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Posterior shape models

机译：后形模型

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摘要

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 mul-tivariate 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.
机译：我们介绍了一种计算统计形状模型的条件分布给定部分数据。结果是“后形模型”，其再次是与原始模型相同的形式的统计形状模型。这允许其直接用在各种算法中，包括关于具有统计形状模型的一类形状的可变性的先验知识。然后，后形模型提供统计上的声音且简单的方法，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，股骨骨骼，由Mul-Tivariate正常分布建模。但是，因为在许多应用中，形状的某些部分是已知的，所以在给出已知部分的情况下模拟整个形状的后部分布非常兴趣。这些可以是隔离地标点或形状的大部分，如病理或受损器官的健康部分。但是，由于对于大多数形状模型，数据的维度远高于示例的数量，正常分布是单数的，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，我们展示了后型模型如何以标准形式有效地计算为统计形状模型，并在任何形状模型算法中使用。我们通过自由实施我们的算法来补充本文。其次，我们表明，在文献中提出的最常见方法是克服这一点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使用，我们将它们应用于医学图像分析的两个问题：基于模型的图像分割，包括来自地标的先验知识，以及针对Trochlear发育不良患者的解剖学矫正膝关节形状的预测，构成了一种新型医学应用。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。

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