### Abstract

We consider the classical optical flow algorithm due to Horn and Schunck for estimating the motion of brightness patterns between image pairs. We use a modified smoothness condition based on the divergence and curl of the velocity field. In previous work, we have developed well-posed stochastic state-space models for these optical flow methods in two dimensions. This paper extends our results to 3-D. We first show that by using the first order DIV-CURL spline, it is not possible to obtain a first order linear differential well-posed model in 3-D. Next, we employ the second order DIV-CURL spline smoothness condition and develop well-posed state-space models.

Original language | English (US) |
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Pages | 929-932 |

Number of pages | 4 |

State | Published - Dec 1 1996 |

Event | Proceedings of the 1996 IEEE International Conference on Image Processing, ICIP'96. Part 2 (of 3) - Lausanne, Switz Duration: Sep 16 1996 → Sep 19 1996 |

### Other

Other | Proceedings of the 1996 IEEE International Conference on Image Processing, ICIP'96. Part 2 (of 3) |
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City | Lausanne, Switz |

Period | 9/16/96 → 9/19/96 |

### ASJC Scopus subject areas

- Hardware and Architecture
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering

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## Cite this

Gupta, S. N., & Prince, J. L. (1996).

*On DIV-CURL regularization for motion estimation in 3-D volumetric imaging*. 929-932. Paper presented at Proceedings of the 1996 IEEE International Conference on Image Processing, ICIP'96. Part 2 (of 3), Lausanne, Switz, .