Segmentation of 3D Anatomically Diffused Tissues in Magnetic Resonance Images Through Edge-Preserving Constrained Center-Free Fuzzy $C$-Means

Anatomically diffused tissues (ADTs) refer to soft tissues containing many anatomical regions that are spatially dispersed and structurally irregular. In magnetic resonance images, ADTs exhibit blurred morphology and heterogeneous texture, making the accurate extraction of their 3D anatomy challenging. Center-free fuzzy
$C$
-means (FCM) can effectively partition nonlinear or nonspherical clusters, providing a promising scheme for ADT segmentation. It solves the uncertainty arising from unreliable center estimation by introducing a similarity criterion. However, the similarity criterion is sensitive to the number of target objects and their adjacent members in the images. Moreover, memberships of the existing algorithms are susceptible to losing real ADT details. To handle these issues, we propose an edge-preserving constrained center-free FCM algorithm for segmenting 3D ADTs in magnetic resonance images. To overcome the sensitivity of the similarity criterion, a novel object-to-cluster similarity measure is first proposed to utilize refined member-to-object adjacency. Specifically, the similarity measure focuses on members in the feature space, which share approximately homogeneous characteristics with each target object. Gradient-domain edge-preserving filtering is then combined with the improved similarity criterion to construct the novel objective function of center-free FCM. With the assistance of the designed image-driven edge-preserving regularization, the gradient information of clusters is constrained, eventually approaching that of ADTs in the guidance image. Experiments are conducted on two public brain datasets and one local intrahepatic vein dataset. The results demonstrate that the proposed algorithm is more effective for ADT segmentation than the state-of-the-art peers, exhibiting superior generalization capability.