Subspace Procrustes Analysis

Xavier Perez-Sala, Fernando De la Torre, Laura Igual, Sergio Escalera, Cecilio Angulo

    Research output: Contribution to journalArticleResearchpeer-review

    2 Citations (Scopus)

    Abstract

    © 2016, Springer Science+Business Media New York. 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.
    Original languageEnglish
    Pages (from-to)327-343
    JournalInternational Journal of Computer Vision
    Volume121
    Issue number3
    DOIs
    Publication statusPublished - 1 Feb 2017

    Keywords

    • Functional subspace learning
    • Learning 2D shape models
    • Procrustes analysis

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  • Cite this

    Perez-Sala, X., De la Torre, F., Igual, L., Escalera, S., & Angulo, C. (2017). Subspace Procrustes Analysis. International Journal of Computer Vision, 121(3), 327-343. https://doi.org/10.1007/s11263-016-0938-x