Peter Adrian, Rangarajan Anand
Dept. of ECE, University of Florida, Gainesville, FL, USA.
Med Image Comput Comput Assist Interv. 2006;9(Pt 1):249-56. doi: 10.1007/11866565_31.
Shape matching plays a prominent role in the analysis of medical and biological structures. Recently, a unifying framework was introduced for shape matching that uses mixture-models to couple both the shape representation and deformation. Essentially, shape distances were defined as geodesics induced by the Fisher-Rao metric on the manifold of mixture-model represented shapes. A fundamental drawback of the Fisher-Rao metric is that it is NOT available in closed-form for the mixture model. Consequently, shape comparisons are computationally very expensive. Here, we propose a new Riemannian metric based on generalized phi-entropy measures. In sharp contrast to the Fisher-Rao metric, our new metric is available in closed-form. Geodesic computations using the new metric are considerably more efficient. Discriminative capabilities of this new metric are studied by pairwise matching of corpus callosum shapes. Comparisons are conducted with the Fisher-Rao metric and the thin-plate spline bending energy.
形状匹配在医学和生物结构分析中起着重要作用。最近，引入了一个统一框架用于形状匹配，该框架使用混合模型来耦合形状表示和变形。本质上，形状距离被定义为由费希尔 - 拉奥度量在混合模型表示的形状流形上诱导的测地线。费希尔 - 拉奥度量的一个基本缺点是它对于混合模型没有封闭形式。因此，形状比较在计算上非常昂贵。在这里，我们基于广义φ - 熵测度提出一种新的黎曼度量。与费希尔 - 拉奥度量形成鲜明对比的是，我们的新度量具有封闭形式。使用新度量进行测地线计算效率要高得多。通过胼胝体形状的成对匹配研究了这种新度量的判别能力。与费希尔 - 拉奥度量和薄板样条弯曲能量进行了比较。
