A Relationship Between Spline-Based Deformable Models and Weighted Graphs in Non-Rigid Matching
Abstract
Deformable models are central to non-rigid motion analysis, shape matching and non-rigid medical image registration. Spline-based deformations are a very popular class of parameterizations of deformable models and have been heavily used in multiple domains. In a somewhat separate sub-field, weighted graphs are a frequently used object parameterization. Graph matching using weighted graph object parameterizations finds application in a spectrum ranging from rigid pose estimation to deformable object recognition. Here, we demonstrate a hitherto unsuspected relationship between spline-based deformable models and weighted graphs. It turns out that spline parameterizations in the kernel representation can be used to construct equivalent weighted graphs. With this connection established, we envision a cross-fertilization between these two seemingly disparate sub-fields of computer vision.
Cite
Text
Rangarajan et al. "A Relationship Between Spline-Based Deformable Models and Weighted Graphs in Non-Rigid Matching." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2001. doi:10.1109/CVPR.2001.990617Markdown
[Rangarajan et al. "A Relationship Between Spline-Based Deformable Models and Weighted Graphs in Non-Rigid Matching." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2001.](https://mlanthology.org/cvpr/2001/rangarajan2001cvpr-relationship/) doi:10.1109/CVPR.2001.990617BibTeX
@inproceedings{rangarajan2001cvpr-relationship,
title = {{A Relationship Between Spline-Based Deformable Models and Weighted Graphs in Non-Rigid Matching}},
author = {Rangarajan, Anand and Chui, Haili and Mjolsness, Eric},
booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
year = {2001},
pages = {I:897-904},
doi = {10.1109/CVPR.2001.990617},
url = {https://mlanthology.org/cvpr/2001/rangarajan2001cvpr-relationship/}
}