Nonlinear Statistical Shape Modeling for Ankle Bone Segmentation Using a Novel Kernelized Robust PCA

Abstract

Statistical shape models (SSMs) are widely employed in medical image segmentation. However, an inferior SSM will degenerate the quality of segmentations. It is challenging to derive an efficient model because: (1) often the training datasets are corrupted by noise and/or artifacts; (2) conventional SSM is not capable to capture nonlinear variabilities of a population of shape. Addressing these challenges, this work aims to create SSMs that are not only robust to abnormal training data but also satisfied with nonlinear distribution. As Robust PCA is an efficient tool to seek a clean low-rank linear subspace, a novel kernelized Robust PCA (KRPCA) is proposed to cope with nonlinear distribution for statistical shape modeling. In evaluation, the built nonlinear model is used in ankle bone segmentation where 9 bones are separately distributed. Evaluation results show that the model built with KRPCA has a significantly higher quality than other state-of-the-art methods.