Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

Modelling water droplet movement on a leaf surface

The central aim for the research undertaken in this PhD thesis is the development of a model for simulating water droplet movement on a leaf surface and to compare the model behavior with experimental observations. A series of five papers has been presented to explain systematically the way in which this droplet modelling work has been realised. Knowing the path of the droplet on the leaf surface is important for understanding how a droplet of water, pesticide, or nutrient will be absorbed through the leaf surface. An important aspect of the research is the generation of a leaf surface representation that acts as the foundation of the droplet model. Initially a laser scanner is used to capture the surface characteristics for two types of leaves in the form of a large scattered data set. After the identification of the leaf surface boundary, a set of internal points is chosen over which a triangulation of the surface is constructed. We present a novel hybrid approach for leaf surface fitting on this triangulation that combines Clough-Tocher (CT) and radial basis function (RBF) methods to achieve a surface with a continuously turning normal. The accuracy of the hybrid technique is assessed using numerical experimentation. The hybrid CT-RBF method is shown to give good representations of Frangipani and Anthurium leaves. Such leaf models facilitate an understanding of plant development and permit the modelling of the interaction of plants with their environment. The motion of a droplet traversing this virtual leaf surface is affected by various forces including gravity, friction and resistance between the surface and the droplet. The innovation of our model is the use of thin-film theory in the context of droplet movement to determine the thickness of the droplet as it moves on the surface. Experimental verification shows that the droplet model captures reality quite well and produces realistic droplet motion on the leaf surface. Most importantly, we observed that the simulated droplet motion follows the contours of the surface and spreads as a thin film. In the future, the model may be applied to determine the path of a droplet of pesticide along a leaf surface before it falls from or comes to a standstill on the surface. It will also be used to study the paths of many droplets of water or pesticide moving and colliding on the surface.

Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term

In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and Gr¨unwald-Letnikov(GL) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Bayes factor based speaker clustering for speaker diarization

This paper proposes the use of the Bayes Factor to replace the Bayesian Information Criterion (BIC) as a criterion for speaker clustering within a speaker diarization system. The BIC is one of the most popular decision criteria used in speaker diarization systems today. However, it will be shown in this paper that the BIC is only an approximation to the Bayes factor of marginal likelihoods of the data given each hypothesis. This paper uses the Bayes factor directly as a decision criterion for speaker clustering, thus removing the error introduced by the BIC approximation. Results obtained on the 2002 Rich Transcription (RT-02) Evaluation dataset show an improved clustering performance, leading to a 14.7% relative improvement in the overall Diarization Error Rate (DER) compared to the baseline system.

Fusing shrinking and expanding active contour models for robust IRIS segmentation

The performance of iris recognition systems is significantly affected by the segmentation accuracy, especially in non- ideal iris images. This paper proposes an improved method to localise non-circular iris images quickly and accurately. Shrinking and expanding active contour methods are consolidated when localising inner and outer iris boundaries. First, the pupil region is roughly estimated based on histogram thresholding and morphological operations. There- after, a shrinking active contour model is used to precisely locate the inner iris boundary. Finally, the estimated inner iris boundary is used as an initial contour for an expanding active contour scheme to find the outer iris boundary. The proposed scheme is robust in finding exact the iris boundaries of non-circular and off-angle irises. In addition, occlusions of the iris images from eyelids and eyelashes are automatically excluded from the detected iris region. Experimental results on CASIA v3.0 iris databases indicate the accuracy of proposed technique.

A comparison of two business cycle dating methods

We study the suggestion that Markov switching (MS) models should be used to determine cyclical turning points. A Kalman filter approximation is used to derive the dating rules implicit in such models. We compare these with dating rules in an algorithm that provides a good approximation to the chronology determined by the NBER. We find that there is very little that is attractive in the MS approach when compared with this algorithm. The most important difference relates to robustness. The MS approach depends on the validity of that statistical model. Our approach is valid in a wider range of circumstances.

Metaheuristic approaches to the hybrid flow shop scheduling problem with a cost-related criterion

In the paper, the flow-shop scheduling problem with parallel machines at each stage (machine center) is studied. For each job its release and due date as well as a processing time for its each operation are given. The scheduling criterion consists of three parts: the total weighted earliness, the total weighted tardiness and the total weighted waiting time. The criterion takes into account the costs of storing semi-manufactured products in the course of production and ready-made products as well as penalties for not meeting the deadlines stated in the conditions of the contract with customer. To solve the problem, three constructive algorithms and three metaheuristics (based one Tabu Search and Simulated Annealing techniques) are developed and experimentally analyzed. All the proposed algorithms operate on the notion of so-called operation processing order, i.e. the order of operations on each machine. We show that the problem of schedule construction on the base of a given operation processing order can be reduced to the linear programming task. We also propose some approximation algorithm for schedule construction and show the conditions of its optimality.

A global vision system for a robot soccer team

This paper describes the real time global vision system for the robot soccer team the RoboRoos. It has a highly optimised pipeline that includes thresholding, segmenting, colour normalising, object recognition and perspective and lens correction. It has a fast ‘paint’ colour calibration system that can calibrate in any face of the YUV or HSI cube. It also autonomously selects both an appropriate camera gain and colour gains robot regions across the field to achieve colour uniformity. Camera geometry calibration is performed automatically from selection of keypoints on the field. The system achieves a position accuracy of better than 15mm over a 4m × 5.5m field, and orientation accuracy to within 1°. It processes 614 × 480 pixels at 60Hz on a 2.0GHz Pentium 4 microprocessor.

Wide-angle visual feature matching for outdoor localization

Wide-angle images exhibit significant distortion for which existing scale-space detectors such as the scale-invariant feature transform (SIFT) are inappropriate. The required scale-space images for feature detection are correctly obtained through the convolution of the image, mapped to the sphere, with the spherical Gaussian. A new visual key-point detector, based on this principle, is developed and several computational approaches to the convolution are investigated in both the spatial and frequency domain. In particular, a close approximation is developed that has comparable computation time to conventional SIFT but with improved matching performance. Results are presented for monocular wide-angle outdoor image sequences obtained using fisheye and equiangular catadioptric cameras. We evaluate the overall matching performance (recall versus 1-precision) of these methods compared to conventional SIFT. We also demonstrate the use of the technique for variable frame-rate visual odometry and its application to place recognition.

Design of a Web interface for anatomical images

Interactive documents for use with the World Wide Web have been developed for viewing multi-dimensional radiographic and visual images of human anatomy, derived from the Visible Human Project. Emphasis has been placed on user-controlled features and selections. The purpose was to develop an interface which was independent of host operating system and browser software which would allow viewing of information by multiple users. The interfaces were implemented using HyperText Markup Language (HTML) forms, C programming language and Perl scripting language. Images were pre-processed using ANALYZE and stored on a Web server in CompuServe GIF format. Viewing options were included in the document design, such as interactive thresholding and two-dimensional slice direction. The interface is an example of what may be achieved using the World Wide Web. Key applications envisaged for such software include education, research and accessing of information through internal databases and simultaneous sharing of images by remote computers by health personnel for diagnostic purposes.