Spatial and Hierarchical Riemannian Dimensionality Reduction and Dictionary Learning for Segmenting Multichannel Images

In this paper, we proposed an automated method for segmenting objects of weak boundaries and similar intensities on volumetric multichannel images. This method relied on a multiresolution classifier that tackled class overlaps by using the Riemannian geometry of the RCDs of the multiscale patches of every multichannel image and reducing the dimensionality of these RCDs through a novel method that incorporated the intra-and inter-class neighborhoods of the RCDs in the Riemannian space and the spatial and hierarchical relationships between their corresponding patches. The reduced dimensional RCDs were then used to learn resolution-specific dictionaries for coding and classifications. To speed up the optimizations and to avoid convergence to local extrema, the dictionaries and the codes got initialized by a novel scheme that used the Riemannian geometry of the RCDs. This method was evaluated on the challenging task of segmenting cardiac adipose tissues on fat-water MR images.