18 February 2009 Compressive acquisition of ray-space using radon transform
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Abstract
In this paper, we propose a method for compressive acquisition of Ray-Space. Briefly speaking, incomplete data which directly captured by a specific device is transformed to full information by Radon transform. Ray-Space, which represents 3D images, describes position and direction of rays on reference plane in real space. Ray-Space has information of many rays. In conventional acquisition of Ray-Space, multiple cameras are used and 1 pixel on a camera captures 1 ray. Thus we need many pixels and we must capture the large amount of data. However Ray-Space has redundancy because Ray-Space consists of set of lines which depend on the depth of objects. We use the Radon transform to exploit this redundancy. The Radon transform is set of projection data along different directions. The Radon transform of Ray-Space show uneven distribution. Thus Ray-Space can be reconstructed from projection data in limited range by the inverse Radon transform. Capturing the part of projection data correspond to capturing sums of several rays by 1 pixel. A sum of several rays means a sum of brightness of rays. In this paper, we have simulated reconstruction of Ray-Space projection data which was computed by the Radon Transform of Ray-Space. This experiment showed that Ray-Space could be reconstructed from the parts of projection data. As a result, using fewer pixels than rays, we could reduce the amount of data to reconstruct Ray-Space.
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Keiji Yamashita, Tomohiro Yendo, Masayuki Tanimoto, Toshiaki Fujii, "Compressive acquisition of ray-space using radon transform", Proc. SPIE 7237, Stereoscopic Displays and Applications XX, 723715 (18 February 2009); doi: 10.1117/12.807085; https://doi.org/10.1117/12.807085
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