Kurtek Sebastian, Klassen Eric, Ding Zhaohua, Avison Malcolm J, Srivastava Anuj
Department of Statistics, Florida State University, Tallahassee, FL, USA.
Inf Process Med Imaging. 2011;22:147-58. doi: 10.1007/978-3-642-22092-0_13.
We consider the task of computing shape statistics and classification of 3D anatomical structures (as continuous, parameterized surfaces). This requires a Riemannian metric that allows re-parameterizations of surfaces by isometries, and computations of geodesics. This allows computing Karcher means and covariances of surfaces, which involves optimal re-parameterizations of surfaces and results in a superior alignment of geometric features across surfaces. The resulting means and covariances are better representatives of the original data and lead to parsimonious shape models. These two moments specify a normal probability model on shape classes, which are used for classifying test shapes into control and disease groups. We demonstrate the success of this model through improved random sampling and a higher classification performance. We study brain structures and present classification results for Attention Deficit Hyperactivity Disorder. Using the mean and covariance structure of the data, we are able to attain an 88% classification rate.
我们考虑计算三维解剖结构（作为连续的、参数化曲面）的形状统计量和分类的任务。这需要一种黎曼度量，它允许通过等距变换对曲面进行重新参数化，并计算测地线。这使得能够计算曲面的卡彻均值和协方差，这涉及到曲面的最优重新参数化，并导致跨曲面几何特征的更好对齐。由此产生的均值和协方差是原始数据的更好代表，并导致简洁的形状模型。这两个矩指定了形状类别的正态概率模型，用于将测试形状分类为对照组和疾病组。我们通过改进随机抽样和更高的分类性能证明了该模型的成功。我们研究脑结构，并给出注意力缺陷多动障碍的分类结果。利用数据的均值和协方差结构，我们能够达到88%的分类率。
