Generalised cross-correlation functions for engineering applications. Application to experimental data

Abstract

 A recent generalisation of cross-correlation (GC-C) makes it possible to model transformations between data such as pairs of images by sets of parameterised functions as opposed to constant shifts, rotations etc. as employed in conventional cross-correlation. Typical applications of GC-C are in areas such as particle image velocimetry (PIV), or two-dimensional or three-dimensional surface strain field determinations. As the flow, strain etc. descriptions developed by GC-C are global or zonal, the parameters required are estimated using all or a large fraction of the information in the images typically used to provide the basic data in such techniques. This is in complete contrast to traditional cross-correlation methods used in PIV, where the image domains are segmented into small sub-regions and a constant shift, rotation etc. is determined separately in each local cell. Such local cellular methods inevitably introduce a compromise between spatial resolution and the statistical confidence that can be placed in the estimates of the shifts, rotations etc. GC-C removes the need for such compromises. This paper examines the application of the small perturbation form of GC-C to real experimental data sets with special emphasis on showing the effects of the analytical approximations employed in the perturbation scheme. In particular, the key issue of the effects of the bandwidth of the images used are explored and a very simple procedure is described for checking that optimal results are being obtained.