Sparse and Low Rank Matrix Decomposition Based Local Morphological Analysis and Its Application to Diagnosis of Cirrhosis Livers

Cirrhosis liver is a terrible disease which is threatening our lives. Meanwhile, cirrhosis will cause significant hepatic morphological changes. While it is well known that the livers from different subjects have similar global shape structure which means liver shape ensemble should be low-rank. However the deformation which caused by cirrhosis can be considered as sparse compared with the whole liver. Therefore, in this study, we proposed to apply spare and low-rank matrix decomposition to partition the local deformation part (sparse error matrix E) from the global similar structure (low-rank matrix A) using the input liver shape D, which is the landmark coordinates of liver shapes and already have been aligned by the current rigid registration methods firstly. And then sparse matrix E is used for diagnosis. In common sense, the normal liver should have less local deformation than that of abnormal liver, which means that the norm of sparse matrix E for normal liver is smaller than the norm for abnormal one. Thus, we can simply use a threshold classify normal and abnormal livers using the norm of E for these two categories. The proposed method is evaluated by a liver database which includes 30 normal livers and 30 abnormal livers. The experimental results of proposed method is better than those of state of the art statistical shape model(SSM) based methods.