Learning Shape Trends: Parameter Estimation in Diffusions on Shape Manifolds
Abstract
Learning the dynamics of shape is at the heart of many computer vision problems: object tracking, change detection, longitudinal shape analysis, trajectory classification, etc. In this work we address the problem of statistical inference of diffusion processes of shapes. We formulate a general Itô diffusion on the manifold of deformable landmarks and propose several drift models for the evolution of shapes. We derive explicit formulas for the maximum likelihood estimators of the unknown parameters in these models, and demonstrate their convergence properties on simulated sequences when true parameters are known. We further discuss how these models can be extended to a more general non-parametric approach to shape estimation.
Cite
Text
Staneva and Younes. "Learning Shape Trends: Parameter Estimation in Diffusions on Shape Manifolds." IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 2017. doi:10.1109/CVPRW.2017.101Markdown
[Staneva and Younes. "Learning Shape Trends: Parameter Estimation in Diffusions on Shape Manifolds." IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 2017.](https://mlanthology.org/cvprw/2017/staneva2017cvprw-learning/) doi:10.1109/CVPRW.2017.101BibTeX
@inproceedings{staneva2017cvprw-learning,
title = {{Learning Shape Trends: Parameter Estimation in Diffusions on Shape Manifolds}},
author = {Staneva, Valentina and Younes, Laurent},
booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops},
year = {2017},
pages = {717-725},
doi = {10.1109/CVPRW.2017.101},
url = {https://mlanthology.org/cvprw/2017/staneva2017cvprw-learning/}
}