TY - GEN
T1 - Shape analysis with hyperbolic wasserstein distance
AU - Shi, Jie
AU - Zhang, Wen
AU - Wang, Yalin
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/12/9
Y1 - 2016/12/9
N2 - Shape space is an active research field in computer vision study. The shape distance defined in a shape space may provide a simple and refined index to represent a unique shape. Wasserstein distance defines a Riemannian metric for the Wasserstein space. It intrinsically measures the similarities between shapes and is robust to image noise. Thus it has the potential for the 3D shape indexing and classification research. While the algorithms for computing Wasserstein distance have been extensively studied, most of them only work for genus-0 surfaces. This paper proposes a novel framework to compute Wasserstein distance between general topological surfaces with hyperbolic metric. The computational algorithms are based on Ricci flow, hyperbolic harmonic map, and hyperbolic power Voronoi diagram and the method is general and robust. We apply our method to study human facial expression, longitudinal brain cortical morphometry with normal aging, and cortical shape classification in Alzheimer's disease (AD). Experimental results demonstrate that our method may be used as an effective shape index, which outperforms some other standard shape measures in our AD versus healthy control classification study.
AB - Shape space is an active research field in computer vision study. The shape distance defined in a shape space may provide a simple and refined index to represent a unique shape. Wasserstein distance defines a Riemannian metric for the Wasserstein space. It intrinsically measures the similarities between shapes and is robust to image noise. Thus it has the potential for the 3D shape indexing and classification research. While the algorithms for computing Wasserstein distance have been extensively studied, most of them only work for genus-0 surfaces. This paper proposes a novel framework to compute Wasserstein distance between general topological surfaces with hyperbolic metric. The computational algorithms are based on Ricci flow, hyperbolic harmonic map, and hyperbolic power Voronoi diagram and the method is general and robust. We apply our method to study human facial expression, longitudinal brain cortical morphometry with normal aging, and cortical shape classification in Alzheimer's disease (AD). Experimental results demonstrate that our method may be used as an effective shape index, which outperforms some other standard shape measures in our AD versus healthy control classification study.
UR - http://www.scopus.com/inward/record.url?scp=84986267671&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84986267671&partnerID=8YFLogxK
U2 - 10.1109/CVPR.2016.546
DO - 10.1109/CVPR.2016.546
M3 - Conference contribution
AN - SCOPUS:84986267671
T3 - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
SP - 5051
EP - 5061
BT - Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016
PB - IEEE Computer Society
T2 - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016
Y2 - 26 June 2016 through 1 July 2016
ER -