PointSCNet: Point Cloud Structure and Correlation Learning Based on Space-Filling Curve-Guided Sampling

Geometrical structures and the internal local region relationship, such as symmetry, regular array, junction, etc., are essential for understanding a 3D shape. This paper proposes a point cloud feature extraction network named PointSCNet, to capture the geometrical structure information and local region correlation information of a point cloud. The PointSCNet consists of three main modules: the space-filling curve-guided sampling module, the information fusion module, and the channel-spatial attention module. The space-filling curve-guided sampling module uses Z-order curve coding to sample points that contain geometrical correlation. The information fusion module uses a correlation tensor and a set of skip connections to fuse the structure and correlation information. The channel-spatial attention module enhances the representation of key points and crucial feature channels to refine the network. The proposed PointSCNet is evaluated on shape classification and part segmentation tasks. The experimental results demonstrate that the PointSCNet outperforms or is on par with state-of-the-art methods by learning the structure and correlation of point clouds effectively.

Detection Power of Separability Criteria Based on a Correlation Tensor: A Case Study

Detection power of separability criteria based on a correlation tensor is tested within a family of generalized isotropic states in [Formula: see text]. For [Formula: see text] all these criteria are weaker than the positive partial transposition (PPT) criterion. Interestingly, our analysis supports the recent conjecture that a criterion based on symmetrically informationally complete positive operator-valued measure (SIC-POVMs) is stronger than realignment criterion.

Unraveling micro-architectural modulations in neural tissue upon ischemia by Correlation Tensor MRI

ABSTRACTNoninvasively detecting and characterizing modulations in cellular scale micro-architecture is a desideratum for contemporary neuroimaging. Diffusion MRI (dMRI) has become the mainstay methodology for probing microstructure, and, in ischemia, its contrasts have revolutionized stroke management. However, the biological underpinnings of the contrasts observed in conventional dMRI in general and in ischemia in particular are still highly debated since the markers only indirectly reporter on microstructure. Here, we present Correlation Tensor MRI (CTI), a method that rather than measuring diffusion, harnesses diffusion correlations as its source of contrast. We show that CTI can resolve the sources of diffusional kurtosis, which in turn, provide dramatically enhanced specificity and sensitivity towards ischemia. In particular, the sensitivity towards ischemia nearly doubles, both in grey matter (GM) and white matter (WM), and unique signatures for neurite beading, cell swelling, and edema are inferred from CTI. The enhanced sensitivity and specificity endowed by CTI bodes well for future applications in biomedicine, basic neuroscience, and in the clinic.