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Second order total variation (SOTV) models have advantages for image reconstruction over their first order counterparts including their ability to remove the staircase artefact in the reconstructed image. However, such models tend to blur the recovered image when discretised for a numerical solution [1–5]. To overcome this drawback, we introduce a novel tensor weighted second order (TWSO) variational model for image reconstruction. Specifically, we develop a new regulariser for the original SOTV model that uses the Frobenius norm of the product of the Hessian matrix and a diffusion tensor, which has the duel effects of sharpening edges and introducing anisotropy to the model. We then efficiently solve the proposed model by breaking the original problem into several closed-form subproblems using the alternating direction method of multipliers. The proposed method is compared with state-of-the-art approaches such as the tensor-based anisotropic diffusions, total generalised variation, and Euler’s elastica. We validate the TWSO model using extensive experiments on numerous images from the Berkeley BSDS500. We also show that our method effectively reduces both the staircase and blurring effects and outperforms existing approaches for image inpainting and denoising applications.
Digital Signal Processing, 2017.

Segmentation and analysis of histological images provides a valuable tool to gain insight into the biology and function of microglial cells in health and disease. Common image segmentation methods are not suitable for inhomogeneous histology image analysis and accurate classification of microglial activation states has remained a challenge. In this paper, we introduce an automated image analysis framework capable of efficiently segmenting microglial cells from histology images and analysing their morphology. The framework makes use of variational methods and the fast-split Bregman algorithm for image denoising and segmentation, and of multifractal analysis for feature extraction to classify microglia by their activation states. Experiments show that the proposed framework is accurate and scalable to large datasets and provides a useful tool for the study of microglial biology.
IEEE/ACM Trans. Comput. Biol. Bioinform, 2016.

A new framework for automatically tracking subsurface tracers in electrical resistivity tomography (ERT) monitoring images is presented. Using computer vision and Bayesian inference techniques, in the form of a Kalman filter, the trajectory of a subsurface tracer is monitored by predicting and updating a state model representing its movements. Observations for the Kalman filter are gathered using the maximally stable volumes algorithm, which is used to dynamically threshold local regions of an ERT image sequence to detect the tracer at each time step. The application of the framework to the results of 2-D and 3-D tracer monitoring experiments show that the proposed method is effective for detecting and tracking tracer plumes in ERT images in the presence of noise, without intermediate manual intervention.
WRR, 2016.

This paper proposes a novel method for parametrisation and remeshing incomplete and irregular polygonal meshes. Spherical harmonics basis functions are used for parametrisation. This involves least squares fitting of spherical harmonics basis functions to the surface mesh. Tikhonov regularisation is then used to improve the parametrisation before remeshing the surface. Experiments show that the proposed techniques are effective for parametrising and remeshing polygonal meshes.
Mathematical Problems in Engineering, 2015.

Multi-view reconstruction has been an active research topic in the computer vision community for decades. However, state of the art 3D reconstruction systems have lacked the speed, accuracy, and ease to use properties required by the industry. The work described in this paper is part of the effort to produce a multi-view reconstruction system for a UK company. A novel variational level set method is developed for reconstructing an accurate implicit surface for a set of unorganised points (point cloud). The variational model consists of three energy terms to ensure accurate and smooth surface reconstruction whilst preserving the fine details of the point cloud and increasing speed. The model also completely eliminated the need for reinitialisation associated with the level set method. Implementation details of the variational model using gradient descent optimisation are given, and the roles of its three energy terms are illustrated through numerical experiments. Experiments show that the proposed method outperformed the state of the art surface reconstruction approaches.
SGAI 2015: Research and Development in Intelligent Systems XXXII, 2015.

Retinal blood vessels have been implicated in a large number of diseases including diabetic retinopathy and cardiovascular diseases, which cause damages to retinal blood vessels. The availability of retinal vessel imaging provides an excellent opportunity for monitoring and diagnosis of retinal diseases, and automatic analysis of retinal vessels will help with the processes. However, state of the art vascular analysis methods such as counting the number of branches or measuring the curvature and diameter of individual vessels are unsuitable for the microvasculature. There has been published research using fractal analysis to calculate fractal dimensions of retinal blood vessels, but so far there has been no systematic research extracting discriminant features from retinal vessels for classifications. This paper introduces new methods for feature extraction from multifractal spectra of retinal vessels for classification. Two publicly available retinal vascular image databases are used for the experiments, and the proposed methods have produced accuracies of 85.5% and 77% for classification of healthy and diabetic retinal vasculatures. Experiments show that classification with multiple fractal features produces better rates compared with methods using a single fractal dimension value. In addition to this, experiments also show that classification accuracy can be affected by the accuracy of vessel segmentation algorithms.
Physics in Medicine and Biology, 2015.

Dewatering systems used for mining and quarrying operations often result in highly artificial and complex groundwater conditions, which can be difficult to characterise and monitor using borehole point sampling approaches. Here automated time-lapse electrical resistivity tomography (ALERT) is considered as a means of monitoring subsurface groundwater dynamics associated with changes in the dewatering regime in an operational sand and gravel quarry. We considered two scenarios: the first was unplanned interruption to dewatering due to a pump failure for a period of several days, which involved comparing ALERT monitoring results before and after groundwater rebound; the second involved a planned interruption to pumping over a period of 6 h, for which near-continuous ALERT monitoring of groundwater rebound and drawdown was undertaken. The results of the second test were analysed using distribution guided clustering (DGC) to provide a more quantitative and objective assessment of changes in the subsurface over time. ALERT successfully identified groundwater level changes during both monitoring scenarios. It provided a more useful indication of the rate of water level rise and maximum water levels than piezometer monitoring results. This was due to the piezometers rapidly responding to pressure changes at depth, whilst ALERT/DGC provided information of slower changes associated with the storage and delayed drainage of water within the sediment. By applying DGC we were able to automatically and quantitatively define changes in the resistivity sections, which correlated well with the direct observations of groundwater at site. For ERT monitoring applications that generate numerous time series, the use of DGC could significantly enhance the efficiency of data interpretation, and provide a means of automating groundwater monitoring through assigning alarm thresholds associated with rapid changes in groundwater conditions.
Engineering Geology, 2015.

This paper investigates the use of multifractal formalism for characterising 3D brain vasculature of 2 different mammalian species. Multifractal properties were found across all the 3D vascular models. Variations in the analysis results appear to correspond with vessel density ans morphology. The implication of the research is that multifractal analysis could potentially provide a useful tool for clinical assessment of diseases that are known to alter density and structure of brain microvasculature.
CICARE, 2014.

Blood vessel segmentation is of great importance in medical diagnostic applications. Filter based methods that make use of Hessian matrices have been found to be very useful for blood vessel segmentation in both 2D and 3D medical images. However, these methods often fail on images that contain high density microvessels and background noise. The errors in the form of missing, undesired broken or incorrectly merged vessels eventually lead to poor segmentation results. In this paper, we present a novel method for 3D vessel segmentation that is also suitable for segmenting microvessels, incorporating the advantages of a line filter and a Hessian-based vessel filter to overcome the problems. The proposed method is shown to be reliable for noisy and inhomogeneous images. Vessels can also be separated based on their scale/thickness so that the method can be used for different medical applications. Furthermore, a quantitative vessel analysis method based on the multifractal analysis is performed on the segmented vasculature and fractal properties are found in all images.
Phys. Med. Biol., 2014.

For groundwater-surface water interactions to be understood in complex wetland settings, the architecture of the underlying deposits requires investigation at a spatial resolution sufficient to characterize significant hydraulic pathways. Discrete intrusive sampling using conventional approaches provides insufficient sample density and can be difficult to deploy on soft ground. Here a noninvasive geophysical imaging approach combining three-dimensional electrical resistivity tomography (ERT) and the novel application of gradient and isosurface-based edge detectors is considered as a means of illuminating wetland deposit architecture. The performance of three edge detectors were compared and evaluated against ground truth data, using a lowland riparian wetland demonstration site. Isosurface-based methods correlated well with intrusive data and were useful for defining the geometries of key geological interfaces (i.e., peat/gravels and gravels/Chalk). The use of gradient detectors approach was unsuccessful, indicating that the assumption that the steepest resistivity gradient coincides with the associated geological interface can be incorrect. These findings are relevant to the application of this approach in settings with a broadly layered geology with strata of contrasting resistivities. In addition, ERT revealed substantial structures in the gravels related to the depositional environment (i.e., braided fluvial system) and a complex distribution of low-permeability putty Chalk at the bedrock surface—with implications for preferential flow and variable exchange between river and groundwater systems. These results demonstrate that a combined approach using ERT and edge detectors can provide valuable information to support targeted monitoring and inform hydrological modeling of wetlands.
WRR, 2014.

A novel method for the effective identification of bedrock subsurface elevation from electrical resistivity tomography images is described. Identifying subsurface boundaries in the topographic data can be difficult due to smoothness constraints used in inversion, so a statistical population-based approach is used that extends previous work in calculating isoresistivity surfaces. The analysis framework involves a procedure for guiding a clustering approach based on the fuzzy c-means algorithm. An approximation of resistivity distributions, found using kernel density estimation, was utilized as a means of guiding the cluster centroids used to classify data. A fuzzy method was chosen over hard clustering due to uncertainty in hard edges in the topography data, and a measure of clustering uncertainty was identified based on the reciprocal of cluster membership. The algorithm was validated using a direct comparison of known observed bedrock depths at two 3-D survey sites, using real-time GPS information of exposed bedrock by quarrying on one site, and borehole logs at the other. Results show similarly accurate detection as a leading isosurface estimation method, and the proposed algorithm requires significantly less user input and prior site knowledge. Furthermore, the method is effectively dimension-independent and will scale to data of increased spatial dimensions without a significant effect on the runtime. A discussion on the results by automated versus supervised analysis is also presented.
GJI, 2014.

A growing body of evidence suggests that there is a strong association between neurodegenerative diseases such as Alzheimer’s Diseases and the abnormality of the cerebral vasculature, in particular the microvessels/capillaries that are responsible for the exchange of nutrients across the blood-brain barrier. Many microvessels are described as being kinked or distorted, implying that they are modified by some destructive process. Imaging devices such as microCT can achieve resolutions on the order of several μm, allowing imaging the three dimensional (3D) microvasculature down to the capillary level. However, the main weakness of using microCT for vascular research is considered to be the lack of software for 3D quantification of microvasculature and microvascular image databases for developing and testing algorithms. In this paper we describe a multifractal analysis method for the microvasculature automatically segmented from microCT images of the mouse brain. Due to the lack of a benchmark microCT image database, the method has been tested using a surrogate database - a publicly available retinal vessel database. The results are preliminary indication of the multifractal properties of mouse brain vasculature. A potential solution to automated classification of healthy and disease brains are discussed.
EMBC, 2013.