Invariance to Affine-Permutation Distortions
Abstract
An object imaged from various viewpoints appears very different. Hence, effective shape representation of objects becomes central in many applications of computer vision. We consider affine and permutation distortions. We derive the affine-permutation shape space that extends, to include permutation distortions, the affine only shape space (the Grassmannian). We compute the affine-permutation shape space metric, the sample mean of multiple shapes, the geodesic defined by two shapes, and a canonical representative for a shape equivalence class. We illustrate our approach in several applications including clustering and morphing of shapes of different objects along a geodesic path. The experimental results on key benchmark datasets demonstrate the effectiveness of our framework.
Cite
Text
Gui et al. "Invariance to Affine-Permutation Distortions." IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 2019. doi:10.1109/CVPRW.2019.00151Markdown
[Gui et al. "Invariance to Affine-Permutation Distortions." IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 2019.](https://mlanthology.org/cvprw/2019/gui2019cvprw-invariance/) doi:10.1109/CVPRW.2019.00151BibTeX
@inproceedings{gui2019cvprw-invariance,
title = {{Invariance to Affine-Permutation Distortions}},
author = {Gui, Liang-Yan and Sepiashvili, David A. and Moura, José M. F.},
booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops},
year = {2019},
pages = {1157-1161},
doi = {10.1109/CVPRW.2019.00151},
url = {https://mlanthology.org/cvprw/2019/gui2019cvprw-invariance/}
}