Version 1
: Received: 16 February 2024 / Approved: 19 February 2024 / Online: 19 February 2024 (10:24:49 CET)
How to cite:
Köhler, A.; Kahra, M.; Breuß, M. A First Approach to Quantum Logical Shape Classification Framework. Preprints2024, 2024021042. https://doi.org/10.20944/preprints202402.1042.v1
Köhler, A.; Kahra, M.; Breuß, M. A First Approach to Quantum Logical Shape Classification Framework. Preprints 2024, 2024021042. https://doi.org/10.20944/preprints202402.1042.v1
Köhler, A.; Kahra, M.; Breuß, M. A First Approach to Quantum Logical Shape Classification Framework. Preprints2024, 2024021042. https://doi.org/10.20944/preprints202402.1042.v1
APA Style
Köhler, A., Kahra, M., & Breuß, M. (2024). A First Approach to Quantum Logical Shape Classification Framework. Preprints. https://doi.org/10.20944/preprints202402.1042.v1
Chicago/Turabian Style
Köhler, A., Marvin Kahra and Michael Breuß. 2024 "A First Approach to Quantum Logical Shape Classification Framework" Preprints. https://doi.org/10.20944/preprints202402.1042.v1
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 device suitable applications. This article aims to propose for the first time an approach to use quantum logic in image processing at hand of a process 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 to initiate the principal component analysis. At hand of experiments, we explore the possibility to distinguish between different geometrical objects and discuss the results in terms of quantum logical interpretation.
Keywords
quantum logic; principal component analysis; shape classification; Hilbert space
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
