Abstract
A probabilistic group-wise similarity registration technique based on Student's t-mixture model (TMM) and a multi-resolution extension of the same (mr-TMM) are proposed in this study, to robustly align shapes and establish valid correspondences, for the purpose of training statistical shape models (SSMs). Shape analysis across large cohorts requires automatic generation of the requisite training sets. Automated segmentation and landmarking of medical images often result in shapes with varying proportions of outliers and consequently require a robust method of alignment and correspondence estimation. Both TMM and mrTMM are validated by comparison with state-of-the-art registration algorithms based on Gaussian mixture models (GMMs), using both synthetic and clinical data. Four clinical data sets are used for validation: (a) 2D femoral heads (K= 1000 samples generated from DXA images of healthy subjects); (b) control-hippocampi (K= 50 samples generated from T1-weighted magnetic resonance (MR) images of healthy subjects); (c) MCI-hippocampi (K= 28 samples generated from MR images of patients diagnosed with mild cognitive impairment); and (d) heart shapes comprising left and right ventricular endocardium and epicardium (K= 30 samples generated from short-axis MR images of: 10 healthy subjects, 10 patients diagnosed with pulmonary hypertension and 10 diagnosed with hypertrophic cardiomyopathy). The proposed methods significantly outperformed the state-of-the-art in terms of registration accuracy in the experiments involving synthetic data, with mrTMM offering significant improvement over TMM. With the clinical data, both methods performed comparably to the state-of-the-art for the hippocampi and heart data sets, which contained few outliers. They outperformed the state-of-the-art for the femur data set, containing large proportions of outliers, in terms of alignment accuracy, and the quality of SSMs trained, quantified in terms of generalization, compactness and specificity.
Highlights
Statistical shape models (SSMs) have found widespread use in a variety of medical image analysis applications in recent years such as segmentation (Patenaude et al, 2011; Castro-Mateos et al, 2015), shape-based prediction of tissue anisotropy (Lekadir et al, 2014), quantitative shape analysis and classification for computeraided-diagnosis (Styner et al, 2004; Shen et al, 2012; Gooya et al, 2015b), to name a few
joint registration of multiple point clouds (JRMPC) shows good robustness and achieves marginally lower errors for samples 3 and 4, it is unable to recover the rotation for sample 2 and results in significantly higher errors
While multi-resolution extension to the TMM algorithm (mrTMM) offers some improvement over single-resolution t-mixture model (TMM), as the training sets of hippocampi shapes contained no visibly apparent outliers, both proposed methods showed no significant difference in performance compared to Gaussian mixture models (GMMs) and group-wise CPD (gCPD)
Summary
Statistical shape models (SSMs) have found widespread use in a variety of medical image analysis applications in recent years such as segmentation (Patenaude et al, 2011; Castro-Mateos et al, 2015), shape-based prediction of tissue anisotropy (Lekadir et al, 2014), quantitative shape analysis and classification for computeraided-diagnosis (Styner et al, 2004; Shen et al, 2012; Gooya et al, 2015b), to name a few. In order to facilitate large-scale statistical shape analysis of anatomical structures using automated pre-processing techniques to generate the required training set, a robust framework capable of aligning and establishing anatomically valid correspondences across the group of shapes, is imperative Such a framework forms the main contribution of this study. Medial models are ’skeleton-like’ representations which yield more compact shape descriptions than landmarkbased approaches but utilise surface boundaries parametrised by SPHARM and have identical topological constraints Based on these factors, in this study we focus on point-based representations of shapes as the main purpose is to formulate a topology independent, automatic and robust framework for training SSMs
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