Comparing Cross Correlation-Based Similarities

The real-valued Jaccard and coincidence indices, in addition to their conceptual and computational simplicity, have been verified to be able to provide promising results in tasks such as template matching, tending to yield peaks that are sharper and narrower than those typically obtained by standard cross-correlation, while also attenuating substantially secondary matchings. In this work, the multiset-based correlations based on the real-valued multiset Jaccard and coincidence indices are compared from the perspective of template matching, with encouraging results which have implications for pattern recognition, deep learning, and scientific modeling in general. The multiset-based correlation methods, and especially the coincidence index, presented remarkable performance characterized by sharper and narrower peaks while secondary peaks were attenuated, which was maintained even in presence of intense levels of noise. In particular, the two methods derived from the coincidence index led to particularly interesting results. The cross correlation, however, presented the best robustness to symmetric additive noise, which suggested a new combination of the considered approaches. After a preliminary investigation of the relative performance of the multiset approaches, as well as the classic cross-correlation, a systematic comparison framework is proposed and applied for the study of the aforementioned methods. Several results are reported, including the confirmation, at least for the considered type of data, of the coincidence correlation as providing enhanced performance regarding detection of narrow, sharp peaks while secondary matches are duly attenuated. The combined method also resulted promising for dealing with signals in presence of intense additive noise.