The Generalized Log-Ratio Transformation: Learning Shape and Adjacency Priors for Simultaneous Thigh Muscle Segmentation

Abstract—We present a novel probabilistic shape represen-tation that implicitly includes prior anatomical volume and adjacency information, termed the generalized log-ratio (GLR) representation. We demonstrate the usefulness of this repre-sentation in the task of thigh muscle segmentation. Analysis of the shapes and sizes of thigh muscles can lead to a better understanding of the effects of chronic obstructive pulmonary disease (COPD), which often results in skeletal muscle weakness in lower limbs. However, segmenting these muscles from one another is difficult due to a lack of distinctive features and inter-muscular boundaries that are difficult to detect. We overcome these difficulties by building a shape model in the space of GLR representations. We remove pose variability from the model by employing a presegmentation-based alignment scheme. We also design a rotationally invariant random forest boundary detec-tor that learns common appearances of the interface between muscles from training data. We combine the shape model and the boundary detector into a fully automatic globally optimal segmentation technique. Our segmentation technique produces a probabilistic segmentation that can be used to generate uncer-tainty information, which can be used to aid subsequent analysis. Our experiments on challenging 3D magnetic resonance imaging data sets show that the use of the GLR representation improves the segmentation accuracy, and yields an average Dice similarity coefficient of 0.808 ± 0.074, comparable to other state-of-the-art thigh segmentation techniques