Masters Degrees (Applied Mathematics)
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- ItemAccurate camera position determination by means of moiré pattern analysis(Stellenbosch : Stellenbosch University, 2015-03) Zuurmond, Gideon Joubert; Brink, Willie; Herbst, B. M.; Stellenbosch University. Faculty of Science. Department of Applied Mathematics.ENGLISH ABSTRACT : We introduce a method for determining the position of a camera with accuracy beyond that which is obtainable through conventional methods, using a single image of a specially constructed calibration object. This is achieved by analysing the moiré pattern that emerges when two high spatial frequency patterns are superimposed, such that one pattern on a plane is observed through another pattern on a second, semi-transparent parallel plane, with the geometry of both the patterns and the planes known. Such an object can be created by suspending printed glass over printed paper or by suspending printed glass over a high resolution video display such as an OLED display or LCD. We show how the camera’s coordinate along the axis perpendicular to the planes can be estimated directly from frequency analysis of the moiré pattern relative to a set of guide points in one of the planes. This method does not require any prior camera knowledge. We further show how the choice of the patterns allows, within limits, arbitrary accuracy of this coordinate estimate at the cost of a stricter limit on the span along that coordinate for which the technique is usable. This improved accuracy is illustrated in simulation. With a sufficiently accurate estimate of the camera’s full set of 3D coordinates, obtained by conventional methods, we show how phase analysis of the moiré pattern in relation to the guides allows calculation of a new estimate of position in the two axes parallel to the planes. This new estimate is shown in simulation to offer significant improvement in accuracy.
- ItemAnalysis of Extreme Events in the Coastal Engineering Environment(Stellenbosch : Stellenbosch University, 2015-12) Stander, Cornel; Diedericks, Gerhardus Petrus Jacobus; Fidder-Woudberg, Sonia; Stellenbosch University. Faculty of Science. Department of Mathematical Sciences (Applied Mathematics)ENGLISH ABSTRACT : Coastal zones are subject to storm events and extreme waves with certain return periods. The return period of such events is defined as the average time interceding two independent, consecutive events, similar in nature, i.e., with the same return level. Coastal structures have to be designed to provide sufficient protection against flooding or erosion to a desired return level associated with a particular return period, for example 100 years. Statistical analyses of measured wave data over a time series are used for these estimations. In this study, wave data, measured by a Datawell Waverider buoy, is analysed by means of extreme value analyses. This dataset covers only approximately 18 years. Extreme value theory provides a framework that enables extrapolation in order to estimate the probability of events that are more extreme than any that have already been observed. It can, for example, be used to estimate wave return levels over the next 100 years given only an 18 year history. Different methods for making these estimations are implemented and evaluated. Datasets containing periods where data values are absent (i.e., gaps in a dataset), as well as the effects these missing values have on the estimation of extreme values, are also investigated. Methods for the treatment of gaps are evaluated by using NCEP (National Centre for Environmental Prediction) hindcast data, containing no missing values, and creating incomplete datasets from this data. Estimations are then made based on these incomplete sets. The resulting estimations are compared to the estimations made based on the complete NCEP dataset. Finally, recommendations are made for conducting optimal extreme value analyses, based on this study.
- ItemApplication of convolutional neural networks to building segmentation in aerial images(Stellenbosch : Stellenbosch University, 2018-12) Olaleye, Kayode Kolawole; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Applied Mathematics.; Fantaye, YabebalENGLISH ABSTRACT : Aerial image labelling has found relevance in diverse areas including urban management, agriculture, climate, mining, and cartography. As a result, research efforts have been intensified to find fast and accurate algorithms. The current state-of-the-art results in this context have been achieved by deep convolutional neural networks (CNNs). This has been possible because of advances in computing technologies such as fast GPUs and the discovery of optimal architectures. One of the main challenges in using deep CNNs is the need for a large set of ground truth labels during the training phase. Moreover, one has to choose optimal values for the many hyperparameters involved in the model construction to get a good result. In this thesis we focus on building segmentation from aerial images, and study the effect of different hyperparameter values, paying particular attention to the generalisation ability of the resulting models. For all our experiments we use the same architecture and performance metric as the one used in Mnih & Hinton (2012). Our investigation found the following main results: 1) when it comes to the size of CNN filters, small size filters perform as good or even better than large sized filters; 2) the LeakyReLU activation functions lead to a better precision-recall curve than ReLU (Rectified Linear unit) and Tanh activation functions; 3) batch-normalization leads to a slightly poor breakeven point than without batch-normalization - this is contrary to what has been found in other studies with different architectures. In addition, we also investigate how well our models generalise to the task of interpreting contexts that are different from the training sets. Drawing from our findings, we gave recommendations on how to make deep CNN models more robust to variations in aerial images of other continent such as Africa where annotations are either unavailable or in short supply.
- ItemApplications of natural language processing for low-resource languages in the healthcare domain(Stellenbosch : Stellenbosch University., 2020-03) Daniel, Jeanne Elizabeth; Brink, Willie; Stellenbosch University. Faculty of Science. Department of Mathematical Sciences (Applied Mathematics).ENGLISH ABSTRACT: Since 2014 MomConnect has provided healthcare information and emotional support in all 11 official languages of South Africa to over 2.6 million pregnant and breastfeeding women, via SMS and WhatsApp. However, the service has struggled to scale efficiently with the growing user base and increase in incoming questions, resulting in a current median response time of 20 hours. The aim of our study is to investigate the feasibility of automating the manual answering process. This study consists of two parts: i) answer selection, a form of information retrieval, and ii) natural language processing (NLP), where computers are taught to interpret human language. Our problem is unique in the NLP space, as we work with a closed-domain question-answering dataset, with questions in 11 languages, many of which are low-resource, with English template answers, unreliable language labels, code-mixing, shorthand, typos, spelling errors and inconsistencies in the answering process. The shared English template answers and code-mixing in the questions can be used as cross-lingual signals to learn cross-lingual embedding spaces. We combine these embeddings with various machine learning models to perform answer selection, and find that the Transformer architecture performs best, achieving a top-1 test accuracy of 61:75% and a top-5 test accuracy of 91:16%. It also exhibits improved performance on low-resource languages when compared to the long short-term memory (LSTM) networks investigated. Additionally, we evaluate the quality of the cross-lingual embeddings using parallel English-Zulu question pairs, obtained using Google Translate. Here we show that the Transformer model produces embeddings of parallel questions that are very close to one another, as measured using cosine distance. This indicates that the shared template answer serves as an effective cross-lingual signal, and demonstrates that our method is capable of producing high quality cross-lingual embeddings for lowresource languages like Zulu. Further, the experimental results demonstrate that automation using a top-5 recommendation system is feasible.
- ItemAutomated elephant detection and classification from aerial infrared and colour images using deep learning(Stellenbosch : Stellenbosch University, 2018-03) Marais, Jacques Charles; Brink, Willie; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematics)ENGLISH ABSTRACT : In this study we attempt to detect and classify elephants in aerial images using deep learning. This is not a trivial task even for a human since elephants naturally blend in with their surroundings, making it a challenging and meaningful problem to solve. Possible applications of this work extend into general animal conservation and search-and-rescue operations, with natural extension to satellite imagery as input source. We create a region proposal algorithm that relies on digital image processing techniques and morphological operations on infrared images that correspond to the RGB images. The goal is to create a fast and computationally cheap algorithm that reduces the work that needs to be done by our deep learning classification models. The algorithm reaches our accuracy goal, detecting 98% of all ground truth elephants in the dataset. The resulting regions are mapped onto the corresponding RGB images using a plane-to-plane homography along with adjustment heuristics to overcome alignment issues caused by sensor vibration. We train multiple convolutional neural network models, using various network architectures and weight initialisation techniques, including transfer learning. Two sets of models were trained, in 2015 and 2017 respectively, using different techniques, software, and hardware. The best performing model reduces the manual verification workload by 97% while missing only 1% of the elephants detected by the region proposal algorithm. We find that convolutional neural networks, as well as the advancements in deep learning, hold significant promise in detecting elephants from aerial images for real world applications
- ItemAutomatic video captioning using spatiotemporal convolutions on temporally sampled frames(Stellenbosch : Stellenbosch University., 2020-03) Nyatsanga, Simbarashe Linval; Brink, Willie; Stellenbosch University. Faculty of Science. Department of Mathematical Sciences (Applied Mathematics).ENGLISH ABSTRACT: Being able to concisely describe content in a video has tremendous potential to enable better categorisation, indexed based-search and fast content-based retrieval from large video databases. Automatic video captioning requires the simultaneous detection of local and global motion dynamics of objects, scenes and events, to summarise them into a single coherent natural language description. Given the size and complexity of video data, it is important to understand how much temporally coherent visual information is required to adequately describe the video. In order to understand the association between video frames and sentence descriptions, we carry out a systematic study to determine how the quality of generated captions changes with respect to densely or sparsely sampling video frames in the temporal dimension. We conduct a detailed literature review to better understand the background work in image and video captioning. We describe our methodology for building a video caption generator, which is based on deep neural networks called encoder-decoders. We then outline the implementation details of our video caption generator and our experimental setup. In our experimental setup, we explore the role of word embeddings for generating sensible captions with pretrained, jointly trained and finetuned embeddings. We train and evaluate our caption generator on the Microsoft Video Description (MSVD) dataset. Using the standard caption generation evaluation metrics, namely BLEU, METEOR, CIDEr and ROUGE, our experimental results show that sparsely sampling video frames with either finetuned or jointly trained embeddings, results in the best caption quality. Our results are promising in the sense that high quality videos with a large memory footprint could be categorised through a sensible description obtained through sampling a few frames. Finally, our method can be extended such that the sampling rate adapts according to the quality of the video.
- ItemBayesian forecasting of stock returns using simultaneous graphical dynamic linear models(Stellenbosch : Stellenbosch University, 2022-12) Kyakutwika, Nelson; Bartlett, Bruce; Becker, Ronnie; Stellenbosch University. Faculty of Science. Dept. of Applied Mathematics.ENGLISH ABSTRACT: Cross-series dependencies are crucial in obtaining accurate forecasts when forecast- ing a multivariate time series. Simultaneous Graphical Dynamic Linear Models (SGDLMs) are Bayesian models that elegantly capture cross-series dependencies. This study aims to forecast returns of a 40-dimensional time series of stock data using SGDLMs. The SGDLM approach involves constructing a customised dy- namic linear model (DLM) for each univariate time series. Every day, the DLMs are recoupled using importance sampling and decoupled using mean-field varia- tional Bayes. We summarise the standard theory on DLMs to set the foundation for studying SGDLMs. We discuss the structure of SGDLMs in detail and give de- tailed explanations of the proofs of the formulae involved. Our analyses are run on a CPU-based computer; an illustration of the intensity of the computations is given. We give an insight into the efficacy of the recoupling/decoupling techniques. Our results suggest that SGDLMs forecast the stock data accurately and respond to market gyrations nicely.
- ItemA catalytic model for SARS-CoV-2 reinfections : performing simulation-based validation and extending the model to include nth infections(Stellenbosch : Stellenbosch University, 2023-12) Lombard, Belinda; Van Schalkwyk, Cari; Pulliam, Juliet; Stellenbosch University. Faculty of Science. Dept. of Applied Mathematics.ENGLISH SUMMARY: Background: A global pandemic of COVID-19, caused by SARS-CoV-2, was declared in March 2020. Subsequently, studies have revealed a high seroprevalence of SARS-CoV-2 in both South African and global populations, along with instances of multiple reinfections. Among various models, a catalytic model has been developed for detecting population-level increases in risk of reinfection, following primary infection. This thesis aims to assess how potential biases from imperfect data observation processes affect the catalytic model’s ability to detect increases in reinfection risk. Furthermore, the thesis extends the catalytic model to detect increases in the risk of multiple reinfections. Methods: Simulation-based validation involved creating different reinfection scenarios representing real life data, which were then used in the model’s fitting and projection procedure. Observed reinfections were simulated using a time-series of primary infections, representative of South African data. Scenarios included considering both imperfect observation (with constant observation probability or a probability dependent on primary infection count) and mortality. The method’s ability to detect increases in the reinfection risk was measured by determining both the clusters of reinfections and the proportion of points that fell above the projection interval. Following simulation-based validation, the method was extended to detect population-level increases in the risk of 𝑛𝑡ℎ infections. This extended method was applied to observed third infections in South Africa, with an additional model parameter representing increased reinfections during the Omicron wave. Simulation-based validation was conducted on the extended method to assess its ability to detect increases of varying magnitudes in the risk of third infection. Results: During the simulation-based validation of the original catalytic model, model parameters converged in most scenarios. Failure to converge was mostly related to insufficient cases to properly inform the model parameters during the fitting procedure. Scenarios where the model parameters did not converge, or where the simulated data did not accurately fit the model, were excluded from interpretation. Introducing an increase in the reinfection risk resulted in successful detection of an increase (even with small increments), although with delayed timing under lower observed infection numbers. Mortality from first infections, unaccounted for in the model, did not impact the method’s ability to detect increases in the reinfection risk. The method demonstrated high specificity, reliably distinguishing true increases in the reinfection risk from noise. The catalytic model was extended to detect increases in the risk of 𝑛𝑡ℎ infections, and the extended method’s ability to detect increases in the risk of third infections was validated. The additional third infection hazard representing increased reinfection risk observed during the Omicron wave was successfully fitted to the data, and the method effectively detected increases in the risk of third infections. Conclusion: The findings highlight the need for sufficient infection data and the importance of convergence as a prerequisite for result interpretation. The extended model reliably detected increases in the risk of two or more reinfections and demonstrated robustness under different observation processes and increases in reinfection risk scenarios.
- ItemThe class imbalance problem in computer vision(Stellenbosch : Stellenbosch University, 2022-04) Crous, Willem Hendrik; Brink, Willie; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematics)ENGLISH ABSTRACT: Class imbalance is a naturally occurring phenomenon, typically characterised as a dataset consisting of classes with varying numbers of samples. When trained on class imbalanced data, networks tend to favour frequently occurring (majority) classes over the less frequent (minority) classes. This poses chal- lenges for tasks reliant upon accurate recognition of the less frequent classes. The aim of this thesis is to investigate general methods towards addressing this problem. First we establish why a network may favour majority classes. We contend that as less frequent classes are likely to under-represent the re- quired underlying distribution for a given task, training may produce a decision boundary that transgresses the feature space of minority classes. Additionally we find that the weight norms of the classification layer in a neural network may tend towards the distribution of the training data, thus affecting the de- cision boundary. We determine that this decision boundary shift impacts both the accuracy and confidence calibration of neural networks. We investigate several approaches to shift the decision boundary. The first approach acquires additional data and increases the representation of minority classes. This is achieved through either creating synthetic samples following a distribution- aware regularisation method, or utilising additional unlabelled data in a semi- supervised setting. The second approach aims to adjust the classifier weight norms by separately training the classifier and feature extractor. We find that implementing an effective regularisation method with a simple decoupled sam- pling scheme can provide considerable improvements over standard sampling methods. Furthermore we find that utilising additional unlabelled data may lead to additional gains given certain dataset characteristics are taken into consideration.
- ItemComparison of methods for solving Sylvester systems(Stellenbosch : Stellenbosch University, 2018-12) Kirsten, Gerhardus Petrus; Hale, Nicholas Peter; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Applied Mathematics.ENGLISH ABSTRACT :This thesis serves as a comparative study of numerical methods for solving Sylvester equations, which are linear matrix equations of the form AX + XB + C = 0. These equations have important applications in many areas of science and engineering, such as signal processing, control theory, and systems engineering, and their efficient solution is therefore of practical significance. As with standard linear systems (i.e., those of the form Ax = b), algorithms for the efficient solution of Sylvester equations typically fall into two categories, namely direct and iterative methods. As a naive approach, one can convert a Sylvester equation to a standard linear system (of larger size) using Kronecker operations, and then apply standard methods from numerical linear algebra. We shall see, however, that unless the matrix is very sparse and structured, this approach is usually inefficient. Instead, modern algorithms for solving Sylvester equations are applied directly to the equation in Sylvester form. When the matrices A and B are small and dense, direct methods such as Bartels–Stewart and Hessenberg–Schur, which are based on suitable factorisations of A and B, are efficient. As the matrices become larger, however, one typically switches to a projectionbased or some other iterative method. The projection methods considered in this thesis use Krylov subspace techniques to project the system onto a much smaller subspace, which can be solved efficiently using one of the direct methods mentioned above as an internal solver. In this thesis we consider two different subspaces for the comparison of projection methods, namely the standard Krylov subspace and an enriched approximation space known as the extended Krylov subspace. We shall see that when the matrix C is of low rank, then the extended Krylov subspace method is competitive with direct methods, even when the system size is relatively small. Each of the methods discussed above are compared, both theoretically by consideration of floating point operation counts and numerically by computational efficiency and accuracy, when used to solve several example problems arising in applications. Based on the results of these experiments, it is concluded that a method based on the eigenvalue decompositions of A and B is the most efficient direct method, although to some degree at the expense of numerical stability. In the class of projection methods, we find that the extended Krylov subspace to be the most efficient approximation space.
- ItemConvolutional and fully convolutional neural networks for the detection of landmarks in tsetse fly wing images(Stellenbosch : Stellenbosch University, 2021-12) Makhubele, Mulanga; Brink, Willie; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Applied Mathematics.ENGLISH ABSTRACT: Tsetse flies are a species of bloodsucking flies in the house fly family, that are only found in Africa. They cause animal and human African trypanosomiasis (AAT and HAT), commonly referred to as nagana and sleeping sickness. Effective tsetse fly eradication requires area-wide control, which means understanding the population dynamics of the tsetse flies in an area. Among the factors that entomologists believe to be critical to this understanding, fly size and fly wing shape are considered most important. Fly size can be deduced by calculating the distance between specific landmarks on a wing. The South African Centre for Epidemiological Modelling and Analysis (SACEMA) conducts research into tsetse fly population management and have a database of wings. To use landmarks on the wings for biological deductions about the tsetse flies in the area, researchers will need to manually annotate individual images of the wings by marking the important landmarks by hand, which is slow and error-prone. The purpose of this research is to assess the feasibility of automating the process of landmark detection in tsetse fly wing images using machine learning algorithms with a limited dataset. Extensive research has been done into automatic landmark detection. Particular focus has been given to detection of human body parts but there are a number of notable cases of animal landmark detection. Convolutional neural networks (CNNs) have been used as backbone architectures for most state-of-the-art detection systems. We compare the performance of fully convolutional networks (FCNs) against conventional LeNet style CNNs for the regression task of landmark detection in a fly wing image. The FCN accepts an image input and returns a segmentation mask as output. A Gaussian function is used to convert the response coordinate pairs into heat maps, which are combined to form a segmentation mask. After model training the heat maps produced by the FCN model are converted back to coordinate pairs using a weighted average method. Three types of models were trained: a baseline artificial neural network (ANN), LeNet style CNNs and FCNs. The ANN model had a root mean square error (RMSE) of 282.62 pixels and mean absolute error (MAE) of 181.33 pixels. The best LeNet model, LeNet3 with dropout, had an RMSE of 53.58 and MAE of 41.05. The best FCN model FCN8 with batch size 32 and Adam optimization, had an RMSE of 1.12 and MAE of 0.88. All trained models were best at predicting landmark points 5, 8 and 10 and struggled to predict landmark points 1, 4 and 6. The results indicate that machine learning models can be used to automatically and accurately detect landmark points on tsetse fly wing images. Furthermore, for our limited dataset FCNs outperform conventional LeNet style CNNs.
- ItemData-driven river flow routing using deep learning: predicting flow along the lower Orange river, Southern Africa(Stellenbosch : Stellenbosch University, 2019-04) Briers, C. J.; Brink, Willie; Smit, G. J. F.; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Applied Mathematics.ENGLISH ABSTRACT : The Vanderkloof Dam, located on the Orange River, is responsible for the water supply to consumers along its 1 400 km reach up to where it flows into the Atlantic Ocean. The Vaal River, which joins the Orange River approximately 200 km downstream of the dam, contributes significant volumes of water to the flow in the Orange River. These contributions are, however, not taken into account when planning for releases from the Vanderkloof Dam. In this thesis we aimed to develop an accurate and robust flow routing model of the Orange and Vaal River system to predict the effects of releases from the Vanderkloof Dam and anticipate inflows from the Vaal River. Since the factors that impact on flow rate and volume along the river are hard to quantify over long distances, a data-driven approach is followed which uses machine learning to predict the flow rate at downstream flow gauging stations based on flow rates recorded at upstream gauging stations. We restrict the model input to data that would be readily available in an operational setting, making the model practically implementable. A variety of neural network architectures, including fully-connected networks, convolutional neural networks (CNNs) and recurrent neural networks (RNNs), were investigated. It was found that fully-connected networks produce results with accuracy comparable to a simple linear regression model, but display a superior ability to predict the timing of peaks and troughs in flow rate trends. CNNs and RNNs displayed the same ability, as well as showing improvements in accuracy. The best-performing CNN model had a mean absolute percentage error (MAPE) of 14.5 % compared to 16.9 % of a linear regression model. To anticipate contributions from the Vaal River we investigated including inflows recorded at stations on the Vaal River and two of its tributaries, the Modder and Riet Rivers. Both approaches which were investigated, i.e. incorporating these inflows as part of multi-dimensional input into a CNN, and using a parallel CNN model architecture, showed promise with a MAPE of 21.6 % and 23.5 %, respectively. Although these models did not achieve a high level of accuracy, they did display the ability to anticipate contributions from the Vaal River system. It is believed that they could, with additional refinement or using appropriate safety factors, be practically applied in an operational setting. We further investigated including seasonal data as input into our models. Including the time of the year, and including evaporation data recorded at meteorological stations in the recent past, both resulted in improved MAPE accuracy (14.4 % and 14.8 %, respectively, compared to 18.4 % for a model including no seasonal data). Observations of errors staying relatively constant over time prompted us to include errors made in the recent past as input into subsequent predictions. A model trained with this additional data achieved a MAPE of 10.2 %, a significant improvement over other applied methods
- ItemDeveloping a methodology for the assessment of wave energy along the South African Coast(Stellenbosch : Stellenbosch University, 2018-03-19) Gweba, Bafana; Diedericks, G. P. J.; Wilms, Josefine M.; Rautenbach, C.; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematics)ENGLISH ABSTRACT : Ocean wave energy can become one of the alternative energy resources for fossil-fuelled power generation in South Africa. Due to global warming, several studies about the generation of wave energy have been done to find cleaner and sustainable renewable energy resources. An array of Wave Energy Converters (WECs) in a form of a wave farm may be used to harness the energy resource to generate electricity. Nearshore wave field effects due to the presence of a wave farm must be investigated particularly at the coastline as it will be affected. The principal objective of this thesis is to investigate the impacts induced by a wave farm on the nearshore wave field region through numerical modelling. Another objective is to give guidance about some of the parameters and input conditions for numerical modelling of wave transformations. In the present study, wave conditions have been assessed at selected locations of the South African coast. The JONSWAP model, which is the most frequently used spectral model to describe wind-generated waves, was used to represent wave energy spectrum along chosen locations. The JONSWAP model was fitted into the measured data along the coast to obtain the peak enhancement factor (gamma) values for chosen locations. The measured data was found to consist of bimodal spectra, local winds and distant storms and also multiple peaks in the spectra were observed. The spectral decomposition method was then applied to split the data into wind sea and swell to assess a more realistic description of the wave system. It was found that the method is effective in splitting bimodal spectra but is not successful in multi-peaked spectra. Saldanha Bay was chosen as the case study for installation of a wave farm due to its abundance of wave energy. A nested numerical wave model, referred to as SWAN (SimulatingWAves Nearshore), was used to simulate the nearshore wave field conditions in Saldanha Bay. The obtained gamma value for Saldanha Bay was used to set the wave model. Two model simulations in the study were considered, model simulations in the presence of a wave farm and model simulations in the absence of a wave farm. The difference in significant wave height and wave energy spectrum with and without the wave farm was assessed. The results show a reduction in significant wave height and a change in wave energy spectrum at the selected output locations. A gradual redirection of waves induced by the presence of wave farm has been observed for all selected boundary wave direction conditions. The overall results of the study indicate the change in the nearshore wave field during the presence of wave farm. A sensitivity assessment was conducted to investigate the change in wave energy due to the orientation of the original wave farm layout and the addition of two devices in the original wave farm layout. A proposed methodology for the assessment of wave energy was presented to evaluate the wave energy resource along the South African coast. The proposed methodology is based on analysis that was conducted in the study.
- ItemEar-based biometric authentication(Stellenbosch : Stellenbosch University, 2019-04) Kohlakala, Aviwe; Coetzer, Johannes; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Applied Mathematics.ENGLISH ABSTRACT : In this thesis novel semi-automated and fully automated ear-based biometric authentication systems are proposed. Within the context of the semiautomated system, a region of interest (ROI) that contains the entire ear shell is manually speci ed by a human operator. However, in the case of the fully automated system the ROI is automatically detected using a suitable convolutional neural network (CNN), followed by morphological post-processing. The purpose of the CNN is to classify sub-images as either foreground (part of the ear shell) or background (homogeneous skin, jewellery, or hair). Independent of the ROI-detection procedure, each grey-scale input image, in its entirety, is subjected to Gaussian smoothing, followed by edge detection through an appropriate Canny- lter, and morphological edge dilation. The detected ROI serves as a mask for retaining only those edges associated with prominent contours of the ear shell. Features are subsequently extracted from each binary contour image using the discrete Radon transform (DRT). The aforementioned features are normalised in such a way that they are translation, rotation and scale invariant. A Euclidean distance measure is employed for the purpose of feature matching. Ear-based authentication is nally achieved by constructing a ranking veri er. Exhaustive experiments are conducted on two large international datasets. It is assumed that only one reference ear is available for each individual enrolled into the system. An experimental protocol is adopted that appropriately partitions the respective datasets based on ears that belong to training, validation, ranking and evaluation individuals. It is demonstrated that the pro ciency of the novel systems developed in this thesis compares favourably to those of existing systems.
- ItemEvaluating the effectiveness of neural network techniques in the forecasting of South African basic fuel prices(Stellenbosch : Stellenbosch University, 2019-04) Kingwill, Russell; Brink, Willie; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Applied Mathematics.ENGLISH ABSTRACT : South Africa has a number of fuel grades available to consumers, one of the most popular being the 95 unleaded standard. The price of this fuel is comprised of many components including transport fees, taxes and the basic fuel price. The basic fuel price is the cost in Rand of Brent crude oil used to re ne the unit of petrol fuel, and is often the most signi cant component of the fuel price as well as the most volatile. Having a reliable forecasting methodology for the basic fuel price would be a helpful planning tool for many individuals and small enterprises. The forecasting of general fuel prices has been studied in the past with various forecasting techniques ranging from machine learning to ARIMA and regression models. In this study various deep learning models, including feed forward, recurrent and convolutional neural networks are assessed for their ability to accurately forecast the basic fuel price. These models are ranked by their ability to reduce the mean absolute percentage error on a common test data set. A number of time series data sets are used as input for the models under review, which include the closing daily price of Brent crude oil and the closing daily US Dollar exchange rate. The e ect of inputting the 30 day rolling future contracts for both the closing oil price and exchange rates is also investigated. Overall it is determined that, of the models evaluated during this study, the recurrent network performs the most favourably. On the nal test set, with optimal model and input parameters, the individual observation errors range from less than 1 % to more than 10 %. The average test error of 4.57 % can be a bit misleading due to the observed range of individual errors. Hence it is not as reliable of a forecast as one would hope for. However, the model did prove to have a fairly reliable attribute to correctly forecast the direction of the basic fuel price change. It did so in about 86% of the test data set observations, and was o by only a few cents when an incorrect direction was forecast. It is concluded that neural network models can be used to some degree for the task of forecasting the South African basic fuel price. Such models are sensitive to the amount of data provided and hence future work in this area should prioritise obtaining more data and if possible incorporating additional data sources.
- ItemFruit detection in an orchard using deep learning approaches(Stellenbosch : Stellenbosch University, 2022-04) Koech, Kiprono Elijah; Bah, Bubacarr; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematics)ENGLISH ABSTRACT: Over the last few years, we have witnessed rapid advancement in technology in different fields: communication, transport security, finance, and medicine. Agriculture is no exception. Today, agriculture is practised with sophisticated technologies such as satellite imaging, soil and water sensors, weather tracking, and robots. Fruit detection is a critical process in robot harvesting and yield estimation. With the rise in deep learning, state-of-the-art object detectors have been developed. In this paper, we deploy two state-of-the-art model detectors; namely, Mask Region-based CNN (Mask R-CNN), and You Only Look Once (YOLOv5), in the context of fruit detection. The training data are orchard images of apples and mangoes taken under natural outdoor conditions. The images are taken under varied illumination conditions to ensure that the models learn rich features allowing them to generalize well in a new dataset. Ablation studies are presented to understand how the two models compare in terms of accuracy and speed at inference time. We also investigated the significance of transfer learning in such an application. In particular, we considered weight initialization using ImageNet, COCO, and weights from models trained on a di erent orchard dataset. As a post-processing step, we implemented ensemble techniques on the detection results of the two models. Mask R-CNN and YOLOv5 attained an F1 score of 93% on mangoes datasets and 88% on apple images, and ensembling led to an up to 3% increase in F1 score.
- ItemHand vein-based biometric authentication with limited training samples(Stellenbosch : Stellenbosch University, 2018-03) Beukes, Emile; Coetzer, Johannes; Swanepoel, J.; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematics)ENGLISH ABSTRACT : A number of novel hand vein-based biometric authentication systems are proposed. Said systems are non-intrusive and may for example assist with user authentication at automated teller machines. An infrared image of either the dorsal or ventral surface of an individual's hand is acquired through specialised equipment, after which the geometrical properties of the hand are used to extract a suitable region of interest (ROI). A novel protocol, which is based on morphological reconstruction, is employed for the purpose of isolating the veins within the ROI. Feature vectors are extracted from the isolated veins through the calculation of the discrete Radon transform. The feature vectors are appropriately normalised in order to ensure rotational, translational and scale invariance. The dissimilarity between the corresponding feature vectors extracted from a questioned image and a reference image belonging to the claimed client are represented by an average Euclidean or dynamic time warping-based distance. A score-based or rank-based classi er is subsequently employed for authentication purposes. It is demonstrated that, when only one training sample (of arbitrary quality) is available per client, and the client is granted six opportunities for authentication, an average error rate (AER) of 2.85% is achievable for a data set that contains dorsal hand vein patterns from 100 individuals. In a scenario where the single training sample is guaranteed to be of very high quality and the client is granted only three opportunities for authentication, the AER may be reduced to 0.77%.
- ItemHandover in a distributed system of UAVs: application to wildlife monitoring(Stellenbosch : Stellenbosch University, 2020-12) Marcos, Juliana Thomasia Chakirath; Utete, Simukai Wanzira; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Applied Mathematics.ENGLISH ABSTRACT: Wildlife surveillance is of significant interest for the protection of animals and their habitats. In this study, a distributed system of unmanned aerial vehicles (UAVs) or drones is designed for single-animal tracking in terrestrial settings. The system involves four main components which constitute key contributions of the study. The main component is a visual object tracking approach based on the use of a particle filter that switches between measurements from two sources: a simple and fast approach based on colour image segmentation and a slower but more sophisticated method based on a deep learning object detector, the third version of the You Only Look Once detector (YOLOv3). The particle filter switches between the measurement sources using the structural similarity (SSIM) index from the image-processing literature. The SSIM index is also applied in the study for handover of tracking between a pair of drones. Some of the components of the monitoring system have been simulated using wildlife footage recorded by drone (obtained from an animal behaviour group). Extensive simulation tests were carried out during the study. These demonstrate, amongst other results, that better real-time object detection is obtained by replacing YOLOv3 by techniques such as boosting and channel and spatial reliability tracking (CSRT). The design developed and components tested suggest some directions for single-animal tracking by a distributed system of drones. Keywords: Animal tracking algorithm, boosting, channel and spatial reliability tracking (CSRT), drone, handover, multiple instance learning (MIL), particle filter, structural similarity (SSIM), unmanned aerial vehicle (UAV), You Only Look Once version 3 (YOLOv3).
- ItemHydrodynamic permeability of staggered and non-staggered regular arrays of squares(Stellenbosch : Stellenbosch University, 2003-12) Lloyd, Cindy; Du Plessis, J. P.; Stellenbosch University. Faculty of Science. Department of Mathematical Sciences.ENGLISH ABSTRACT: This work entails an analysis of two-dimensional Newtonian flow through a prismatic array of squares. Both in-line and staggered configurations are investigated, as well as the very low velocity Darcy regime, where Stokes' flow predominates, and the Forchheimer regime, where interstitial inertial effects such as recirculation are present. As point of departure two recently developed pore-scale models are discussed and their results compared to Stokes' flow computational analysis for flow through regular arrays of rectangles. The commercial CFX code is also used to analyse the problem and to determine the accuracy of the assumptions used for the development of the pore-scale models. Finally an improvement is suggested to the RRUC model towards more accurate prediction of permeabilities, especially for porosities below 75%, and whereby its quantitative predictive capability is thus enhanced considerably.
- ItemImage and attribute based identification of Protea species(Stellenbosch : Stellenbosch University., 2020-04) Thompson, Peter; Brink, Willie; Stellenbosch University. Faculty of Science. Department of Mathematical Sciences (Applied Mathematics).ENGLISH ABSTRACT: The flowering plant genus Protea is a dominant representative for the biodiversity of the Cape Floristic Region in South Africa, and from a conservation point of view important to monitor. The recent surge in popularity of crowd-sourced wildlife monitoring platforms presents opportunities for automatic image based identification, for improved monitoring of species. We consider the problem of identifying the Proteaspecies in a given image with additional (but optional) attributes linked to the observation, such as location, elevation and date. We collect training and test data from a crowd-sourced platform, and find that the Protea identification problem is exacerbated by considerable inter-class similarity, data scarcity, class imbalance, as well as large variations in image quality, composition and background. Our proposed solution consists of three parts. The first part incorporates a variant of multi-region attention into a pretrained convolutional neural network, to focus on the flowerhead in the image. The second part performs coarser-grained classification on subgenera (superclasses) and then rescales the output of the first part. The third part conditions a probabilistic model on the additional attributes associated with the observation. We perform an ablation study on the proposed model and its constituents, and find that all three components together outperform our baselines and all other variants quite significantly.
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