A novel robust kernel principal component analysis for nonlinear statistical shape modeling from erroneous data

Statistical Shape Models (SSMs) have achieved considerable success in medical image segmentation. A high quality SSM is able to approximate the main plausible variances of a given anatomical structure to guide segmentation. However, it is technically challenging to derive such a quality model because: (1) the distribution of shape variance is often nonlinear or multi-modal which cannot be modeled by standard approaches assuming Gaussian distribution; (2) as the quality of annotations in training data usually varies, heavy corruption will degrade the quality of the model as a whole. In this work, these challenges are addressed by introducing a generic SSM that is able to model nonlinear distribution and is robust to outliers in training data. Without losing generality and assuming a sparsity in nonlinear distribution, a novel Robust Kernel Principal Component Analysis (RKPCA) for statistical shape modeling is proposed with the aim of constructing a low-rank nonlinear subspace where outliers are discarded. The proposed approach is validated on two different datasets: a set of 30 public CT kidney pairs and a set of 49 MRI ankle bones volumes. Experimental results demonstrate a significantly better performance on outlier recovery and a higher quality of the proposed model as well as lower segmentation errors compared to the state-of-the-art techniques.