Hierarchical image simplification and segmentation based on Mumford-Shah-salient level line selection

Hierarchies, such as the tree of shapes, are popular representations for image simplification and segmentation thanks to their multiscale structures. Selecting meaningful level lines (boundaries of shapes) yields to simplify image while preserving intact salient structures. Many image simplification and segmentation methods are driven by the optimization of an energy functional, for instance the celebrated Mumford-Shah functional. In this paper, we propose an efficient approach to hierarchical image simplification and segmentation based on the minimization of the piecewise-constant Mumford-Shah functional. This method conforms to the current trend that consists in producing hierarchical results rather than a unique partition. Contrary to classical approaches which compute optimal hierarchical segmentations from an input hierarchy of segmentations, we rely on the tree of shapes, a unique and well-defined representation equivalent to the image. Simply put, we compute for each level line of the image an attribute function that characterizes its persistence under the energy minimization. Then we stack the level lines from meaningless ones to salient ones through a saliency map based on extinction values defined on the tree-based shape space. Qualitative illustrations and quantitative evaluation on Weizmann segmentation evaluation database demonstrate the state-of-the-art performance of our method.Comment: Pattern Recognition Letters, Elsevier, 201

Unsupervised Multi Class Segmentation of 3D Images with Intensity Inhomogeneities

Intensity inhomogeneities in images constitute a considerable challenge in image segmentation. In this paper we propose a novel biconvex variational model to tackle this task. We combine a total variation approach for multi class segmentation with a multiplicative model to handle the inhomogeneities. Our method assumes that the image intensity is the product of a smoothly varying part and a component which resembles important image structures such as edges. Therefore, we penalize in addition to the total variation of the label assignment matrix a quadratic difference term to cope with the smoothly varying factor. A critical point of our biconvex functional is computed by a modified proximal alternating linearized minimization method (PALM). We show that the assumptions 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 images which was indeed the motivation of our work