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Intensity inhomogeneities in images constitute a considerable challenge inimage segmentation. In this paper we propose a novel biconvex variational modelto tackle this task. We combine a total variation approach for multi classsegmentation with a multiplicative model to handle the inhomogeneities. Ourmethod assumes that the image intensity is the product of a smoothly varyingpart and a component which resembles important image structures such as edges.Therefore, we penalize in addition to the total variation of the labelassignment matrix a quadratic difference term to cope with the smoothly varyingfactor. A critical point of our biconvex functional is computed by a modifiedproximal alternating linearized minimization method (PALM). We show that theassumptions for the convergence of the algorithm are fulfilled by our model.Various numerical examples demonstrate the very good performance of our method.Particular attention is paid to the segmentation of 3D FIB tomographical imageswhich was indeed the motivation of our work.

Unsupervised Multi Class Segmentation of 3D Images with Intensity Inhomogeneities