Department of Applied Mathematics

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3D reconstruction of naturally fragmenting warhead fragments
(Stellenbosch : Stellenbosch University, 2024-03) Sequeira, Jose; Smit, Francois; Coetzer, Johannes; Stellenbosch University. Faculty of Science. Dept. of Applied Mathematics.
ENGLISH ABSTRACT: This study starts with a brief introduction to the South African armaments and ammunition technology industry, highlighting the historical alignment with NATO standards. The focal point is the investigation into the potential of an existing NATO-compliant icosahedral imaging system to ascertain additional geometric features of fragments, such as mass and volume. Building on prior work, the author proposes leveraging extensive image data sets acquired through the icosahedral imaging system to determine these features. The literature study explores two key approaches: stereo vision and shape-from-silhouette 3D reconstruction. The latter emerges as the favored method, particularly due to how well the technique complements the icosahedral camera arrangement. Subsequently, attention is directed toward the electro-mechanical design of the icosahedral imaging instrument and the creation of shape-from-silhouette reconstruction software. Challenges in calibrating the multi-imaging system are addressed through hardware upgrades. The study advances to experimental results, involving the analysis of fragments recovered from a warhead arena test. Average presented areas are determined, and 3D reconstructed models are obtained using the shape-from-silhouette technique, with errors ranging from 2% to 54%. A detailed discussion follows, highlighting the similar average presented area measurements for diﬀerent icosahedral imaging systems. The inclusion of shadow regions is noted to signiﬁcantly impact the accuracy of the 3D reconstruction process. Furthermore, slender fragments exhibit smaller errors compared to non-slender counterparts. The study concludes by aﬃrming the achievement of the primary objectives, namely, the ability to use fragment silhouettes obtained during average presented area measurements to produce close-ﬁt 3D models of fragments. Future work is underscored, building upon the strong foundation laid by this investigation. Recommendations, improvements, and suggestions for future research are provided, emphasizing the potential for enhanced reconstruction accuracy, particularly for non-slender fragments, with increased camera deployment.
Dental implant recognition
(Stellenbosch : Stellenbosch University, 2023-09) Kohlakala, Aviwe; Coetzer, Johannes; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics Division.
ENGLISH ABSTRACT: Deep learning-based frameworks have recently been steadily outperforming existing state-of-the-art systems in a number of computer vision applications, but these models require a large number of training samples in order to effectively train the model parameters. Within the medical field the limited availability of training data is one of the main challenges faced when using deep learning to create practical clinical applications in medical imaging. In this dissertation a novel algorithm for generating artificial training samples from triangulated three-dimensional (3D) surface models within the context of dental implant recognition is proposed. The proposed algorithm is based on the calculation of two-dimensional (2D) parallel projections from a number of different angles of 3D volumetric representations of computer-aided design (CAD) surface models. A fully convolutional network (FCN) is subsequently trained on the artificially generated X-ray images for the purpose of automatically identifying the connection type associated with a specific dental implant in an actual X-ray image. An ensemble of image processing and deep learning-based techniques capable of distinguishing between pixels that belong to an implant from those belonging to the background in an actual X-ray image is developed. Normalisation and preprocessing techniques are subsequently applied to the segmented dental implants within the questioned actual X-ray image. The normalised dental implants are presented to the trained FCN for classification purposes. Experiments are conducted on two data sets that contain the simulated and actual X-ray images in order to gauge the proficiency of the proposed systems. Given the fact that the novel systems proposed in this study utilise an ensemble of techniques that has not been employed for the purpose of dental implant classification/recognition on any previous occasion, the results achieved in this study are encouraging and constitute a significant contribution to the current state of the art, especially in scenarios where the proposed systems are combined with existing systems.
Ear-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.
Hand vein-based biometric authentication using neural networks
(Stellenbosch : Stellenbosch University, 2024-03) Beukes, Emile; Coetzer, Johannes; Stellenbosch University. Faculty of Science. Dept. of Applied Mathematics.
ENGLISH ABSTRACT: The feasibility of employing convolutional neural networks for the purpose of authenticating an individual based on a near infra-red image of his/her dorsal hand vein pattern is inves- tigated in this study. The proficiency of different architectural designs associated with sim- ilarity measure networks (SMNs), in particular two-channel SMNs and Siamese SMNs, are compared. Four different combinations of neural network layers are investigated for each of the aforementioned SMNs. Three different levels of preprocessing are applied to the hand vein images in order to investigate the relevance of information surrounding the actual hand veins on the proficiency of the networks. The proficiency of the proposed systems is gauged within the context of two real-world scenarios, namely the individual dependent scenario (IDS) and the individual independent scenario (IIS). A tailor-made network is trained for each client during enrolment in mere minutes within the context of the IDS, while a single net- work is trained in a once-off fashion prior to the enrolment of any clients within the context of the IIS. Two publicly available hand vein databases namely the Bosphorus and Wilches databases are investigated within the context of this study. An artificially generated hand vein database, namely the GenVeins database, is developed in this study for the purpose of acquiring a set of training individuals that is large enough so as to be representative of the entire population. The motivation behind the creation of the GenVeins database constitutes the fact that experimental results indicate that system proficiency is severely impaired when training on an insufficient number of different individuals within the context of the IIS. The systems proposed in this study are therefore considered implementation-ready in the sense that they are either trained in a (1) tailor-made fashion for each client enrolled into the sys- tem in real time or in a (2) once-off fashion on a set of fictitious individuals that is sufficiently representative of the entire population. The proposed systems do therefore not merely serve as so-called proofs-of-concept (POCs) in which a system is trained and tested on the same set of individuals. These POCs are clearly not feasible within the context of any real world scenario.
Hand 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%.
Modifying and generalising the Radon transform for improved curve-sensitive feature extraction
(Stellenbosch : Stellenbosch University, 2017-12-01) Fick, Carlien; Coetzer, Johannes; Swanepoel, Jacques Philip; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Applied Mathematics.
ENGLISH ABSTRACT : In this thesis a novel and generic feature extraction protocol that is based on the well-known standard discrete Radon transform (SDRT) is presented. The SDRT is traditionally associated with computerised tomography and involves the calculation of projection profiles of an image from a finite set of angles. Although the SDRT has already been successfully employed for the purpose of feature extraction, it is limited to the detection of straight lines. The proposed feature extraction protocol is based on modifications to the SDRT that facilitate the detection of not only straight lines, but also curved lines (with various curvatures), as well as textural information. This is made possible by first constructing a novel appropriately normalised multiresolution polar transform (MPT) of the image in question. The origin of said MPT may be adjusted according to the type of features targeted. The SDRT, or the novel modified discrete Radon transform (MDRT) conceptualised in this thesis, is subsequently applied to the MPT. The extraction of textural information based on different textural periodicities is facilitated by considering different projection angles associated with the MDRT, while the extraction of textural information based on different textural orientations is facilitated by specifying different origins for the MPT. The extraction of information pertaining to curved lines is made possible by specifying origins for the MPT that are located at different distances from the edge of the image in question – the SDRT is subsequently applied to a given MPT from a specific angle of 90 . An existing system that only employs SDRT-based features constitutes a benchmark. Two novel texture-based systems, that target different textural periodicities and orientations respectively, are developed. A novel system, that constitutes a generalisation of the SDRT-based benchmark, and is geared towards the detection of different curved lines, is also developed. The proficiency of the proposed systems is gauged by considering a data set that contains authentic handwritten signature images and skilled forgeries associated with 51 writers. All of the proposed systems outperform the SDRTbased benchmark. The improvement in proficiency associated with each individual texture-based system is statistically significant. The proficiency of the proposed systems also compares favourably with that of existing state-of-theart systems within the context of offline signature verification.
Offline writer authentication
(Stellenbosch : Stellenbosch University, 2021-12) Shumba, Sandura; Coetzer, Johannes; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Applied Mathematics.
ENGLISH ABSTRACT: In this thesis a number of systems are proposed for the purpose of offline writer authentication. A text-dependent approach is adopted, since a very specific targeted handwritten word is considered for authentication purposes. Feature extraction is facilitated by calculating a number of projections of the targeted word from different angles. Two distinct categories of systems are proposed. The first category employs template matching and is based on the computation of the Euclidean distance and a dynamic time warping (DTW) distance between corresponding feature vectors, while the second category relies on machine learning techniques, that is support vector machines (SVMs) and quadratic discriminant analysis (QDA). Within the context of the proposed machine learning-based systems, a writer-independent protocol is followed. This is achieved by employing a DTW-based dichotomy transformation which converts a feature set in feature space into a dissimilarity vector-based representation in dissimilarity space. This dichotomy transformation is followed by writer-specific dissimilarity vector normalisation which significantly improves interclass separability. The DTW-based dichotomy transformation and writer-specific dissimilarity vector normalisation are novel within the context of offline writer authentication. The systems developed in this study are evaluated on a subset of the CEDAR-LETTER data set. It is demonstrated that the proficiency of the systems developed in this study are at least on par when compared to existing systems. The most proficient SVM-based system developed in this study achieves an AUC of 93% and an equal error rate (EER) of 14.93%.
The study of similarity score calculation methods for minutia-based fingerprint matching algorithms
(Stellenbosch : Stellenbosch University, 2016-11) De Kock, Antonie Johannes; Coetzer, Johannes; Mathekga, Mmamolatelo E.; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematic)
ENGLISH ABSTRACT : This study aims to establish guidelines for calculating the similarity score between two minutia point representations of ngerprints for minutia-based ngerprint matching. Existing research does not provide clear guidelines on how to calculate the similarity score between two minutia point representations and the reported performance of most existing algorithms include those comparisons for which the point matching algorithm failed. This study therefore compares the performance of existing similarity score calculation methods after the erroneous comparisons from the point matching algorithm have been removed. It furthermore investigates in which way and to what extent these methods are a ected by intra-class variations and inter-class similarities. The results indicate that none of the existing similarity score calculation methods is superior to all the others when implemented on the FVC2002 and FVC2004 ngerprint databases. This study also proposes an improved local descriptor for local similarity score calculation and investigates whether the combination of di erent types of similarity score calculation methods better addresses intraclass variations and inter-class similarities and therefore improves pro ciency. The results indicate that similarity score calculation methods that address both global and local inter-class similarities, and are robust to intra-class variations, perform better across multiple databases. Even though this study concludes that the combination of di erent types of similarity score calculation methods generally improves pro ciency, high levels of noise and nonlinear distortion still adversely a ect performance. Future work should therefore focus on improving the stages preceding the similarity score calculation stage, i.e. minutia extraction and point matching.
Towards automated detection of dicentric chromosomes in metaphase images
(Stellenbosch : Stellenbosch University, 2021-03) Galloway, Sarah; Coetzer, Johannes; Muller, N.; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Applied Mathematics.
ENGLISH ABSTRACT: The aim of the proposed research is to investigate methods to identify objects of interest and classify dicentric and normal chromosomes in metaphase images using suitable digital image processing techniques. Dicentric chromosomes are abnormal chromosomes with two centromeres (instead of one) created by a variety of processes, including irradiation. When a chromosome is exposed to radiation, two chromosome segments, each with a centromere may join together resulting in a dicentric chromosome. An acentric fragment, i.e. a partial chromosome with no centromere, is also formed. The first stage of the proposed system is geared towards the detection of objects of interest, i.e. isolated normal and isolated dicentric chromosomes, as well as acentric fragments and clusters of overlapping chromosomes. The last stage of the proposed system is geared towards the classification of isolated chromosomes as either normal or dicentric. The proposed system automatically detects objects of interest not associated with dirt. The classification of the aforementioned objects into isolated and clustered chromosomes, as well as acentric fragments, is conducted manually, while the automation of this stage is reserved for future work. The proposed system subsequently automatically categorises isolated chromosomes as either normal or dicentric. It is demonstrated that the system correctly detects and classifies a significant number of the aforementioned chromosomes within metaphase images provided by iThemba LABS.
The use of deep learning to predict HER2 status in breast cancer directly from histopathology slides
(Stellenbosch : Stellenbosch University, 2024-03) Smith, Alexandra Nicole; Coetzer, Johannes; Stellenbosch University. Faculty of Science. Dept. of Applied Mathematics.
ENGLISH ABSTRACT: The treatment of breast cancer is significantly influenced by the identification of various molecular biomarkers, including Human Epidermal Growth Factor Receptor 2 (HER2). Current techniques for determining HER2 status involve immunohistochemistry (IHC) and in-situ hybridisation (ISH) methods. HER2 testing, which is routinely applied in cases of invasive breast cancer, serves as the primary biomarker guiding HER2-targeted therapies. HE-stained whole slide images, which are more cost-effective, time-efficient, and routinely produced during pathological examinations, present an opportunity for leveraging deep learning to enhance the accuracy, speed, and affordability of HER2 status determination. This thesis introduces a deep learning framework for predicting HER2 status directly from the morphological features observed in histopathological slides. The proposed system has two stages: initially, a deep learning model is employed to differentiate between benign and malignant tissues in whole slide images, using annotated regions of invasive tumours. Following this, the effectiveness of Inception-v4 and Inception-ResNet-v2 architectures in biomarker status prediction is explored, comparing their performance against previous model architectures utilised for this task, namely Inception-v3 and ResNet34. The study utilises a dataset comprising whole slide images from 147 patients, sourced from the publicly available Cancer Genome Atlas (TCGA). Models are trained using 256 ◊ 256 patches extracted from these slides. The best-performing model, Inception-v4, achieved an area under the receiver operating characteristic curve (AUC) of 0.849 (95% confidence interval (CI): 0.845 ≠ 0.853) per-tile and 0.767 (CI:0.556 ≠ 0.955) per-slide in the test set. This research demonstrates the capability of deep learning models to accurately predict HER2 status directly from histopathological whole slide images, offering a more cost- and time-efficient method for identifying clinical biomarkers, with the potential to inform and accelerate the selection of breast cancer treatments.
Writer-independent handwritten signature verification
(Stellenbosch : Stellenbosch University, 2015-12) Swanepoel, Jacques Philip; Coetzer, Johannes; Stellenbosch University. Faculty of Science. Department of Mathematical Sciences (Applied Mathematics).
AFRIKAANSE OPSOMMING : In hierdie verhandeling stel ons 'n nuwe strategie vir outomatiese handtekening-verifikasie voor. Die voorgestelde raamwerk gebruik 'n skrywer-onafhanklike benadering tot handtekening- modellering en is dus in staat om bevraagtekende handtekeninge, wat aan enige skrywer behoort, te bekragtig, op voorwaarde dat minstens een outentieke voorbeeld vir vergelykingsdoeleindes beskikbaar is. Ons ondersoek die tradisionele statiese geval (waarin 'n bestaande pen-op-papier handtekening vanuit 'n versyferde dokument onttrek word), asook die toenemend gewilde dinamiese geval (waarin handtekeningdata outomaties tydens ondertekening m.b.v. gespesialiseerde elektroniese hardeware bekom word). Die statiese kenmerk-onttrekkingstegniek behels die berekening van verskeie diskrete Radontransform (DRT) projeksies, terwyl dinamiese handtekeninge deur verskeie ruimtelike en temporele funksie-kenmerke in die kenmerkruimte voorgestel word. Ten einde skryweronafhanklike handtekening-ontleding te bewerkstellig, word hierdie kenmerkstelle na 'n verskil-gebaseerde voorstelling d.m.v. 'n geskikte digotomie-transformasie omgeskakel. Die klassikasietegnieke, wat vir handtekeking-modellering en -verifikasie gebruik word, sluit kwadratiese diskriminant-analise (KDA) en steunvektormasjiene (SVMe) in. Die hoofbydraes van hierdie studie sluit twee nuwe tegnieke, wat op die bou van 'n robuuste skrywer-onafhanklike handtekeningmodel gerig is, in. Die eerste, 'n dinamiese tydsverbuiging digotomie-transformasie vir statiese handtekening-voorstelling, is in staat om vir redelike intra-klas variasie te kompenseer, deur die DRT-projeksies voor vergelyking nie-lineêr te belyn. Die tweede, 'n skrywer-spesieke verskil-normaliseringstrategie, is in staat om inter-klas skeibaarheid in die verskilruimte te verbeter deur slegs streng relevante statistieke tydens die normalisering van verskil-vektore te beskou. Die normaliseringstrategie is generies van aard in die sin dat dit ewe veel van toepassing op beide statiese en dinamiese handtekening-modelkonstruksie is. Die stelsels wat in hierdie studie ontwikkel is, is spesi ek op die opsporing van hoë-kwaliteit vervalsings gerig. Stelselvaardigheid-afskatting word met behulp van 'n omvattende eksperimentele protokol bewerkstellig. Verskeie groot handtekening-datastelle is oorweeg. In beide die statiese en dinamiese gevalle vaar die voorgestelde SVM-gebaseerde stelsel beter as die voorgestelde KDA-gebaseerde stelsel. Ons toon ook aan dat die stelsels wat in hierdie studie ontwikkel is, die meeste bestaande stelsels wat op dieselfde datastelle ge evalueer is, oortref. Dit is selfs meer belangrik om daarop te let dat, wanneer hierdie stelsels met bestaande tegnieke in die literatuur vergelyk word, ons aantoon dat die gebruik van die nuwe tegnieke, soos in hierdie studie voorgestel, konsekwent tot 'n statisties beduidende verbetering in stelselvaardigheid lei.

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Browsing Department of Applied Mathematics by browse.metadata.advisor "Coetzer, Johannes"

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