Dilation correlation functions and their applications

A development of the cross-/autocorrelation function is introduced which is capable of detecting and quantifying stretching or contraction between functions. Its analytic properties are described and discrete algorithms are deduced for its application to experimental data sets. Tests for ascertaining whether stretching or displacement models are appropriate arise naturally out of the analysis. A range of illustrations are included together with an application to the detection of thermal expansion effects on images of combustion in internal combustion engines