### Abstract

Image regression allows for time-discrete imaging data to be modeled continuously, and is a crucial tool for conducting statistical analysis on longitudinal images. Geodesic models are particularly well suited for statistical analysis, as image evolution is fully characterized by a baseline image and initial momenta. However, existing geodesic image regression models are parameterized by a large number of initial momenta, equal to the number of image voxels. In this paper, we present a sparse geodesic image regression framework which greatly reduces the number of model parameters. We combine a control point formulation of deformations with a L^{1} penalty to select the most relevant subset of momenta. This way, the number of model parameters reflects the complexity of anatomical changes in time rather than the sampling of the image. We apply our method to both synthetic and real data and show that we can decrease the number of model parameters (from the number of voxels down to hundreds) with only minimal decrease in model accuracy. The reduction in model parameters has the potential to improve the power of ensuing statistical analysis, which faces the challenging problem of high dimensionality.

Original language | English (US) |
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Title of host publication | Geometric Science of Information - First International Conference, GSI 2013, Proceedings |

Pages | 95-102 |

Number of pages | 8 |

Volume | 8085 LNCS |

DOIs | |

State | Published - 2013 |

Event | 1st International SEE Conference on Geometric Science of Information, GSI 2013 - Paris, France Duration: Aug 28 2013 → Aug 30 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8085 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 1st International SEE Conference on Geometric Science of Information, GSI 2013 |
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Country | France |

City | Paris |

Period | 8/28/13 → 8/30/13 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Geometric Science of Information - First International Conference, GSI 2013, Proceedings*(Vol. 8085 LNCS, pp. 95-102). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8085 LNCS). https://doi.org/10.1007/978-3-642-40020-9_9

**Geodesic image regression with a sparse parameterization of diffeomorphisms.** / Fishbaugh, James; Prastawa, Marcel; Gerig, Guido; Durrleman, Stanley.

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

*Geometric Science of Information - First International Conference, GSI 2013, Proceedings.*vol. 8085 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8085 LNCS, pp. 95-102, 1st International SEE Conference on Geometric Science of Information, GSI 2013, Paris, France, 8/28/13. https://doi.org/10.1007/978-3-642-40020-9_9

}

TY - GEN

T1 - Geodesic image regression with a sparse parameterization of diffeomorphisms

AU - Fishbaugh, James

AU - Prastawa, Marcel

AU - Gerig, Guido

AU - Durrleman, Stanley

PY - 2013

Y1 - 2013

N2 - Image regression allows for time-discrete imaging data to be modeled continuously, and is a crucial tool for conducting statistical analysis on longitudinal images. Geodesic models are particularly well suited for statistical analysis, as image evolution is fully characterized by a baseline image and initial momenta. However, existing geodesic image regression models are parameterized by a large number of initial momenta, equal to the number of image voxels. In this paper, we present a sparse geodesic image regression framework which greatly reduces the number of model parameters. We combine a control point formulation of deformations with a L1 penalty to select the most relevant subset of momenta. This way, the number of model parameters reflects the complexity of anatomical changes in time rather than the sampling of the image. We apply our method to both synthetic and real data and show that we can decrease the number of model parameters (from the number of voxels down to hundreds) with only minimal decrease in model accuracy. The reduction in model parameters has the potential to improve the power of ensuing statistical analysis, which faces the challenging problem of high dimensionality.

AB - Image regression allows for time-discrete imaging data to be modeled continuously, and is a crucial tool for conducting statistical analysis on longitudinal images. Geodesic models are particularly well suited for statistical analysis, as image evolution is fully characterized by a baseline image and initial momenta. However, existing geodesic image regression models are parameterized by a large number of initial momenta, equal to the number of image voxels. In this paper, we present a sparse geodesic image regression framework which greatly reduces the number of model parameters. We combine a control point formulation of deformations with a L1 penalty to select the most relevant subset of momenta. This way, the number of model parameters reflects the complexity of anatomical changes in time rather than the sampling of the image. We apply our method to both synthetic and real data and show that we can decrease the number of model parameters (from the number of voxels down to hundreds) with only minimal decrease in model accuracy. The reduction in model parameters has the potential to improve the power of ensuing statistical analysis, which faces the challenging problem of high dimensionality.

UR - http://www.scopus.com/inward/record.url?scp=84884939408&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884939408&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-40020-9_9

DO - 10.1007/978-3-642-40020-9_9

M3 - Conference contribution

AN - SCOPUS:84884939408

SN - 9783642400193

VL - 8085 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 95

EP - 102

BT - Geometric Science of Information - First International Conference, GSI 2013, Proceedings

ER -