MisMatch: Calibrated Segmentation via Consistency on Differential Morphological Feature Perturbations With Limited Labels.

Semi-supervised learning (SSL) is a promising machine learning paradigm to address the ubiquitous issue of label scarcity in medical imaging. The state-of-the-art SSL methods in image classification utilise consistency regularisation to learn unlabelled predictions which are invariant to input level perturbations. However, image level perturbations violate the cluster assumption in the setting of segmentation. Moreover, existing image level perturbations are hand-crafted which could be sub-optimal. In this paper, we propose MisMatch, a semi-supervised segmentation framework based on the consistency between paired predictions which are derived from two differently learnt morphological feature perturbations. MisMatch consists of an encoder and two decoders. One decoder learns positive attention for foreground on unlabelled data thereby generating dilated features of foreground. The other decoder learns negative attention for foreground on the same unlabelled data thereby generating eroded features of foreground. We normalise the paired predictions of the decoders, along the batch dimension. A consistency regularisation is then applied between the normalised paired predictions of the decoders. We evaluate MisMatch on four different tasks. Firstly, we develop a 2D U-net based MisMatch framework and perform extensive cross-validation on a CT-based pulmonary vessel segmentation task and show that MisMatch statistically outperforms state-of-the-art semi-supervised methods. Secondly, we show that 2D MisMatch outperforms state-of-the-art methods on an MRI-based brain tumour segmentation task. We then further confirm that 3D V-net based MisMatch outperforms its 3D counterpart based on consistency regularisation with input level perturbations, on two different tasks including, left atrium segmentation from 3D CT images and whole brain tumour segmentation from 3D MRI images. Lastly, we find that the performance improvement of MisMatch over the baseline might originate from its better calibration. This also implies that our proposed AI system makes safer decisions than the previous methods.

Properties of Spherically Symmetric Black Holes in the Generalized Brans-Dicke Modified Gravitational Theory.

The many problems faced by the theory of general relativity (GR) have always motivated us to explore the modified theory of GR. Considering the importance of studying the black hole (BH) entropy and its correction in gravity physics, we study the correction of thermodynamic entropy for a kind of spherically symmetric black hole under the generalized Brans-Dicke (GBD) theory of modified gravity. We derive and calculate the entropy and heat capacity. It is found that when the value of event horizon radius r+ is small, the effect of the entropy-correction term on the entropy is very obvious, while for larger values r+, the contribution of the correction term on entropy can be almost ignored. In addition, we can observe that as the radius of the event horizon increases, the heat capacity of BH in GBD theory will change from a negative value to a positive value, indicating that there is a phase transition in black holes. Given that studying the structure of geodesic lines is important for exploring the physical characteristics of a strong gravitational field, we also investigate the stability of particles' circular orbits in static spherically symmetric BHs within the framework of GBD theory. Concretely, we analyze the dependence of the innermost stable circular orbit on model parameters. In addition, the geodesic deviation equation is also applied to investigate the stable circular orbit of particles in GBD theory. The conditions for the stability of the BH solution and the limited range of radial coordinates required to achieve stable circular orbit motion are given. Finally, we show the locations of stable circular orbits, and obtain the angular velocity, specific energy, and angular momentum of the particles which move in circular orbits.