  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.
