  The segmentation of liver lesions is crucial for detection, diagnosis and
monitoring progression of liver cancer. However, design of accurate automated
methods remains challenging due to high noise in CT scans, low contrast between
liver and lesions, as well as large lesion variability. We propose a 3D
automatic, unsupervised method for liver lesions segmentation using a phase
separation approach. It is assumed that liver is a mixture of two phases:
healthy liver and lesions, represented by different image intensities polluted
by noise. The Cahn-Hilliard equation is used to remove the noise and separate
the mixture into two distinct phases with well-defined interfaces. This
simplifies the lesion detection and segmentation task drastically and enables
to segment liver lesions by thresholding the Cahn-Hilliard solution. The method
was tested on 3Dircadb and LITS dataset.
