Equivalence of digital image correlation criteria for pattern matching

In digital image correlation (DIC), to obtain the displacements of each point of interest, a correlation criterion must be predefined to evaluate the similarity between the reference subset and the target subset. The correlation criterion is of fundamental importance in DIC, and various correlation criteria have been designed and used in literature. However, little research has been carried out to investigate their relations. In this paper, we first provide a comprehensive overview of various correlation criteria used in DIC. Then we focus on three robust and most widely used correlation criteria, i.e., a zero-mean normalized cross-correlation (ZNCC) criterion, a zero-mean normalized sum of squared difference (ZNSSD) criterion, and a parametric sum of squared difference (PSSD(ab)) criterion with two additional unknown parameters, since they are insensitive to the scale and offset changes of the target subset intensity and have been highly recommended for practical use in literature. The three correlation criteria are analyzed to establish their transversal relationships, and the theoretical analyses clearly indicate that the three correlation criteria are actually equivalent, which elegantly unifies these correlation criteria for pattern matching. Finally, the equivalence of these correlation criteria is further validated by numerical simulation and actual experiment.