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SPM 2014 Poster Tomographic Surface Reconstruction from Point Cloud For more information, please contact Yukie Nagai at [email protected] Generating transmission-length maps ・・・ Sinogram (transmission‐length maps from various directions) Tomogram (CT image) Isosurface ・・・ 1. Computing transmission length Surface reconstruction by simulating CT scanning for point cloud Emanating virtual parallel cylindrical rays Transmission length: Transmission length Transmission‐ length map = ∑ ݍ െ ∑ ݍ ݍ/ : distance from the ray source to a local maximum of the density of points on the front/back side ݍ ଶ ݍ ଵ ݍ ଶ ݍ ଵ Recognizing the front/back sides based on the direction of normals Omitting the points with normals almost orthogonal to the ray Ray source Point cloud with normals Principles of X-ray CT used for simulation Measuring X‐ray intensity with projection angles ߠ (generally #detectors ) Transmission length ≡ the sum of the lengths of intersections of the object and a ray Sinogram ൎ transmission‐length maps Mean shift and merging Point density local maxima of point density Number of the maxima is odd Order of the sides of object (should be f, b, f, b, …) is wrong Local diffusion X X Tomogram 600 ଷ voxels Robustness to missing parts / noise Point cloud About 2.6 million points Transmission-length maps from various projection directions Using randomly selected directions as projection directions, the geometry which the conventional projection directions cannot capture is better acquired Point cloud with missing parts Isosurface Conventional projection directions … … Conventional Proposal Randomly selected projection directions Future work Point cloud: about 170 thousand points Sinogram: 500x500 pixels Tomogram: 500 ଷ voxels SPoisson Wavelet Proposal Reconstructed mesh Detectors Rotation table X‐ray Object ߠ ܫ Improving computational time (currently, several tens of minutes) and estimation of transmission length Better expression of fine features and smooth surfaces Point cloud About 20 thousand points Noise robustness Missing parts Sinogram (sequential maps of െlog బ that is rational to transmission length) ߠൌ ߠଵ ߠൌ ߠଶ ߠൌ ߠே ൌ ଵ ଶ 2. CT reconstruction (OSEM method [Hudson and Larkin 94] and Laplacian smoothing) Point cloud About 1.8 million points SPoisson Proposal Sinogram 512x512 pixels 512 projections Proposal * SPoisson * * SPoisson: [Kazhdan and Hoppe 13] Sinogram 256x256 pixels 256 projections ** Wavelet: [Manzon et al. 08] Approximation error of SPoisson , Wavelet and proposal * ** Evaluation Lambert-Beer law: ܫൌ ܫ exp െߤ X‐ray with intensity ܫ :ߤattenuation coefficient Yukie Nagai, Yutaka Ohtake, Hiromasa Suzuki School of Engineering, The University of Tokyo
