We study pseudo labelling and its generalisation for semi-supervised segmentation of medical images. Pseudo labelling has achieved great empirical successes in semi-supervised learning, by utilising raw inferences on unlabelled data as pseudo labels for self-training. In our paper, we build a connection between pseudo labelling and the Expectation Maximization algorithm which partially explains its empirical successes. We thereby realise that the original pseudo labelling is an empirical estimation of its underlying full formulation. Following this insight, we demonstrate the full generalisation of pseudo labels under Bayes' principle, called Bayesian Pseudo Labels. We then provide a variational approach to learn to approximate Bayesian Pseudo Labels, by learning a threshold to select good quality pseudo labels. In the rest of the paper, we demonstrate the applications of Pseudo Labelling and its generalisation Bayesian Psuedo Labelling in semi-supervised segmentation of medical images on: 1) 3D binary segmentation of lung vessels from CT volumes; 2) 2D multi class segmentation of brain tumours from MRI volumes; 3) 3D binary segmentation of brain tumours from MRI volumes. We also show that pseudo labels can enhance the robustness of the learnt representations.

This work presents a single-step deep-learning framework for longitudinal image analysis, coined Segis-Net. To optimally exploit information available in longitudinal data, this method concurrently learns a multi-class segmentation and nonlinear registration. Segmentation and registration are modeled using a convolutional neural network and optimized simultaneously for their mutual benefit. An objective function that optimizes spatial correspondence for the segmented structures across time-points is proposed. We applied Segis-Net to the analysis of white matter tracts from N=8045 longitudinal brain MRI datasets of 3249 elderly individuals. Segis-Net approach showed a significant increase in registration accuracy, spatio-temporal segmentation consistency, and reproducibility comparing with two multistage pipelines. This also led to a significant reduction in the sample-size that would be required to achieve the same statistical power in analyzing tract-specific measures. Thus, we expect that Segis-Net can serve as a new reliable tool to support longitudinal imaging studies to investigate macro- and microstructural brain changes over time.

To accurately analyze changes of anatomical structures in longitudinal imaging studies, consistent segmentation across multiple time-points is required. Existing solutions often involve independent registration and segmentation components. Registration between time-points is used either as a prior for segmentation in a subsequent time point or to perform segmentation in a common space. In this work, we propose a novel hybrid convolutional neural network (CNN) that integrates segmentation and registration into a single procedure. We hypothesize that the joint optimization leads to increased performance on both tasks. The hybrid CNN is trained by minimizing an integrated loss function composed of four different terms, measuring segmentation accuracy, similarity between registered images, deformation field smoothness, and segmentation consistency. We applied this method to the segmentation of white matter tracts, describing functionally grouped axonal fibers, using N=8045 longitudinal brain MRI data of 3249 individuals. The proposed method was compared with two multistage pipelines using two existing segmentation methods combined with a conventional deformable registration algorithm. In addition, we assessed the added value of the joint optimization for segmentation and registration separately. The hybrid CNN yielded significantly higher accuracy, consistency and reproducibility of segmentation than the multistage pipelines, and was orders of magnitude faster. Therefore, we expect it can serve as a novel tool to support clinical and epidemiological analyses on understanding microstructural brain changes over time.

Tract-specific diffusion measures, as derived from brain diffusion MRI, have been linked to white matter tract structural integrity and neurodegeneration. As a consequence, there is a large interest in the automatic segmentation of white matter tract in diffusion tensor MRI data. Methods based on the tractography are popular for white matter tract segmentation. However, because of the limited consistency and long processing time, such methods may not be suitable for clinical practice. We therefore developed a novel convolutional neural network based method to directly segment white matter tract trained on a low-resolution dataset of 9149 DTI images. The method is optimized on input, loss function and network architecture selections. We evaluated both segmentation accuracy and reproducibility, and reproducibility of determining tract-specific diffusion measures. The reproducibility of the method is higher than that of the reference standard and the determined diffusion measures are consistent. Therefore, we expect our method to be applicable in clinical practice and in longitudinal analysis of white matter microstructure.