Implementation and evaluation of medical imaging techniques based on conformal geometric algebra

Medical imaging tasks, such as segmentation, 3D modeling, and registration of medical images, involve complex geometric problems, usually solved by standard linear algebra and matrix calculations. In the last few decades, conformal geometric algebra (CGA) has emerged as a new approach to geometric computing that offers a simple and efficient representation of geometric objects and transformations. However, the practical use of CGA-based methods for big data image processing in medical imaging requires fast and efficient implementations of CGA operations to meet both real-time processing constraints and accuracy requirements. The purpose of this study is to present a novel implementation of CGA-based medical imaging techniques that makes them effective and practically usable. The paper exploits a new simplified formulation of CGA operators that allows significantly reduced execution times while maintaining the needed result precision. We have exploited this novel CGA formulation to re-design a suite of medical imaging automatic methods, including image segmentation, 3D reconstruction and registration. Experimental tests show that the re-formulated CGA-based methods lead to both higher precision results and reduced computation times, which makes them suitable for big data image processing applications. The segmentation algorithm provides the Dice index, sensitivity and specificity values of 98.14%, 98.05% and 97.73%, respectively, while the order of magnitude of the errors measured for the registration methods is 10-5

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282

Visualization and Analysis of Flow Fields based on Clifford Convolution

Vector fields from flow visualization often containmillions of data values. It is obvious that a direct inspection of the data by the user is tedious. Therefore, an automated approach for the preselection of features is essential for a complete analysis of nontrivial flow fields. This thesis deals with automated detection, analysis, and visualization of flow features in vector fields based on techniques transfered from image processing. This work is build on rotation invariant template matching with Clifford convolution as developed in the diploma thesis of the author. A detailed analysis of the possibilities of this approach is done, and further techniques and algorithms up to a complete segmentation of vector fields are developed in the process. One of the major contributions thereby is the definition of a Clifford Fourier transform in 2D and 3D, and the proof of a corresponding convolution theorem for the Clifford convolution as well as other major theorems. This Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vectorvalued filters, as well as an acceleration of the convolution computation as a fast transform exists. The depth and precision of flow field analysis based on template matching and Clifford convolution is studied in detail for a specific application, which are flow fields measured in the wake of a helicopter rotor. Determining the features and their parameters in this data is an important step for a better understanding of the observed flow. Specific techniques dealing with subpixel accuracy and the parameters to be determined are developed on the way. To regard the flow as a superposition of simpler features is a necessity for this application as close vortices influence each other. Convolution is a linear system, so it is suited for this kind of analysis. The suitability of other flow analysis and visualization methods for this task is studied here as well. The knowledge and techniques developed for this work are brought together in the end to compute and visualize feature based segmentations of flow fields. The resulting visualizations display important structures of the flow and highlight the interesting features. Thus, a major step towards robust and automatic detection, analysis and visualization of flow fields is taken

Pattern Recognition

Pattern recognition is a very wide research field. It involves factors as diverse as sensors, feature extraction, pattern classification, decision fusion, applications and others. The signals processed are commonly one, two or three dimensional, the processing is done in real- time or takes hours and days, some systems look for one narrow object class, others search huge databases for entries with at least a small amount of similarity. No single person can claim expertise across the whole field, which develops rapidly, updates its paradigms and comprehends several philosophical approaches. This book reflects this diversity by presenting a selection of recent developments within the area of pattern recognition and related fields. It covers theoretical advances in classification and feature extraction as well as application-oriented works. Authors of these 25 works present and advocate recent achievements of their research related to the field of pattern recognition

Recent Trends in Computational Intelligence

Traditional models struggle to cope with complexity, noise, and the existence of a changing environment, while Computational Intelligence (CI) offers solutions to complicated problems as well as reverse problems. The main feature of CI is adaptability, spanning the fields of machine learning and computational neuroscience. CI also comprises biologically-inspired technologies such as the intellect of swarm as part of evolutionary computation and encompassing wider areas such as image processing, data collection, and natural language processing. This book aims to discuss the usage of CI for optimal solving of various applications proving its wide reach and relevance. Bounding of optimization methods and data mining strategies make a strong and reliable prediction tool for handling real-life applications

Modelling and tracking objects with a topology preserving self-organising neural network

Human gestures form an integral part in our everyday communication. We use gestures not only to reinforce meaning, but also to describe the shape of objects, to play games, and to communicate in noisy environments. Vision systems that exploit gestures are often limited by inaccuracies inherent in handcrafted models. These models are generated from a collection of training examples which requires segmentation and alignment. Segmentation in gesture recognition typically involves manual intervention, a time consuming process that is feasible only for a limited set of gestures. Ideally gesture models should be automatically acquired via a learning scheme that enables the acquisition of detailed behavioural knowledge only from topological and temporal observation. The research described in this thesis is motivated by a desire to provide a framework for the unsupervised acquisition and tracking of gesture models. In any learning framework, the initialisation of the shapes is very crucial. Hence, it would be beneficial to have a robust model not prone to noise that can automatically correspond the set of shapes. In the first part of this thesis, we develop a framework for building statistical 2D shape models by extracting, labelling and corresponding landmark points using only topological relations derived from competitive hebbian learning. The method is based on the assumption that correspondences can be addressed as an unsupervised classification problem where landmark points are the cluster centres (nodes) in a high-dimensional vector space. The approach is novel in that the network can be used in cases where the topological structure of the input pattern is not known a priori thus no topology of fixed dimensionality is imposed onto the network. In the second part, we propose an approach to minimise the user intervention in the adaptation process, which requires to specify a priori the number of nodes needed to represent an object, by utilising an automatic criterion for maximum node growth. Furthermore, this model is used to represent motion in image sequences by initialising a suitable segmentation that separates the object of interest from the background. The segmentation system takes into consideration some illumination tolerance, images as inputs from ordinary cameras and webcams, some low to medium cluttered background avoiding extremely cluttered backgrounds, and that the objects are at close range from the camera. In the final part, we extend the framework for the automatic modelling and unsupervised tracking of 2D hand gestures in a sequence of k frames. The aim is to use the tracked frames as training examples in order to build the model and maintain correspondences. To do that we add an active step to the Growing Neural Gas (GNG) network, which we call Active Growing Neural Gas (A-GNG) that takes into consideration not only the geometrical position of the nodes, but also the underlined local feature structure of the image, and the distance vector between successive images. The quality of our model is measured through the calculation of the topographic product. The topographic product is our topology preserving measure which quantifies the neighbourhood preservation. In our system we have applied specific restrictions in the velocity and the appearance of the gestures to simplify the difficulty of the motion analysis in the gesture representation. The proposed framework has been validated on applications related to sign language. The work has great potential in Virtual Reality (VR) applications where the learning and the representation of gestures becomes natural without the need of expensive wear cable sensors

Machine Intelligence for Advanced Medical Data Analysis: Manifold Learning Approach

In the current work, linear and non-linear manifold learning techniques, specifically Principle Component Analysis (PCA) and Laplacian Eigenmaps, are studied in detail. Their applications in medical image and shape analysis are investigated. In the first contribution, a manifold learning-based multi-modal image registration technique is developed, which results in a unified intensity system through intensity transformation between the reference and sensed images. The transformation eliminates intensity variations in multi-modal medical scans and hence facilitates employing well-studied mono-modal registration techniques. The method can be used for registering multi-modal images with full and partial data. Next, a manifold learning-based scale invariant global shape descriptor is introduced. The proposed descriptor benefits from the capability of Laplacian Eigenmap in dealing with high dimensional data by introducing an exponential weighting scheme. It eliminates the limitations tied to the well-known cotangent weighting scheme, namely dependency on triangular mesh representation and high intra-class quality of 3D models. In the end, a novel descriptive model for diagnostic classification of pulmonary nodules is presented. The descriptive model benefits from structural differences between benign and malignant nodules for automatic and accurate prediction of a candidate nodule. It extracts concise and discriminative features automatically from the 3D surface structure of a nodule using spectral features studied in the previous work combined with a point cloud-based deep learning network. Extensive experiments have been conducted and have shown that the proposed algorithms based on manifold learning outperform several state-of-the-art methods. Advanced computational techniques with a combination of manifold learning and deep networks can play a vital role in effective healthcare delivery by providing a framework for several fundamental tasks in image and shape processing, namely, registration, classification, and detection of features of interest

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 20. bis 22.7. 2015, Bauhaus-Universität Weimar

The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 20th till 22nd July 2015. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference