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학술지 Three-dimensional Multiscale Discrete Radon and John Transforms
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저자
Jose G. Marichal-Hernandez, Oscar Gomez-Cardenes, Fernando Rosa, 김도형, Jose M. Rodriguez-Ramosa
발행일
202009
출처
Optical Engineering, v.59 no.9, pp.1-23
ISSN
0091-3286
출판사
SPIE
DOI
https://dx.doi.org/10.1117/1.OE.59.9.093104
협약과제
19HS5200, 차세대 플렌옵틱 콘텐츠 제작 플랫폼 기술 개발, 김도형
초록
Two algorithms are introduced for the computation of discrete integral transforms with a multiscale approach operating in discrete three-dimensional (3-D) volumes while considering its real-time implementation. The first algorithm, referred to as 3-D discrete Radon transform of planes, will compute the summation set of values lying in discrete planes in a cube that imitates, in discrete data, the integrals on two-dimensional planes in a 3-D volume similar to the continuous Radon transform. The normals of these planes, equispaced in ascents, cover a quadrilateralized hemisphere and comprise 12 dodecants. The second proposed algorithm, referred to as the 3-D discrete John transform of lines, will sum elements lying on discrete 3-D lines while imitating the behavior of the John or x-ray continuous transform on 3-D volumes. These discrete integral transforms do not perform interpolation on input or intermediate data, and they can be computed using only integer arithmetic with linearithmic complexity, thus outperforming the methods based on the Fourier slice-projection theorem for real-time applications. We briefly prove that these transforms have fast inversion algorithms that are exact for discrete inputs.
키워드
discrete Radon transform, integral transforms, John transform, linearithmic complexity, Radon transform, x-ray transform
KSP 제안 키워드
Discrete data, Discrete planes, Integer arithmetic, Intermediate data, Inversion algorithms, Multi-scale approach, Projection theorem, Real-Time Implementation, Real-time application, Three dimensional(3D), discrete Radon transform