A First Approach to Quantum Logical Shape Classification Framework

Alexander Köhler (), Marvin Kahra and Michael Breuß
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Alexander Köhler: Institute of Mathematics, Brandenburg University of Technology (BTU) Cottbus-Senftenberg, Platz der Deutschen Einheit 1, 03046 Cottbus, Germany
Marvin Kahra: Institute of Mathematics, Brandenburg University of Technology (BTU) Cottbus-Senftenberg, Platz der Deutschen Einheit 1, 03046 Cottbus, Germany
Michael Breuß: Institute of Mathematics, Brandenburg University of Technology (BTU) Cottbus-Senftenberg, Platz der Deutschen Einheit 1, 03046 Cottbus, Germany

Mathematics, 2024, vol. 12, issue 11, 1-21

Abstract: Quantum logic is a well-structured theory, which has recently received some attention because of its fundamental relation to quantum computing. However, the complex foundation of quantum logic borrowing concepts from different branches of mathematics as well as its peculiar settings have made it a non-trivial task to devise suitable applications. This article aims to propose for the first time an approach using quantum logic in image processing for shape classification. We show how to make use of the principal component analysis to realize quantum logical propositions. In this way, we are able to assign a concrete meaning to the rather abstract quantum logical concepts, and we are able to compute a probability measure from the principal components. For shape classification, we consider encrypting given point clouds of different objects by making use of specific distance histograms. This enables us to initiate the principal component analysis. Through experiments, we explore the possibility of distinguishing between different geometrical objects and discuss the results in terms of quantum logical interpretation.

Keywords: quantum logic; principal component analysis; shape classification; Hilbert spaces; eigenvectors (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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