Segmentation of images with separating layers by fuzzy c-means and convex optimization

This paper is concerned with the segmentation of two- and three-dimensional images containing separated layers. We tackle this problem by combining the fuzzy c-means algorithm with recently developed convex multi-class segmentation algorithms, where we modify the data term of the corresponding functional to involve the information of the layer structure. We solve the optimization problem numerically by applying an alternating direction method of multipliers in conjunction with the fast discrete cosine transform to solve the involved linear system of equations. We demonstrate the performance of our method on synthetic and real-world images. In particular we deal with the segmentation of three-dimensional images arising from micro-computed tomography of C/SiC-ceramics by synchrotron radiation.