### Abstract

A general formalism to impose topology preserving regularity on a given irregular deformation field is presented. The topology preservation conditions are derived with regard to the discrete approximations to the deformation field Jacobian in a two-dimensional image registration problem. The problem of enforcing topology preservation onto a given deformation field is formulated in terms of the deformation gradients, and solved using a cyclic projections approach. The generalization of the developed algorithm leads to a deformation field regularity control by limiting the per voxel volumetric change within a prescribed interval. Extension of the topology preservation conditions onto a three-dimensional registration problem is also presented, together with a comparative analysis of the proposed algorithm with respect to a Gaussian regularizer that enforces the same topology preservation conditions.

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

Pages (from-to) | 426-437 |

Number of pages | 12 |

Journal | Information processing in medical imaging : proceedings of the ... conference |

Volume | 18 |

State | Published - 2003 |

Externally published | Yes |

### Cite this

*Information processing in medical imaging : proceedings of the ... conference*,

*18*, 426-437.

**Topology preservation and regularity in estimated deformation fields.** / Karaçali, Bilge; Davatzikos, Christos.

Research output: Contribution to journal › Article

*Information processing in medical imaging : proceedings of the ... conference*, vol. 18, pp. 426-437.

}

TY - JOUR

T1 - Topology preservation and regularity in estimated deformation fields.

AU - Karaçali, Bilge

AU - Davatzikos, Christos

PY - 2003

Y1 - 2003

N2 - A general formalism to impose topology preserving regularity on a given irregular deformation field is presented. The topology preservation conditions are derived with regard to the discrete approximations to the deformation field Jacobian in a two-dimensional image registration problem. The problem of enforcing topology preservation onto a given deformation field is formulated in terms of the deformation gradients, and solved using a cyclic projections approach. The generalization of the developed algorithm leads to a deformation field regularity control by limiting the per voxel volumetric change within a prescribed interval. Extension of the topology preservation conditions onto a three-dimensional registration problem is also presented, together with a comparative analysis of the proposed algorithm with respect to a Gaussian regularizer that enforces the same topology preservation conditions.

AB - A general formalism to impose topology preserving regularity on a given irregular deformation field is presented. The topology preservation conditions are derived with regard to the discrete approximations to the deformation field Jacobian in a two-dimensional image registration problem. The problem of enforcing topology preservation onto a given deformation field is formulated in terms of the deformation gradients, and solved using a cyclic projections approach. The generalization of the developed algorithm leads to a deformation field regularity control by limiting the per voxel volumetric change within a prescribed interval. Extension of the topology preservation conditions onto a three-dimensional registration problem is also presented, together with a comparative analysis of the proposed algorithm with respect to a Gaussian regularizer that enforces the same topology preservation conditions.

UR - http://www.scopus.com/inward/record.url?scp=3242705133&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3242705133&partnerID=8YFLogxK

M3 - Article

VL - 18

SP - 426

EP - 437

JO - Information processing in medical imaging : proceedings of the ... conference

JF - Information processing in medical imaging : proceedings of the ... conference

SN - 1011-2499

ER -