Zhang Miaomiao, Fletcher P Thomas
Med Image Comput Comput Assist Interv. 2014;17(Pt 3):121-8. doi: 10.1007/978-3-319-10443-0_16.
Computing a concise representation of the anatomical variability found in large sets of images is an important first step in many statistical shape analyses. In this paper, we present a generative Bayesian approach for automatic dimensionality reduction of shape variability represented through diffeomorphic mappings. To achieve this, we develop a latent variable model for principal geodesic analysis (PGA) that provides a probabilistic framework for factor analysis on diffeomorphisms. Our key contribution is a Bayesian inference procedure for model parameter estimation and simultaneous detection of the effective dimensionality of the latent space. We evaluate our proposed model for atlas and principal geodesic estimation on the OASIS brain database of magnetic resonance images. We show that the automatically selected latent dimensions from our model are able to reconstruct unseen brain images with lower error than equivalent linear principal components analysis (LPCA) models in the image space, and it also outperforms tangent space PCA (TPCA) models in the diffeomorphism setting.
在许多统计形状分析中，计算大量图像中发现的解剖变异性的简洁表示是重要的第一步。在本文中，我们提出了一种生成式贝叶斯方法，用于对通过微分同胚映射表示的形状变异性进行自动降维。为实现这一点，我们开发了一种用于主测地线分析（PGA）的潜在变量模型，该模型为微分同胚上的因子分析提供了一个概率框架。我们的关键贡献是一种贝叶斯推理程序，用于模型参数估计和潜在空间有效维度的同时检测。我们在磁共振图像的OASIS脑数据库上评估了我们提出的用于图谱和主测地线估计的模型。我们表明，从我们的模型中自动选择的潜在维度能够在图像空间中以比等效线性主成分分析（LPCA）模型更低的误差重建未见的脑图像，并且在微分同胚设置中也优于切空间主成分分析（TPCA）模型。
