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Geodesic Regression on the Grassmannian

  • Yi Hong
  • Roland Kwitt
  • Nikhil Singh
  • Brad Davis
  • Nuno Vasconcelos
  • Marc Niethammer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8690)

Abstract

This paper considers the problem of regressing data points on the Grassmann manifold over a scalar-valued variable. The Grassmannian has recently gained considerable attention in the vision community with applications in domain adaptation, face recognition, shape analysis, or the classification of linear dynamical systems. Motivated by the success of these approaches, we introduce a principled formulation for regression tasks on that manifold. We propose an intrinsic geodesic regression model generalizing classical linear least-squares regression. Since geodesics are parametrized by a starting point and a velocity vector, the model enables the synthesis of new observations on the manifold. To exemplify our approach, we demonstrate its applicability on three vision problems where data objects can be represented as points on the Grassmannian: the prediction of traffic speed and crowd counts from dynamical system models of surveillance videos and the modeling of aging trends in human brain structures using an affine-invariant shape representation.

Keywords

Geodesic regression Grassmann manifold Traffic speed prediction Crowd counting Shape regression 

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Supplementary material

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Yi Hong
    • 1
  • Roland Kwitt
    • 2
  • Nikhil Singh
    • 1
  • Brad Davis
    • 3
  • Nuno Vasconcelos
    • 4
  • Marc Niethammer
    • 1
    • 5
  1. 1.Department of Computer ScienceUNC Chapel HillUSA
  2. 2.Department of Computer ScienceUniversity of SalzburgAustria
  3. 3.Kitware Inc.CarrboroUSA
  4. 4.Statistical and Visual Computing LabUCSDUSA
  5. 5.Biomedical Research Imaging CenterUNC Chapel HillUSA

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