Separable and non-separable discrete wavelet transform based texture features and image classification of breast thermograms

Highly sensitive infrared cameras can produce high-resolution diagnostic images of the temperature and vascular changes of breasts. Wavelet transform based features are suitable in extracting the texture difference information of these images due to their scale-space decomposition. The objective of this study is to investigate the potential of extracted features in differentiating between breast lesions by comparing the two corresponding pectoral regions of two breast thermograms. The pectoral regions of breastsare important because near 50% of all breast cancer is located in this region. In this study, the pectoral region of the left breast is selected. Then the corresponding pectoral region of the right breast is identified. Texture features based on the first and the second sets of statistics are extracted from wavelet decomposed images of the pectoral regions of two breast thermograms. Principal component analysis is used to reduce dimension and an Adaboost classifier to evaluate classification performance. A number of different wavelet features are compared and it is shown that complex non-separable 2D discrete wavelet transform features perform better than their real separable counterparts.

Order tracking for discrete-random separation in variable speed conditions

The transmission path from the excitation to the measured vibration on the surface of a mechanical system introduces a distortion both in amplitude and in phase. Moreover, in variable speed conditions, the amplification/attenuation and the phase shift, due to the transfer function of the mechanical system, varies in time. This phenomenon reduces the effectiveness of the traditionally tachometer based order tracking, compromising the results of a discrete-random separation performed by a synchronous averaging. In this paper, for the first time, the extent of the distortion is identified both in the time domain and in the order spectrum of the signal, highlighting the consequences for the diagnostics of rotating machinery. A particular focus is given to gears, providing some indications on how to take advantage of the quantification of the disturbance to better tune the techniques developed for the compensation of the distortion. The full theoretical analysis is presented and the results are applied to an experimental case.

Visualization of predictive distributions for discrete spatial-temporal log Cox processes approximated with MCMC

An important aspect of decision support systems involves applying sophisticated and flexible statistical models to real datasets and communicating these results to decision makers in interpretable ways. An important class of problem is the modelling of incidence such as fire, disease etc. Models of incidence known as point processes or Cox processes are particularly challenging as they are ‘doubly stochastic’ i.e. obtaining the probability mass function of incidents requires two integrals to be evaluated. Existing approaches to the problem either use simple models that obtain predictions using plug-in point estimates and do not distinguish between Cox processes and density estimation but do use sophisticated 3D visualization for interpretation. Alternatively other work employs sophisticated non-parametric Bayesian Cox process models, but do not use visualization to render interpretable complex spatial temporal forecasts. The contribution here is to fill this gap by inferring predictive distributions of Gaussian-log Cox processes and rendering them using state of the art 3D visualization techniques. This requires performing inference on an approximation of the model on a discretized grid of large scale and adapting an existing spatial-diurnal kernel to the log Gaussian Cox process context.

Shrinking the keys of discrete-log-type lossy trapdoor functions

To this day, realizations in the standard-model of (lossy) trapdoor functions from discrete-log-type assumptions require large public key sizes, e.g., about Θ(λ 2) group elements for a reduction from the decisional Diffie-Hellman assumption (where λ is a security parameter). We propose two realizations of lossy trapdoor functions that achieve public key size of only Θ(λ) group elements in bilinear groups, with a reduction from the decisional Bilinear Diffie-Hellman assumption. Our first construction achieves this result at the expense of a long common reference string of Θ(λ 2) elements, albeit reusable in multiple LTDF instantiations. Our second scheme also achieves public keys of size Θ(λ), entirely in the standard model and in particular without any reference string, at the cost of a slightly more involved construction. The main technical novelty, developed for the second scheme, is a compact encoding technique for generating compressed representations of certain sequences of group elements for the public parameters.

Möbius transforms, coincident Boolean functions and non-coincidence property of Boolean functions

Boolean functions and their Möbius transforms are involved in logical calculation, digital communications, coding theory and modern cryptography. So far, little is known about the relations of Boolean functions and their Möbius transforms. This work is composed of three parts. In the first part, we present relations between a Boolean function and its Möbius transform so as to convert the truth table/algebraic normal form (ANF) to the ANF/truth table of a function in different conditions. In the second part, we focus on the special case when a Boolean function is identical to its Möbius transform. We call such functions coincident. In the third part, we generalize the concept of coincident functions and indicate that any Boolean function has the coincidence property even it is not coincident.

A disaggregate discrete choice model of transportation demand by elderly and disabled people in rural Virginia

This paper uses a correlated multinomial logit model and a Poisson regression model to measure the factors affecting demand for different types of transportation by elderly and disabled people in rural Virginia. The major results are: (a) A paratransit system providing door-to-door service is highly valued by transportation-handicapped people; (b) Taxis are probably a potential but inferior alternative even when subsidized; (c) Buses are a poor alternative, especially in rural areas where distances to bus stops may be long; (d) Making buses handicap-accessible would have a statistically significant but small effect on mode choice; (e) Demand is price inelastic; and (f) The total number of trips taken is insensitive to mode availability and characteristics. These results suggest that transportation-handicapped people take a limited number of trips. Those they do take are in some sense necessary (given the low elasticity with respect to mode price or availability). People will substitute away from relying upon others when appropriate transportation is available, at least to some degree. But such transportation needs to be flexible enough to meet the needs of the people involved.

Two dynamic discrete choice estimation problems and simulation method solutions

This paper considers two problems that frequently arise in dynamic discrete choice problems but have not received much attention with regard to simulation methods. The first problem is how to simulate unbiased simulators of probabilities conditional on past history. The second is simulating a discrete transition probability model when the underlying dependent variable is really continuous. Both methods work well relative to reasonable alternatives in the application discussed. However, in both cases, for this application, simpler methods also provide reasonably good results.

Discrete phase-locked loop systems and spreadsheets

This paper demonstrates the use of a spreadsheet in exploring non-linear difference equations that describe digital control systems used in radio engineering, communication and computer architecture. These systems, being the focus of intensive studies of mathematicians and engineers over the last 40 years, may exhibit extremely complicated behaviour interpreted in contemporary terms as transition from global asymptotic stability to chaos through period-doubling bifurcations. The authors argue that embedding advanced mathematical ideas in the technological tool enables one to introduce fundamentals of discrete control systems in tertiary curricula without learners having to deal with complex machinery that rigorous mathematical methods of investigation require. In particular, in the appropriately designed spreadsheet environment, one can effectively visualize a qualitative difference in the behviour of systems with different types of non-linear characteristic.

A comparison of techniques for the reconstruction of leaf surfaces from scanned data

The foliage of a plant performs vital functions. As such, leaf models are required to be developed for modelling the plant architecture from a set of scattered data captured using a scanning device. The leaf model can be used for purely visual purposes or as part of a further model, such as a fluid movement model or biological process. For these reasons, an accurate mathematical representation of the surface and boundary is required. This paper compares three approaches for fitting a continuously differentiable surface through a set of scanned data points from a leaf surface, with a technique already used for reconstructing leaf surfaces. The techniques which will be considered are discrete smoothing D2-splines [R. Arcangeli, M. C. Lopez de Silanes, and J. J. Torrens, Multidimensional Minimising Splines, Springer, 2004.], the thin plate spline finite element smoother [S. Roberts, M. Hegland, and I. Altas, Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions, SIAM, 1 (2003), pp. 208--234] and the radial basis function Clough-Tocher method [M. Oqielat, I. Turner, and J. Belward, A hybrid Clough-Tocher method for surface fitting with application to leaf data., Appl. Math. Modelling, 33 (2009), pp. 2582-2595]. Numerical results show that discrete smoothing D2-splines produce reconstructed leaf surfaces which better represent the original physical leaf.

Decision support system for age-related macular degeneration using discrete wavelet transform

Age-related macular degeneration (AMD) affects the central vision and subsequently may lead to visual loss in people over 60 years of age. There is no permanent cure for AMD, but early detection and successive treatment may improve the visual acuity. AMD is mainly classified into dry and wet type; however, dry AMD is more common in aging population. AMD is characterized by drusen, yellow pigmentation, and neovascularization. These lesions are examined through visual inspection of retinal fundus images by ophthalmologists. It is laborious, time-consuming, and resource-intensive. Hence, in this study, we have proposed an automated AMD detection system using discrete wavelet transform (DWT) and feature ranking strategies. The first four-order statistical moments (mean, variance, skewness, and kurtosis), energy, entropy, and Gini index-based features are extracted from DWT coefficients. We have used five (t test, Kullback–Lieber Divergence (KLD), Chernoff Bound and Bhattacharyya Distance, receiver operating characteristics curve-based, and Wilcoxon) feature ranking strategies to identify optimal feature set. A set of supervised classifiers namely support vector machine (SVM), decision tree, k -nearest neighbor ( k -NN), Naive Bayes, and probabilistic neural network were used to evaluate the highest performance measure using minimum number of features in classifying normal and dry AMD classes. The proposed framework obtained an average accuracy of 93.70 %, sensitivity of 91.11 %, and specificity of 96.30 % using KLD ranking and SVM classifier. We have also formulated an AMD Risk Index using selected features to classify the normal and dry AMD classes using one number. The proposed system can be used to assist the clinicians and also for mass AMD screening programs.

Real-time decision making by driverless city vehicles : a discrete event driven approach

This thesis addresses the topic of real-time decision making by driverless (autonomous) city vehicles, i.e. their ability to make appropriate driving decisions in non-simplified urban traffic conditions. After addressing the state of research, and explaining the research question, the thesis presents solutions for the subcomponents which are relevant for decision making with respect to information input (World Model), information output (Driving Maneuvers), and the real-time decision making process. TheWorld Model is a software component developed to fulfill the purpose of collecting information from perception and communication subsystems, maintaining an up-to-date view of the vehicle’s environment, and providing the required input information to the Real-Time Decision Making subsystem in a well-defined, and structured way. The real-time decision making process consists of two consecutive stages. While the first decision making stage uses a Petri net to model the safetycritical selection of feasible driving maneuvers, the second stage uses Multiple Criteria Decision Making (MCDM) methods to select the most appropriate driving maneuver, focusing on fulfilling objectives related to efficiency and comfort. The complex task of autonomous driving is subdivided into subtasks, called driving maneuvers, which represent the output (i.e. decision alternatives) of the real-time decision making process. Driving maneuvers are considered as implementations of closed-loop control algorithms, each capable of maneuvering the autonomous vehicle in a specific traffic situation. Experimental tests in both a 3D simulation and real-world experiments attest that the developed approach is suitable to deal with the complexity of real-world urban traffic situations.

An accuracy assessment of ASTER stereo images-derived digital elevation model by using rational polynomial coefficient model

The along-track stereo images of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) sensor with 15 m resolution were used to generate Digital Elevation Model (DEM) on an area with low and near Mean Sea Level (MSL) elevation in Johor, Malaysia. The absolute DEM was generated by using the Rational Polynomial Coefficient (RPC) model which was run on ENVI 4.8 software. In order to generate the absolute DEM, 60 Ground Control Pointes (GCPs) with almost vertical accuracy less than 10 meter extracted from topographic map of the study area. The assessment was carried out on uncorrected and corrected DEM by utilizing dozens of Independent Check Points (ICPs). Consequently, the uncorrected DEM showed the RMSEz of ± 26.43 meter which was decreased to the RMSEz of ± 16.49 meter for the corrected DEM after post-processing. Overall, the corrected DEM of ASTER stereo images met the expectations.