2011
DOI: 10.1016/j.tcs.2010.11.029
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Abstract: a b s t r a c tThree design strategies for constructing new geometric transformations on quantum images from other transformations are proposed. The strategies focus on the affected areas in the images, the separability, and smoothness of the transformations by exploiting a representation of images on quantum computers extensively. The complexity in terms of the number of basic gates and the depth of the corresponding circuits are analyzed to understand the advantages and disadvantages of each strategy. Exampl… Show more

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Cited by 122 publications
(90 citation statements)
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“…In addition, a lot of the e®ort in QIP has been focused on designing algorithms to manipulate the position and color information encoded using the FRQI and its many variants. For instance, FRQIbased fast geometric transformations including (two-point) swapping,°ip, (orthogonal) rotations 14 and restricted geometric transformations to constrain these operations to a speci¯ed area of an image 15,16 were initially proposed. Recently, NEQR-based quantum image translation to map the position of each picture element in an input image into a new position in an output image 17 and quantum image scaling to resize a quantum image 18 were discussed.…”
Section: 2mentioning
confidence: 99%
“…In addition, a lot of the e®ort in QIP has been focused on designing algorithms to manipulate the position and color information encoded using the FRQI and its many variants. For instance, FRQIbased fast geometric transformations including (two-point) swapping,°ip, (orthogonal) rotations 14 and restricted geometric transformations to constrain these operations to a speci¯ed area of an image 15,16 were initially proposed. Recently, NEQR-based quantum image translation to map the position of each picture element in an input image into a new position in an output image 17 and quantum image scaling to resize a quantum image 18 were discussed.…”
Section: 2mentioning
confidence: 99%
“…Geometric transformations on quantum images (GTQI) [29] are the operations that focus on manipulating the position information of the FRQI quantum images. Using the GTQI operations, classical-like transformations, such as two-point swapping, flip, co-ordinate swapping and orthogonal rotations, can be performed on the quantum images encoded in the FRQI representation using the basic quantum gates.…”
Section: Fast Geometric Transformations On Frqi Quantum Imagesmentioning
confidence: 99%
“…The general structure of circuits for geometric transformations on FRQI quantum images is shown in Figure 5. For an N-sized image, the detailed analysis of quantum circuits shows that the complexity is O(log 2 N ) for two-point swapping and O(logN ) for the other operations [29]. A detailed and astute understanding of the GTQI operations equips quantum circuit designers with the adroitness to realize more complex transformations, restricted GTQI (rGTQI), giving birth to more robust and advanced applications and utilities for quantum image processing.…”
Section: Fast Geometric Transformations On Frqi Quantum Imagesmentioning
confidence: 99%
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