SPM 2014 PosterTomographic Surface Reconstruction from Point Cloud
For more information, please contact Yukie Nagai at [email protected]
Generating transmission-length maps
・・・
Sinogram (transmission‐length mapsfrom 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:
Transmissionlength
Transmission‐length map
= ∑ ∑/ : distance from the ray source to a local maximum
of the density of points on the front/back side
Recognizing the front/back sides based on the direction of normals
Omitting the points with normalsalmost orthogonal to the ray
Raysource
Point cloudwith normals
Principles of X-ray CT used for simulation Measuring X‐ray intensity with projection angles
(generally #detectors )
Transmission length ≡ the sum of the lengths
of intersections of the object and a ray
Sinogram transmission‐length maps
Mean shift and mergingPointdensity
local maxima of point densityNumber of the maxima is odd
Order of the sides of object (should be f, b, f, b, …) is wrong
Local diffusion
X
X
Tomogram600 voxels
Robustness to missing parts / noise
Point cloudAbout 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 pointsSinogram: 500x500 pixelsTomogram: 500 voxels
SPoisson Wavelet Proposal
Reconstructed mesh
Detectors
Rotation table
X‐ray
Object
Improving computational time (currently, several tens of minutes) and estimation of transmission length
Better expression of fine features and smooth surfaces
Point cloudAbout 20 thousand points
Noise robustness
Missing parts
Sinogram(sequential maps of logthat is rational to transmission length)
2. CT reconstruction(OSEM method [Hudson and Larkin 94]
and Laplacian smoothing)
Point cloudAbout 1.8 million points
SPoisson Proposal
Sinogram512x512 pixels512 projections
Proposal
*
SPoisson *
* SPoisson: [Kazhdan and Hoppe 13]
Sinogram256x256 pixels256 projections
** Wavelet: [Manzon et al. 08]
Approximation error of SPoisson , Wavelet and proposal* **
Evaluation
Lambert-Beer law: exp
X‐ray with intensity
:attenuation coefficient
Yukie Nagai, Yutaka Ohtake, Hiromasa SuzukiSchool of Engineering, The University of Tokyo
