### Abstract

The tomographic reconstruction of a planar object from its projections taken at random unknown view angles is a problem that occurs often in medical imaging. Therefore, there is a need to robustly estimate the view angles given random observations of the projections. The widely used locally linear embedding (LLE) technique provides nonlinear embedding of points on a flat manifold. In our case, the projections belong to a sphere. Therefore, we extend LLE and develop a spherical locally linear embedding (sLLE) algorithm, which is capable of embedding data points on a non-flat spherically constrained manifold. Our algorithm, sLLE, transforms the problem of the angle estimation to a spherically constrained embedding problem. It considers each projection as a high dimensional vector with dimensionality equal to the number of sampling points on the projection. The projections are then embedded onto a sphere, which parametrizes the projections with respect to view angles in a globally consistent manner. The image is reconstructed from parametrized projections through the inverse Radon transform. A number of experiments demonstrate that sLLE is particularly effective for the tomography application we consider. We evaluate its performance in terms of the computational efficiency and noise tolerance, and show that sLLE can be used to shed light on the other constrained applications of LLE.

Original language | English (US) |
---|---|

Title of host publication | 2011 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2011 |

Pages | 1129-1136 |

Number of pages | 8 |

DOIs | |

State | Published - Sep 22 2011 |

Event | 2011 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2011 - Colorado Springs, CO, United States Duration: Jun 20 2011 → Jun 25 2011 |

### Other

Other | 2011 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2011 |
---|---|

Country | United States |

City | Colorado Springs, CO |

Period | 6/20/11 → 6/25/11 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Computer Vision and Pattern Recognition

### Cite this

*2011 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2011*(pp. 1129-1136). [5995563] https://doi.org/10.1109/CVPR.2011.5995563

**SLLE : Spherical locally linear embedding with applications to tomography.** / Fang, Yi; Sun, Mengtian; Vishwanathan, S. V.N.; Ramani, Karthik.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2011 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2011.*, 5995563, pp. 1129-1136, 2011 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2011, Colorado Springs, CO, United States, 6/20/11. https://doi.org/10.1109/CVPR.2011.5995563

}

TY - GEN

T1 - SLLE

T2 - Spherical locally linear embedding with applications to tomography

AU - Fang, Yi

AU - Sun, Mengtian

AU - Vishwanathan, S. V.N.

AU - Ramani, Karthik

PY - 2011/9/22

Y1 - 2011/9/22

N2 - The tomographic reconstruction of a planar object from its projections taken at random unknown view angles is a problem that occurs often in medical imaging. Therefore, there is a need to robustly estimate the view angles given random observations of the projections. The widely used locally linear embedding (LLE) technique provides nonlinear embedding of points on a flat manifold. In our case, the projections belong to a sphere. Therefore, we extend LLE and develop a spherical locally linear embedding (sLLE) algorithm, which is capable of embedding data points on a non-flat spherically constrained manifold. Our algorithm, sLLE, transforms the problem of the angle estimation to a spherically constrained embedding problem. It considers each projection as a high dimensional vector with dimensionality equal to the number of sampling points on the projection. The projections are then embedded onto a sphere, which parametrizes the projections with respect to view angles in a globally consistent manner. The image is reconstructed from parametrized projections through the inverse Radon transform. A number of experiments demonstrate that sLLE is particularly effective for the tomography application we consider. We evaluate its performance in terms of the computational efficiency and noise tolerance, and show that sLLE can be used to shed light on the other constrained applications of LLE.

AB - The tomographic reconstruction of a planar object from its projections taken at random unknown view angles is a problem that occurs often in medical imaging. Therefore, there is a need to robustly estimate the view angles given random observations of the projections. The widely used locally linear embedding (LLE) technique provides nonlinear embedding of points on a flat manifold. In our case, the projections belong to a sphere. Therefore, we extend LLE and develop a spherical locally linear embedding (sLLE) algorithm, which is capable of embedding data points on a non-flat spherically constrained manifold. Our algorithm, sLLE, transforms the problem of the angle estimation to a spherically constrained embedding problem. It considers each projection as a high dimensional vector with dimensionality equal to the number of sampling points on the projection. The projections are then embedded onto a sphere, which parametrizes the projections with respect to view angles in a globally consistent manner. The image is reconstructed from parametrized projections through the inverse Radon transform. A number of experiments demonstrate that sLLE is particularly effective for the tomography application we consider. We evaluate its performance in terms of the computational efficiency and noise tolerance, and show that sLLE can be used to shed light on the other constrained applications of LLE.

UR - http://www.scopus.com/inward/record.url?scp=80052894141&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052894141&partnerID=8YFLogxK

U2 - 10.1109/CVPR.2011.5995563

DO - 10.1109/CVPR.2011.5995563

M3 - Conference contribution

AN - SCOPUS:80052894141

SN - 9781457703942

SP - 1129

EP - 1136

BT - 2011 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2011

ER -