Terriberry Timothy B, Damon James N, Pizer Stephen M, Joshi Sarang C, Gerig Guido
Dept. of Computer Science, Univ. of North Carolina, Chapel Hill, NC 27599, USA.
Inf Process Med Imaging. 2007;20:700-12. doi: 10.1007/978-3-540-73273-0_58.
A crucial problem in statistical shape analysis is establishing the correspondence of shape features across a population. While many solutions are easy to express using boundary representations, this has been a considerable challenge for medial representations. This paper uses a new 3-D medial model that allows continuous interpolation of the medial manifold and provides a map back and forth between it and the boundary. A measure defined on the medial surface then allows one to write integrals over the boundary and the object interior in medial coordinates, enabling the expression of important object properties in an object-relative coordinate system. We use these integrals to optimize correspondence during model construction, reducing variability due to the model parameterization that could potentially mask true shape change effects. Discrimination and hypothesis testing of populations of shapes are expected to benefit, potentially resulting in improved significance of shape differences between populations even with a smaller sample size.
统计形状分析中的一个关键问题是在总体中建立形状特征的对应关系。虽然许多解决方案使用边界表示很容易表达，但这对中轴表示来说一直是一个相当大的挑战。本文使用了一种新的三维中轴模型，该模型允许对中轴流形进行连续插值，并在中轴流形和边界之间提供双向映射。然后，在中轴表面上定义的一种度量允许人们在中轴坐标下对边界和物体内部进行积分，从而能够在与物体相关的坐标系中表达重要的物体属性。我们使用这些积分在模型构建过程中优化对应关系，减少由于模型参数化可能掩盖真实形状变化效应而产生的变异性。形状总体的判别和假设检验有望从中受益，即使样本量较小，也可能提高总体之间形状差异的显著性。
