comparing striation patterns in forensic science is presented. To investigate the benefit of this approach, a large database of toolmarks is used.