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Pré-Publication, Document De Travail Année : 2021

Comparing Cross Correlation-Based Similarities

Luciano da Fontoura Costa
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Résumé

Introduced recently, the common product between two multisets, or functions represented as multisets (multifunctions), can be understood as being analogue to the inner product in real vector or function spaces. In addition to providing resources for quantifying joint variations, as well as the similarity between clusters in pattern recognition, the common product also allows a respective multiset convolution/correlation to be derived which, in addition to its conceptual and computational simplicity, has been verified to be able to provide enhanced 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 matching peaks. Given that the multiset convolution can be adapted to employ other similarity functionals, such as the coincidence and addition-based multiset Jaccard index, it remains an interesting subject to compare the performance of multifunction correlations based on these alternative implementations of the multifunction correlation. The present work addresses this subject, with encouraging results that can have immediate applications not only in pattern recognition and deep learning, but also in scientific modeling in general. As expected, the multifunction convolution/correlation methods presented enhanced performance, characterized by sharper and narrower peaks while secondary peaks were attenuated, which was maintained even in presence of increasing levels of noise. In particular, the two methods derived from the coincidence index led to the sharpest and narrowest peaks, as well as intense attenuation of the secondary peaks. The cross correlation, however, presented the best robustness to symmetric additive noise, which suggested a new combined method in which the cross-correlation is applied prior to the multifunction convolution methods, therefore allying the best characteristics of each of these two families of methods.
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Dates et versions

hal-03406688 , version 1 (28-10-2021)
hal-03406688 , version 2 (04-11-2021)
hal-03406688 , version 3 (17-11-2021)
hal-03406688 , version 4 (20-11-2021)

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  • HAL Id : hal-03406688 , version 1

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Luciano da Fontoura Costa. Comparing Cross Correlation-Based Similarities. 2021. ⟨hal-03406688v1⟩
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