Classification of Normal and Diseased Liver Shapes based on Spherical Harmonics Coefficients

Liver-shape analysis and quantification is still an open research subject. Quantitative assessment of the liver is of clinical importance in various procedures such as diagnosis, treatment planning, and monitoring. Liver-shape classification is of clinical importance for corresponding intra-subject and inter-subject studies. In this research, we propose a novel technique for the liver-shape classification based on Spherical Harmonics (SH) coefficients. The proposed liver-shape classification algorithm consists of the following steps: (a) Preprocessing, including mesh generation and simplification, point-set matching, and surface to template alignment; (b) Liver-shape parameterization, including surface normalization, SH expansion followed by parameter space registration; (c) Feature selection and classification, including frequency based feature selection, feature space reduction by Principal Component Analysis (PCA), and classification. The above multi-step approach is novel in the sense that registration and feature selection for liver-shape classification is proposed and implemented and validated for the normal and diseases liver in the SH domain. Various groups of SH features after applying conventional PCA and/or ordered by p-value PCA are employed in two classifiers including Support Vector Machine (SVM) and k-Nearest Neighbor (k-NN) in the presence of 101 liver data sets. Results show that the proposed specific features combined with classifiers outperform existing liver-shape classification techniques that employ liver surface information in the spatial domain. In the available data sets, the proposed method can successful classify normal and diseased livers with a correct classification rate of above 90 %. The performed result in average is higher than conventional liver-shape classification method. Several standard metrics such as Leave-one-out cross-validation and Receiver Operating Characteristic (ROC) analysis are employed in the experiments and confirm the effectiveness of the proposed liver-shape classification with respect to conventional techniques.