Image Segmentation with Eigenfunctions of an Anisotropic Diffusion Operator

We propose the eigenvalue problem of an anisotropic diffusion operator for image segmentation. The diffusion matrix is defined based on the input image. The eigenfunctions and the projection of the input image in some eigenspace capture key features of the input image. An important property of the model is that for many input images, the first few eigenfunctions are close to being piecewise constant, which makes them useful as the basis for a variety of applications such as image segmentation and edge detection. The eigenvalue problem is shown to be related to the algebraic eigenvalue problems resulting from several commonly used discrete spectral clustering models. The relation provides a better understanding and helps developing more efficient numerical implementation and rigorous numerical analysis for discrete spectral segmentation methods. The new continuous model is also different from energy-minimization methods such as geodesic active contour in that no initial guess is required for in the current model. The multi-scale feature is a natural consequence of the anisotropic diffusion operator so there is no need to solve the eigenvalue problem at multiple levels. A numerical implementation based on a finite element method with an anisotropic mesh adaptation strategy is presented. It is shown that the numerical scheme gives much more accurate results on eigenfunctions than uniform meshes. Several interesting features of the model are examined in numerical examples and possible applications are discussed

On Using Physical Analogies for Feature and Shape Extraction in Computer Vision

There is a rich literature of approaches to image feature extraction in computer vision. Many sophisticated approaches exist for low- and high-level feature extraction but can be complex to implement with parameter choice guided by experimentation, but impeded by speed of computation. We have developed new ways to extract features based on notional use of physical paradigms, with parameterisation that is more familiar to a scientifically-trained user, aiming to make best use of computational resource. We describe how analogies based on gravitational force can be used for low-level analysis, whilst analogies of water flow and heat can be deployed to achieve high-level smooth shape detection. These new approaches to arbitrary shape extraction are compared with standard state-of-art approaches by curve evolution. There is no comparator operator to our use of gravitational force. We also aim to show that the implementation is consistent with the original motivations for these techniques and so contend that the exploration of physical paradigms offers a promising new avenue for new approaches to feature extraction in computer vision

Neuroinflammation and white matter alterations in obesity assessed by Diffusion Basis Spectrum Imaging

Human obesity is associated with low-grade chronic systemic inflammation, alterations in brain structure and function, and cognitive impairment. Rodent models of obesity show that high-calorie diets cause brain inflammation (neuroinflammation) in multiple regions, including the hippocampus, and impairments in hippocampal-dependent memory tasks. To determine if similar effects exist in humans with obesity, we applied Diffusion Basis Spectrum Imaging (DBSI) to evaluate neuroinflammation and axonal integrity. We examined diffusion-weighted magnetic resonance imaging (MRI) data in two independent cohorts of obese and non-obese individuals (Cohort 1: 25 obese/21 non-obese; Cohort 2: 18 obese/41 non-obese). We applied Tract-based Spatial Statistics (TBSS) to allow whole-brain white matter (WM) analyses and compare DBSI-derived isotropic and anisotropic diffusion measures between the obese and non-obese groups. In both cohorts, the obese group had significantly greater DBSI-derived restricted fraction (DBSI-RF; an indicator of neuroinflammation-related cellularity), and significantly lower DBSI-derived fiber fraction (DBSI-FF; an indicator of apparent axonal density) in several WM tracts (all correcte