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      A Riemannian Framework for Linear and Quadratic Discriminant Analysis on the Tangent Space of Shapes

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          Abstract

          We present a Riemannian framework for linear and quadratic discriminant classification on the tangent plane of the shape space of curves. The shape space is infinite dimensional and is constructed out of square root velocity functions of curves. We introduce the notion of mean and covariance of shape-valued random variables and samples from a tangent space to the pre-shapes (invariant to translation and scaling) and then extend it to the full shape space (rotational invariance). The shape observations from the population are approximated by coefficients of a Fourier basis of the tangent space. The algorithms for linear and quadratic discriminant analysis are then defined using reduced dimensional features obtained by projecting the original shape observations on to the truncated Fourier basis. We show classification results on synthetic data and shapes of cortical sulci, corpus callosum curves, as well as facial midline curve profiles from patients with fetal alcohol syndrome (FAS).

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          Author and article information

          Contributors
          Journal
          101554644
          39019
          Conf Comput Vis Pattern Recognit Workshops
          Conf Comput Vis Pattern Recognit Workshops
          Conference on Computer Vision and Pattern Recognition Workshops . IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Workshops
          2160-7508
          2160-7516
          20 July 2017
          24 August 2017
          2017
          01 December 2017
          : 2017
          : 726-734
          Affiliations
          UCLA Brain Mapping Center, University of California, Los Angeles, Los Angeles, CA, USA
          UCLA Brain Mapping Center, University of California, Los Angeles, Los Angeles, CA, USA
          Department of Computer Science, University of California, Los Angeles, Los Angeles, CA, USA
          Department of Pediatrics, Children’s Hospital Los Angeles, University of Southern California, Los Angeles, Los Angeles, CA, USA
          UCLA Brain Mapping Center, University of California, Los Angeles, Los Angeles, CA, USA
          UCLA Brain Mapping Center, University of California, Los Angeles, Los Angeles, CA, USA
          Article
          PMC5710852 PMC5710852 5710852 nihpa884705
          10.1109/CVPRW.2017.102
          5710852
          29201534
          a1867dde-b9c4-4c67-91d4-a3364e59693d
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