Posterior shape models
Posterior shape models
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DOI：
10.1016/j.media.2013.05.010
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发表时间：
2013-12-01
影响因子：
10.9
通讯作者：
Vetter, Thomas
中科院分区：
文献类型：
--
作者：
Albrecht, Thomas;Luethi, Marcel;Vetter, Thomas
我们提出了一种计算给定部分数据的统计形状模型的条件分布的方法。结果是“后验形状模型”，它又是与原始模型具有相同形式的统计形状模型。这使得它可以直接用于各种算法，包括有关具有统计形状模型的一类形状的可变性的先验知识。然后，后验形状模型提供了一种统计上合理且简单的方法，将部分数据集成到这些算法中。通常，形状模型代表一个完整的器官，例如在我们的实验中股骨，通过多元正态分布建模。但由于在许多应用中形状的某些部分是先验已知的，因此在给定已知部分的情况下对整个形状的后验分布进行建模非常有意义。这些可能是孤立的标志点或形状的较大部分，例如病理或受损器官的健康部分。然而，由于对于大多数形状模型来说，数据的维数远高于示例的数量，正态分布是奇异的，并且条件分布不容易获得。在本文中，我们提出了两个主要贡献：首先，我们展示了如何将后验模型有效地计算为标准形式的统计形状模型并在任何形状模型算法中使用。我们通过免费提供的算法实现来补充本文。其次，我们表明文献中提出的最常见的解决此问题的方法相当于概率主成分分析（PPCA）和高斯过程回归。为了说明后部形状模型的用途，我们将其应用于医学图像分析中的两个问题：基于模型的图像分割，结合来自地标的先验知识，以及预测滑车发育不良患者的解剖学上正确的膝盖形状，这构成了一种新颖的医学应用。我们的实验证实，使用条件形状模型进行图像分割提高了整体分割精度和鲁棒性。 (C) 2013 Elsevier B.V. 保留所有权利。
We present a method to compute the conditional distribution of a statistical shape model given partial data. The result is a "posterior shape model", which is again a statistical shape model of the same form as the original model. This allows its direct use in the variety of algorithms that include prior knowledge about the variability of a class of shapes with a statistical shape model. Posterior shape models then provide a statistically sound yet easy method to integrate partial data into these algorithms. Usually, shape models represent a complete organ, for instance in our experiments the femur bone, modeled by a multivariate normal distribution. But because in many application certain parts of the shape are known a priori, it is of great interest to model the posterior distribution of the whole shape given the known parts. These could be isolated landmark points or larger portions of the shape, like the healthy part of a pathological or damaged organ. However, because for most shape models the dimensionality of the data is much higher than the number of examples, the normal distribution is singular, and the conditional distribution not readily available. In this paper, we present two main contributions: First, we show how the posterior model can be efficiently computed as a statistical shape model in standard form and used in any shape model algorithm. We complement this paper with a freely available implementation of our algorithms. Second, we show that most common approaches put forth in the literature to overcome this are equivalent to probabilistic principal component analysis (PPCA), and Gaussian Process regression. To illustrate the use of posterior shape models, we apply them on two problems from medical image analysis: model-based image segmentation incorporating prior knowledge from landmarks, and the prediction of anatomically correct knee shapes for trochlear dysplasia patients, which constitutes a novel medical application. Our experiments confirm that the use of conditional shape models for image segmentation improves the overall segmentation accuracy and robustness. (C) 2013 Elsevier B.V. All rights reserved.