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Applications of Cross-Correlation Functions



Theodore V. Vorburger, Jun-Feng Song, Wei Chu, Li Ma, Xiaoyu A. Zheng, Thomas B. Renegar, Son H. Bui


We describe several examples where we use cross-correlation functions to quantify the similarity of 2D surface profiles or of 3D surface topography images. The applications have included 1) the manufacture of Standard Reference Material (SRM) bullets and casings, 2) methods to assess whether bullets or casings have been fired by the same firearm, 3) research to quantify similarities or differences between profiles of the same surface measured by different techniques or between a master surface and its replicas, and 4) an image stitching approach for linewidth measurement with atomic force microscopy. The cross-correlation maximum is the functional parameter used to quantify similarity. A second parameter, called the relative profile difference for 2D or relative topography difference for 3D, may also be used to quantify differences and to recognize the ambiguous condition when two results have different vertical (Z-) scales but identical shapes. The instruments used in these studies have included stylus instruments, a Nipkow-disk type confocal microscope, and an interferometric microscope. Most of these examples have been applied in support of ballistics inspection methods in crime labs, but the methods are generally useful for estimating the accuracy of surface replication techniques or the ability of different surface topography instruments to measure the same surface and provide the same result. Cross-correlation functions may also be used to assess differences resulting from the use of different filters to modify the same surface profile or topography image.


cross-correlation, surface, roughness, topography, ballistics


Vorburger, T. , Song, J. , Chu, W. , Ma, L. , Zheng, X. , Renegar, T. and Bui, S. (2010), Applications of Cross-Correlation Functions, Wear, [online], (Accessed May 24, 2024)


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Created April 14, 2010, Updated November 10, 2018