Fuzzy measures of pixel cluster compactness

Pixel-scale fine details are often lost during image processing tasks such as image reduction and filtering. Block or region based algorithms typically rely on averaging functions to implement the required operation and traditional function choices struggle to preserve small, spatially cohesive clusters of pixels which may be corrupted by noise. This article proposes the construction of fuzzy measures of cluster compactness to account for the spatial organisation of pixels. We present two construction methods (minimum spannning trees and fuzzy measure decomposition) to generate measures with specific properties: monotonicity with respect to cluster size; invariance with respect to translation, reflection and rotation; and, discrimination between pixel sets of fixed cardinality with different spatial arrangements. We apply these measures within a non-monotonic mode-like averaging function used for image reduction and we show that this new function preserves pixel-scale structures better than existing monotonie averages.

Characterizing compactness of geometrical clusters using fuzzy measures

Certain tasks in image processing require the preservation of fine image details, while applying a broad operation to the image, such as image reduction, filtering, or smoothing. In such cases, the objects of interest are typically represented by small, spatially cohesive clusters of pixels which are to be preserved or removed, depending on the requirements. When images are corrupted by the noise or contain intensity variations generated by imaging sensors, identification of these clusters within the intensity space is problematic as they are corrupted by outliers. This paper presents a novel approach to accounting for spatial organization of the pixels and to measuring the compactness of pixel clusters based on the construction of fuzzy measures with specific properties: monotonicity with respect to the cluster size; invariance with respect to translation, reflection, and rotation; and discrimination between pixel sets of fixed cardinality with different spatial arrangements. We present construction methods based on Sugeno-type fuzzy measures, minimum spanning trees, and fuzzy measure decomposition. We demonstrate their application to generating fuzzy measures on real and artificial images.

Application of real and functional analysis to solve boundary value problems

This thesis is about using appropriate tools in functional analysis arid classical analysis to tackle the problem of existence and uniqueness of nonlinear partial differential equations. There being no unified strategy to deal with these equations, one approaches each equation with an appropriate method, depending on the characteristics of the equation. The correct setting of the problem in appropriate function spaces is the first important part on the road to the solution. Here, we choose the setting of Sobolev spaces. The second essential part is to choose the correct tool for each equation. In the first part of this thesis (Chapters 3 and 4) we consider a variety of nonlinear hyperbolic partial differential equations with mixed boundary and initial conditions. The methods of compactness and monotonicity are used to prove existence and uniqueness of the solution (Chapter 3). Finding a priori estimates is the main task in this analysis. For some types of nonlinearity, these estimates cannot be easily obtained, arid so these two methods cannot be applied directly. In this case, we first linearise the equation, using linear recurrence (Chapter 4). In the second part of the thesis (Chapter 5), by using an appropriate tool in functional analysis (the Sobolev Imbedding Theorem), we are able to improve previous results on a posteriori error estimates for the finite element method of lines applied to nonlinear parabolic equations. These estimates are crucial in the design of adaptive algorithms for the method, and previous analysis relies on, what we show to be, unnecessary assumptions which limit the application of the algorithms. Our analysis does not require these assumptions. In the last part of the thesis (Chapter 6), staying with the theme of choosing the most suitable tools, we show that using classical analysis in a proper way is in some cases sufficient to obtain considerable results. We study in this chapter nonexistence of positive solutions to Laplace's equation with nonlinear Neumann boundary condition. This problem arises when one wants to study the blow-up at finite time of the solution of the corresponding parabolic problem, which models the heating of a substance by radiation. We generalise known results which were obtained by using more abstract methods.

Compact stacked planar inverted-F antenna for passive deep brain stimulation implants

A compact meandered three-layer stacked circular planar inverted-F antenna is designed and simulated at the UHF band (902.75 – 927.25 MHz) for passive deep brain stimulation implants. The UHF band is used because it offers small antenna size, and high data rate. The top and middle radiating layers are meandered, and low cost substrate and superstrate materials are used to limit the radius and height of the antenna to 5 mm and 1.64 mm, respectively. A dielectric substrate of FR-4 of εr= 4.7 and δ= 0.018, and a biocompatible superstrate of silicone of er= 3.7 and d= 0.003 with thickness of 0.2 mm are used in the design. The resonance frequency of the proposed antenna is 918 MHz with a bandwidth of 24 MHz at return loss of −10 dB in free space. The antenna parameter such as 3D gain pattern of the designed antenna within a skin-tissue model is evaluated by using the finite element method. The compactness, wide bandwidth, round shape, and stable characteristics in skin make this antenna suitable for DBS. The feasibility of the wireless power transmission to the implant in the human head is also examined.

Walking for recreation and perceptions of the neighbourhood environment in older chinese urban dwellers

Engagement in walking for recreation can contribute to healthy aging. Although there is growing evidence that the neighborhood environment can influence walking for recreation, the amount of such evidence in relation to older adults is scarce and limited to Western low-density urban locations. Asian urban environments are typified by distinctive environmental and cultural characteristics that may yield different patterns to those observed in Western countries. Therefore, the main aim of this study was to examine associations of perceived environmental attributes with overall and within-neighborhood walking for recreation in Chinese elders (65+ years) residing in Hong Kong, an ultradense Asian metropolis. A sample of 484 elders was recruited from 32 neighborhoods stratified by socio-economic status and walkability (dwelling and intersection densities). Validated questionnaires measuring perceived neighborhood environment and weekly minutes of overall and within-neighborhood walking for recreation were interviewer administered. Results showed that the level of recreational walking was twice to four times higher than that reported in Western adults and elders. While overall walking for recreation showed a general lack of associations with perceived environmental attributes, within-neighborhood recreational walking was positively related with proximity of recreational facilities, infrastructure for walking, indoor places for walking, and presence of bridge/overpasses connecting to services. Age and educational attainment moderated the associations with several perceived environmental attributes with older and less-educated participants showing stronger associations. Traditional cultural views on the benefits of physical activity and the high accessibility of facilities and pedestrian infrastructure of Hong Kong may explain the high levels of walking. Although specific neighborhood attributes, or their perception, may influence recreational walking within the neighborhood, the compactness and public transport affordability of ultradense metropolises such as Hong Kong may make it easy for elders to compensate for the lack of favorable neighborhood attributes by walking outside the neighborhood.

An intelligent decision support system for leukaemia diagnosis using microscopic blood images

This research proposes an intelligent decision support system for acute lymphoblastic leukaemia diagnosis from microscopic blood images. A novel clustering algorithm with stimulating discriminant measures (SDM) of both within- and between-cluster scatter variances is proposed to produce robust segmentation of nucleus and cytoplasm of lymphocytes/lymphoblasts. Specifically, the proposed between-cluster evaluation is formulated based on the trade-off of several between-cluster measures of well-known feature extraction methods. The SDM measures are used in conjuction with Genetic Algorithm for clustering nucleus, cytoplasm, and background regions. Subsequently, a total of eighty features consisting of shape, texture, and colour information of the nucleus and cytoplasm sub-images are extracted. A number of classifiers (multi-layer perceptron, Support Vector Machine (SVM) and Dempster-Shafer ensemble) are employed for lymphocyte/lymphoblast classification. Evaluated with the ALL-IDB2 database, the proposed SDM-based clustering overcomes the shortcomings of Fuzzy C-means which focuses purely on within-cluster scatter variance. It also outperforms Linear Discriminant Analysis and Fuzzy Compactness and Separation for nucleus-cytoplasm separation. The overall system achieves superior recognition rates of 96.72% and 96.67% accuracies using bootstrapping and 10-fold cross validation with Dempster-Shafer and SVM, respectively. The results also compare favourably with those reported in the literature, indicating the usefulness of the proposed SDM-based clustering method.

The early shorebird will catch fewer invertebrates on trampled sandy beaches

Many species of birds breeding on ocean beaches and in coastal dunes are of global conservation concern. Most of these species rely on invertebrates (e.g. insects, small crustaceans) as an irreplaceable food source, foraging primarily around the strandline on the upper beach near the dunes. Sandy beaches are also prime sites for human recreation, which impacts these food resources via negative trampling effects. We quantified acute trampling impacts on assemblages of upper shore invertebrates in a controlled experiment over a range of foot traffic intensities (up to 56 steps per square metre) on a temperate beach in Victoria, Australia. Trampling significantly altered assemblage structure (species composition and density) and was correlated with significant declines in invertebrate abundance and species richness. Trampling effects were strongest for rare species. In heavily trafficked plots the abundance of sand hoppers (Amphipoda), a principal prey item of threatened Hooded Plovers breeding on this beach, was halved. In contrast to the consistently strong effects of trampling, natural habitat attributes (e.g. sediment grain size, compactness) were much less influential predictors. If acute suppression of invertebrates caused by trampling, as demonstrated here, is more widespread on beaches it may constitute a significant threat to endangered vertebrates reliant on these invertebrates. This calls for a re-thinking of conservation actions by considering active management of food resources, possibly through enhancement of wrack or direct augmentation of prey items to breeding territories.

The structure of communities in scale-free networks

Scale-free networks are often used to model a wide range of real-world networks, such as social, technological, and biological networks. Understanding the structure of scale-free networks evolves into a big data problem for business, management, and protein function prediction. In the past decade, there has been a surge of interest in exploring the properties of scale-free networks. Two interesting properties have attracted much attention: the assortative mixing and community structure. However, these two properties have been studied separately in either theoretical models or real-world networks. In this paper, we show that the structural features of communities are highly related with the assortative mixing in scale-free networks. According to the value of assortativity coefficient, scale-free networks can be categorized into assortative, disassortative, and neutral networks, respectively. We systematically analyze the community structure in these three types of scale-free networks through six metrics: node embeddedness, link density, hub dominance, community compactness, the distribution of community sizes, and the presence of hierarchical communities. We find that the three types of scale-free networks exhibit significant differences in these six metrics of community structures. First, assortative networks present high embeddedness, meaning that many links lying within communities but few links lying between communities. This leads to the high link density of communities. Second, disassortative networks exhibit great hubs in communities, which results in the high compactness of communities that nodes can reach each other via short paths. Third, in neutral networks, a big portion of links act as community bridges, so they display sparse and less compact communities. In addition, we find that (dis)assortative networks show hierarchical community structure with power-law-distributed community sizes, while neutral networks present no hierarchy. Understanding the structure of communities from the angle of assortative mixing patterns of nodes can provide insights into the network structure and guide us in modeling information propagation in different categories of scale-free networks.