Pal Susovan, Woods Roger P, Panjiyar Suchit, Sowell Elizabeth, Narr Katherine L, Joshi Shantanu H
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.
Conf Comput Vis Pattern Recognit Workshops. 2017;2017:726-734. doi: 10.1109/CVPRW.2017.102. Epub 2017 Aug 24.
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).
我们提出了一种用于曲线形状空间切平面上线性和二次判别分类的黎曼框架。形状空间是无限维的，由曲线的平方根速度函数构建而成。我们引入了形状值随机变量以及来自预形状切空间（平移和缩放不变）样本的均值和协方差的概念，然后将其扩展到全形状空间（旋转不变）。总体的形状观测值由切空间傅里叶基的系数近似表示。然后，使用通过将原始形状观测值投影到截断傅里叶基上获得的降维特征来定义线性和二次判别分析算法。我们展示了在合成数据、皮质沟回形状、胼胝体曲线以及胎儿酒精综合征（FAS）患者面部中线曲线轮廓上的分类结果。
