A novel quantum representation for log-polar images

Authors:
Yi Zhang;Kai Lu;Yinghui Gao;Kai Xu
Affiliations:
Department of Computer Science, National University of Defense Technology, Changsha, China;Department of Computer Science, National University of Defense Technology, Changsha, China;Department of Electronic Science and Engineering, National University of Defense Technology, Changsha, China;Department of Computer Science, National University of Defense Technology, Changsha, China
Venue:
Quantum Information Processing
Year:
2013

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Abstract

The power of quantum mechanics has been extensively exploited to meet the high computational requirement of classical image processing. However, existing quantum image models can only represent the images sampled in Cartesian coordinates. In this paper, quantum log-polar image (QUALPI), a novel quantum image representation is proposed for the storage and processing of images sampled in log-polar coordinates. In QUALPI, all the pixels of a QUALPI are stored in a normalized superposition and can be operated on simultaneously. A QUALPI can be constructed from a classical image via a preparation whose complexity is approximately linear in the image size. Some common geometric transformations, such as symmetry transformation, rotation, etc., can be performed conveniently with QUALPI. Based on these geometric transformations, a fast rotation-invariant quantum image registration algorithm is designed for log-polar images. Performance comparison with classical brute-force image registration method reveals that our quantum algorithm can achieve a quartic speedup.