A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Generalized Grover Search Algorithm for Arbitrary Initial Amplitude Distribution
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Image retrieval: Ideas, influences, and trends of the new age
ACM Computing Surveys (CSUR)
Image segmentation evaluation: A survey of unsupervised methods
Computer Vision and Image Understanding
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Processing images in entangled quantum systems
Quantum Information Processing
Quantum Information Processing
Region growing: a new approach
IEEE Transactions on Image Processing
Survey of clustering algorithms
IEEE Transactions on Neural Networks
Image storage, retrieval, compression and segmentation in a quantum system
Quantum Information Processing
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Multi-dimensional color image processing has two difficulties: One is that a large number of bits are needed to store multi-dimensional color images, such as, a three-dimensional color image of $$1024 \times 1024 \times 1024$$ 1024 脳 1024 脳 1024 needs $$1024 \times 1024 \times 1024 \times 24$$ 1024 脳 1024 脳 1024 脳 24 bits. The other one is that the efficiency or accuracy of image segmentation is not high enough for some images to be used in content-based image search. In order to solve the above problems, this paper proposes a new representation for multi-dimensional color image, called a $$(n\,+\,1)$$ ( n + 1 ) -qubit normal arbitrary quantum superposition state (NAQSS), where $$n$$ n qubits represent colors and coordinates of $${2^n}$$ 2 n pixels (e.g., represent a three-dimensional color image of $$1024 \times 1024 \times 1024$$ 1024 脳 1024 脳 1024 only using 30 qubits), and the remaining 1 qubit represents an image segmentation information to improve the accuracy of image segmentation. And then we design a general quantum circuit to create the NAQSS state in order to store a multi-dimensional color image in a quantum system and propose a quantum circuit simplification algorithm to reduce the number of the quantum gates of the general quantum circuit. Finally, different strategies to retrieve a whole image or the target sub-image of an image from a quantum system are studied, including Monte Carlo sampling and improved Grover's algorithm which can search out a coordinate of a target sub-image only running in $$O(\sqrt{N/r} )$$ O ( N / r ) where $$N$$ N and $$r$$ r are the numbers of pixels of an image and a target sub-image, respectively.