International Journal of Computer Vision

, Volume 121, Issue 3, pp 327–343 | Cite as

Subspace Procrustes Analysis

  • Xavier Perez-Sala
  • Fernando De la Torre
  • Laura Igual
  • Sergio Escalera
  • Cecilio Angulo
Article
  • 343 Downloads

Abstract

Procrustes analysis (PA) has been a popular technique to align and build 2-D statistical models of shapes. Given a set of 2-D shapes PA is applied to remove rigid transformations. Later, a non-rigid 2-D model is computed by modeling the residual (e.g., PCA). Although PA has been widely used, it has several limitations for modeling 2-D shapes: occluded landmarks and missing data can result in local minima solutions, and there is no guarantee that the 2-D shapes provide a uniform sampling of the 3-D space of rotations for the object. To address previous issues, this paper proposes subspace PA (SPA). Given several instances of a 3-D object, SPA computes the mean and a 2-D subspace that can model rigid and non-rigid deformations of the 3-D object. We propose a discrete (DSPA) and continuous (CSPA) formulation for SPA, assuming that 3-D samples of an object are provided. DSPA extends the traditional PA, and produces unbiased 2-D models by uniformly sampling different views of the 3-D object. CSPA provides a continuous approach to uniformly sample the space of 3-D rotations, being more efficient in space and time. We illustrate the benefits of SPA in two different applications. First, SPA is used to learn 2-D face and body models from 3-D datasets. Experiments on the FaceWarehouse and CMU motion capture (MoCap) datasets show the benefits of our 2-D models against the state-of-the-art PA approaches and conventional 3-D models. Second, SPA learns an unbiased 2-D model from CMU MoCap dataset and it is used to estimate the human pose on the Leeds Sports dataset.

Keywords

Procrustes analysis Learning 2D shape models Functional subspace learning 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Xavier Perez-Sala
    • 1
    • 2
    • 3
    • 5
  • Fernando De la Torre
    • 2
  • Laura Igual
    • 4
    • 5
  • Sergio Escalera
    • 4
    • 5
  • Cecilio Angulo
    • 3
  1. 1.Fundació Privada Sant Antoni AbatVilanova i la GeltrúSpain
  2. 2.Robotics InstituteCarnegie Mellon UniversityPittsburghUSA
  3. 3.Universitat Politècnica de CatalunyaVilanova i la GeltrúSpain
  4. 4.Department of Mathematics and Computer ScienceUniversitat de BarcelonaBarcelonaSpain
  5. 5.Computer Vision CenterUniversitat Autònoma de BarcelonaBellaterraSpain

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