Nonlinear band expansion and nonnegative matrix underapproximation for unsupervised segmentation of a liver from a multi-phase CT image

A methodology is proposed for contrast enhanced unsupervised segmentation of a liver from a twodimensional multi-phase CT image. The multi-phase CT image is represented by a linear mixture model, whereupon each single-phase CT image is modeled as a linear mixture of spatial distributions of the organs present in the image. The methodology exploits concentration and spatial diversities between organs present in the image and consists of nonlinear dimensionality expansion followed by matrix factorization that relies on sparseness between spatial distributions of organs. Dimensionality expansion increases concentration diversity (contrast) between organs. The methodology is demonstrated on an experimental three-phase CT image of a liver of two patients.