Parametric Regression on the Grassmannian

IEEE Transactions on Pattern Analysis and Machine Intelligence
Yi HongMarc Niethammer

Abstract

We address the problem of fitting parametric curves on the Grassmann manifold for the purpose of intrinsic parametric regression. We start from the energy minimization formulation of linear least-squares in Euclidean space and generalize this concept to general nonflat Riemannian manifolds, following an optimal-control point of view. We then specialize this idea to the Grassmann manifold and demonstrate that it yields a simple, extensible and easy-to-implement solution to the parametric regression problem. In fact, it allows us to extend the basic geodesic model to (1) a "time-warped" variant and (2) cubic splines. We demonstrate the utility of the proposed solution on different vision problems, such as shape regression as a function of age, traffic-speed estimation and crowd-counting from surveillance video clips. Most notably, these problems can be conveniently solved within the same framework without any specifically-tailored steps along the processing pipeline.

References

Jan 1, 1994·Brain Research Bulletin·S C JohnsonD D Blatter
Mar 23, 2011·IEEE Transactions on Pattern Analysis and Machine Intelligence·Pavan TuragaRama Chellappa
Oct 25, 2011·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Antoni B Chan, Nuno Vasconcelos
Aug 21, 2013·International Journal of Computer Vision·S DurrlemanN Ayache

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Citations

Jun 30, 2019·Medical Image Analysis·Zhipeng DingUNKNOWN Alzheimer’s Disease Neuroimaging Initiative

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