Weighted robust PCA for statistical shape modeling

Statistical shape models (SSMs) play an important role in medical image analysis. A sufficiently large number of high quality datasets is needed in order to create a SSM containing all possible shape variations. However, the available datasets may contain corrupted or missing data due to the fact that clinical images are often captured incompletely or contain artifacts. In this work, we propose a weighted Robust Principal Component Analysis (WRPCA) method to create SSMs from incomplete or corrupted datasets. In particular, we introduce a weighting scheme into the conventional Robust Principal Component Analysis (RPCA) algorithm in order to discriminate unusable data from meaningful ones in the decomposition of the training data matrix more accurately. For evaluation, the proposed WRPCA is compared with conventional RPCA on both corrupted (63 CT datasets of the liver) and incomplete datasets (15 MRI datasets of the human foot). The results show a significant improvement in terms of reconstruction accuracy on both datasets.