  The early detection, diagnosis and monitoring of liver cancer progression can
be achieved with the precise delineation of metastatic tumours. However,
accurate automated segmentation remains challenging due to the presence of
noise, inhomogeneity and the high appearance variability of malignant tissue.
In this paper, we propose an unsupervised metastatic liver tumour segmentation
framework using a machine learning approach based on discriminant Grassmannian
manifolds which learns the appearance of tumours with respect to normal tissue.
First, the framework learns within-class and between-class similarity
distributions from a training set of images to discover the optimal manifold
discrimination between normal and pathological tissue in the liver. Second, a
conditional optimisation scheme computes nonlocal pairwise as well as
pattern-based clique potentials from the manifold subspace to recognise regions
with similar labelings and to incorporate global consistency in the
segmentation process. The proposed framework was validated on a clinical
database of 43 CT images from patients with metastatic liver cancer. Compared
to state-of-the-art methods, our method achieves a better performance on two
separate datasets of metastatic liver tumours from different clinical sites,
yielding an overall mean Dice similarity coefficient of 90.7 +/- 2.4 in over 50
tumours with an average volume of 27.3 mm3.
