3.5
Manifold learning for motion analysis
Manifold learning is a branch of machine learning techniques that learns a low-dimensional embedding of the studied data by taking into account the local information of the input data during dimensionality reduction. Manifold learning can be used to model statistical distribution of anatomical and functional features for a given population, hence clinical applications including biomarker detection, diagnosis and therapy.
Bhatia et al. [Bhatia et al., 2013] [Bhatia et al., 2014] extended the conventional manifold learning method by utilising local variations to produce spatially-varying manifold embeddings that characterise a given dataset. In their study, a hierarchical model is adopted to repeatedly subdivide the image into smaller patches in order to enforce spatial consistency and allow regional analysis. They applied this hierarchical manifold learning approach to cardiac MRI to learn the different motions occurring in the cardiac and respiratory cycle to determine the phase differences between different heart regions.
Duchateau et al. [Duchateau et al., 2012] compared the myocardial motions of individuals to a population with abnormal motion along a manifold structure. In the first step, the myocardial velocities for each individual are extracted at each time and space point using image-based registration. Then the extracted velocities of each individual are synchronized to a common reference anatomy and compared to that of an atlas of healthy volunteers to generate a 2D p-value maps of abnormalities. In the second step, a relevant manifold for a set of patients is estimated by the isomap algorithm [Tenenbaum et al., 2000]. In the last step, new subjects of patients and healthy volunteers are then mapped to the manifold by interpolation. The performance of this approach is evaluated in the context of cardiac resynchronization therapy (CRT) candidates. Their experiments demonstrated the advantage of non-linear embedding and the relevance of this technique to model a pathological pattern.
Yang et al. [Yang et al., 2011] presented a robust and fast prediction based collaborative 3D tracking algorithm. A prediction is introduced to generate the motion prior using motion manifold learning. The motion manifold is embedded by Isomap using 4D motion vectors from
36 annotated LV motion sequences, of which each sequence has 289 annotated boundary points. Figure 3.6 shows two annotated LV motion sequences and 11 LV motion representations in a low dimensional manifold. Thereafter a hierarchical k-means clustering method is used to learn the motion modes. Collaborative trackers including a detection tracker and a template tracker are then applied to achieve both temporal consistency and failure recovery. The approach is tested on three large datasets (CT or echocardiography) for endocardium, myocardium and whole heart four chambers tracking respectively and achieved very accurate tracking results.
Taimouri et al. [Taimouri and Hua, 2013] presented a novel classification and visualization method based on a medial surface shape space, which considered the cardiac motion as a function defined on the 2D manifold of the surface. In their medial surface shape space, the geodesic distance connecting two points in the space measures the similarity between their corresponding medial surfaces. The experimental results on both synthetic and real imaging data shown that this method can discriminate the myopathic subjects from the healthy control subjects, and is able to detect myopathic regions.
3.6
Conclusion
Cardiac MR images provide accurate imaging of anatomy, morphology, myocardial motion and blood flow with good contrast which are useful for performing global and regional function analysis. In this chapter, we have reviewed recent studies related to the cardiac motion analysis for MR images. Several cardiac motion analysis techniques such as sparse motion tracking, deformable models and registration based algorithms can be applied to both cine MR images and tagged MR images. We also discussed the applications of manifold learning in the field of cardiac motion analysis. Manifold learning is a promising approach in non-parametric dimension reduction and therefore facilitates application of machine learning for medical image analysis. Clinic indices associated with ventricular function assessment and obesity indices are also introduced.
3.6. Conclusion 87
(a)
(b)
Figure 3.6 – Manifold embedding for heart motion patterns. (a) Two LV surface mesh sequences. (b) 11 sequences embedded in a 2D manifold subspace. The ED phase is represented as stars and the ES phase is represented as squares, and each circle denotes a time phase of the cardiac cycle in
addition to ED and ES. Two LV motion tracks are annotated in red and green. Figures from [Yang
et al., 2011].
this thesis focuses on the utilization of cardiac motion information involving motion tracking, quantification of the cardiac function and prediction of clinical variables.
Collaborative landmark detection and
motion tracking in cardiac MR images
The work in this chapter is based on the following published papers:
• Haiyan Wang, Wenzhe Shi, Xiahai Zhuang, Simon Duckett, Kai Pin Tung, Philip Edwards, Reza Razavi, Sebastien Ourselin, and Daniel Rueckert. (2011). Automatic cardiac motion tracking using both untagged and 3D tagged MR images. Statistical Atlases and Computational Models of the Heart: Imaging and Modelling Challenges (STACOM), pages 45-56.
• Wenzhe Shi, Xiahai Zhuang, Haiyan Wang, Simon Duckett, Duy V.N. Luong, Catalina Tobon-Gomez, KaiPin Tung, Philip Edwards, Kawal Rhode, Reza Razavi, Sebastien Ourselin, Daniel Rueckert. (2012). A comprehensive cardiac motion estimation framework using both untagged and 3D tagged MR images based on non-rigid registration. IEEE Transactions on Medical Imaging, 31(6):1263-1275.
4.1. Introduction 89
4.1
Introduction
Cardiac MR imaging provides important information for the quantitative assessment of heart function, such as the measurement of ventricular volume, wall thickness and ejection fraction. The accurate estimation of cardiac motion is becoming increasingly important in quantification of the viability and contractility of the myocardium. However, it requires accurate registration and motion tracking which is too tedious and time-consuming to perform manually.
In this chapter, we propose an automatic approach to identify and track important cardiac landmarks throughout the cardiac cycle. In particular we use a machine learning approach to detect landmarks such as the valve plane simultaneously in three different LA views and employed a collaborative similarity measure simultaneously computed in three different long- axis views to register a sequence of MR images acquired during the cardiac cycle to a reference image acquired at end-diastole. Another contribution is the combination of complementary information from tagged and untagged MR images using a spatially adaptive weighting and a valve plane constraint to construct an accurate and robust cardiac motion analysis framework. The tracked sparse anatomical landmarks in the heart help accurately modelling the cardiac motion while significantly reducing the computational complexity. The overview of the methods is illustrated in Figure 4.1. Spatially Adaptive Weighting Valve Plane Tracking