Statistical Volume Models of Human Anatomy and Their Applications to Computer Aided Diagnostics

提出了一种新的基于张量的多维数据分析方法--广义N维主成分分析（GND-PCA）。我们还提出了一个框架的基础上GND-PCA和三维形状归一化技术的统计体积（纹理）建模的肝脏。3D形状归一化技术用于对肝脏形状进行归一化，以去除肝脏形状变异性并捕获纯纹理变化。GND-PCA用于克服训练样本比数据维数少得多时的过拟合问题。留一法实验的初步结果表明，该方法建立的肝脏统计纹理模型可以很好地表示未经训练的肝脏体积，即使该模式是由较少的样本训练。我们还证明了其潜在的应用程序的分类正常和异常（肿瘤）的肝脏。

We proposed a novel tensor based learning method called generalized N-dimensional principal component analysis(GND-PCA) for multi-dimensional data analysis. We also proposed a framework based on GND-PCA and a 3D shape normalization technique for statistical volume(texture) modeling of the liver. The 3D shape normalization technique is used for normalizing liver shapes in order to remove the liver shape variability and capture pure texture variations. The GND-PCA is used to overcome overfitting problems when the training samples are too much fewer than the dimension of the data. The preliminary results of leave-one-out experiments show that the statistical texture model of the liver built by our method can represent an untrained liver volume well, even though the mode is trained by fewer samples. We also demonstrate its potential application to classification of normal and abnormal(with tumors) livers.