Efficient Model-based 3D Tracking by Using Direct Image Registration

This thesis deals with the problem of efficiently tracking 3D objects in sequences of images. We tackle the efficient 3D tracking problem by using direct image registration. This problem is posed as an iterative optimization procedure that minimizes a brightness error norm. We review the most popular iterative methods for image registration in the literature, turning our attention to those algorithms that use efficient optimization techniques. Two forms of efficient registration algorithms are investigated. The first type comprises the additive registration algorithms: these algorithms incrementally compute the motion parameters by linearly approximating the brightness error function. We centre our attention on Hager and Belhumeur’s factorization-based algorithm for image registration. We propose a fundamental requirement that factorization-based algorithms must satisfy to guarantee good convergence, and introduce a systematic procedure that automatically computes the factorization. Finally, we also bring out two warp functions to register rigid and nonrigid 3D targets that satisfy the requirement. The second type comprises the compositional registration algorithms, where the brightness function error is written by using function composition. We study the current approaches to compositional image alignment, and we emphasize the importance of the Inverse Compositional method, which is known to be the most efficient image registration algorithm. We introduce a new algorithm, the Efficient Forward Compositional image registration: this algorithm avoids the necessity of inverting the warping function, and provides a new interpretation of the working mechanisms of the inverse compositional alignment. By using this information, we propose two fundamental requirements that guarantee the convergence of compositional image registration methods. Finally, we support our claims by using extensive experimental testing with synthetic and real-world data. We propose a distinction between image registration and tracking when using efficient algorithms. We show that, depending whether the fundamental requirements are hold, some efficient algorithms are eligible for image registration but not for tracking.

Combining a Similar Coefficient Identification Algorithm with the Boundary Element Method

The boundary element method (BEM) has been applied successfully to many engineering problems during the last decades. Compared with domain type methods like the finite element method (FEM) or the finite difference method (FDM) the BEM can handle problems where the medium extends to infinity much easier than domain type methods as there is no need to develop special boundary conditions (quiet or absorbing boundaries) or infinite elements at the boundaries introduced to limit the domain studied. The determination of the dynamic stiffness of arbitrarily shaped footings is just one of these fields where the BEM has been the method of choice, especially in the 1980s. With the continuous development of computer technology and the available hardware equipment the size of the problems under study grew and, as the flop count for solving the resulting linear system of equations grows with the third power of the number of equations, there was a need for the development of iterative methods with better performance. In [1] the GMRES algorithm was presented which is now widely used for implementations of the collocation BEM. While the FEM results in sparsely populated coefficient matrices, the BEM leads, in general, to fully or densely populated ones, depending on the number of subregions, posing a serious memory problem even for todays computers. If the geometry of the problem permits the surface of the domain to be meshed with equally shaped elements a lot of the resulting coefficients will be calculated and stored repeatedly. The present paper shows how these unnecessary operations can be avoided reducing the calculation time as well as the storage requirement. To this end a similar coefficient identification algorithm (SCIA), has been developed and implemented in a program written in Fortran 90. The vertical dynamic stiffness of a single pile in layered soil has been chosen to test the performance of the implementation. The results obtained with the 3-d model may be compared with those obtained with an axisymmetric formulation which are considered to be the reference values as the mesh quality is much better. The entire 3D model comprises more than 35000 dofs being a soil region with 21168 dofs the biggest single region. Note that the memory necessary to store all coefficients of this single region is about 6.8 GB, an amount which is usually not available with personal computers. In the problem under study the interface zone between the two adjacent soil regions as well as the surface of the top layer may be meshed with equally sized elements. In this case the application of the SCIA leads to an important reduction in memory requirements. The maximum memory used during the calculation has been reduced to 1.2 GB. The application of the SCIA thus permits problems to be solved on personal computers which otherwise would require much more powerful hardware.

A comparison between PML, infinite elements and an iterative BEM as mesh truncation methods for HP self-adaptive procedures in electromagnetics

Finite element hp-adaptivity is a technology that allows for very accurate numerical solutions. When applied to open region problems such as radar cross section prediction or antenna analysis, a mesh truncation method needs to be used. This paper compares the following mesh truncation methods in the context of hp-adaptive methods: Infinite Elements, Perfectly Matched Layers and an iterative boundary element based methodology. These methods have been selected because they are exact at the continuous level (a desirable feature required by the extreme accuracy delivered by the hp-adaptive strategy) and they are easy to integrate with the logic of hp-adaptivity. The comparison is mainly based on the number of degrees of freedom needed for each method to achieve a given level of accuracy. Computational times are also included. Two-dimensional examples are used, but the conclusions directly extrapolated to the three dimensional case.

Space-time Reconstruction of Oceanic Sea States via Variational Stereo Methods

We present a remote sensing observational method for the measurement of the spatio-temporal dynamics of ocean waves. Variational techniques are used to recover a coherent space-time reconstruction of oceanic sea states given stereo video imagery. The stereoscopic reconstruction problem is expressed in a variational optimization framework. There, we design an energy functional whose minimizer is the desired temporal sequence of wave heights. The functional combines photometric observations as well as spatial and temporal regularizers. A nested iterative scheme is devised to numerically solve, via 3-D multigrid methods, the system of partial differential equations resulting from the optimality condition of the energy functional. The output of our method is the coherent, simultaneous estimation of the wave surface height and radiance at multiple snapshots. We demonstrate our algorithm on real data collected off-shore. Statistical and spectral analysis are performed. Comparison with respect to an existing sequential method is analyzed.

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use.

Efficient methodologies for system matrix modelling in iterative image reconstruction for rotating high-resolution PET

A fully 3D iterative image reconstruction algorithm has been developed for high-resolution PET cameras composed of pixelated scintillator crystal arrays and rotating planar detectors, based on the ordered subsets approach. The associated system matrix is precalculated with Monte Carlo methods that incorporate physical effects not included in analytical models, such as positron range effects and interaction of the incident gammas with the scintillator material. Custom Monte Carlo methodologies have been developed and optimized for modelling of system matrices for fast iterative image reconstruction adapted to specific scanner geometries, without redundant calculations. According to the methodology proposed here, only one-eighth of the voxels within two central transaxial slices need to be modelled in detail. The rest of the system matrix elements can be obtained with the aid of axial symmetries and redundancies, as well as in-plane symmetries within transaxial slices. Sparse matrix techniques for the non-zero system matrix elements are employed, allowing for fast execution of the image reconstruction process. This 3D image reconstruction scheme has been compared in terms of image quality to a 2D fast implementation of the OSEM algorithm combined with Fourier rebinning approaches. This work confirms the superiority of fully 3D OSEM in terms of spatial resolution, contrast recovery and noise reduction as compared to conventional 2D approaches based on rebinning schemes. At the same time it demonstrates that fully 3D methodologies can be efficiently applied to the image reconstruction problem for high-resolution rotational PET cameras by applying accurate pre-calculated system models and taking advantage of the system's symmetries.

Hybrid topological derivative and gradient-based methods for electrical impedance tomography

We present a technique to reconstruct the electromagnetic properties of a medium or a set of objects buried inside it from boundary measurements when applying electric currents through a set of electrodes. The electromagnetic parameters may be recovered by means of a gradient method without a priori information on the background. The shape, location and size of objects, when present, are determined by a topological derivative-based iterative procedure. The combination of both strategies allows improved reconstructions of the objects and their properties, assuming a known background.

Adams methods: implementation as predictor-corrector methods

In this paper, Adams explicit and implicit formulas are obtained in a simple way and a relationship between them is established, allowing for their joint implementation as predictor-corrector methods. It is shown the purposefulness, from a didactic point of view, of Excel spreadsheets for calculations and for the orderly presentation of results in the application of Adams methods to solving initial value problems in ordinary differential equations.

Learning and Assessing Competencies: New challenges for Mathematics in Engineering Degrees in Spain.

The introduction of new degrees adapted to the European Area of Higher Education (EAHE) has involved a radically different approach to the curriculum. The new programs are structured around competencies that should be acquired. Considering the competencies, teachers must define and develop learning objectives, design teaching methods and establish appropriate evaluation systems. While most Spanish universities have incorporated methodological innovations and evaluation systems different from traditional exams, there is enough confusion about how to teach and assess competencies and learning outcomes, as traditionally the teaching and assessment have focused on knowledge. In this paper we analyze the state-of-the-art in the mathematical courses of the new engineering degrees in some Spanish universities.

Changing assessment methods: New rules, new roles

Over the past 20 years,theuse of Computer Algebra Systems(CAS) has helped with the teaching of mathematics inengineer-ingschools. However the traditional use of CAS only in math labs has led to a narrow view by the student: the CAS is an additional work, not included in the learning process. The didactic guidelines of the European Higher Education Area(EHEA) propose a new teaching–learning model based on competencies. We suggest the use of the CAS be adapted to the new rules. In this paper,we present a model for the integrated use of the CAS,and we describe and analyze two experiments carried out in the academic year2011–2012. Our analysis suggests that the use of CAS in all learning and assessment activities has the potential to positively influence the development of competencies.

Persuasive system design methods to deliver a cardio-rehabilitation program of post mi outpatients

Las enfermedades no transmisibles provocan cada ano 38 millones de fallecimientos en el mundo. Entre ellas, tan solo cuatro enfermedades son responsables del 82% de estas muertes: las enfermedades cardiovasculares, las enfermedades crónicas respiratorias, la diabetes, y el cáncer. Se prevé que estas cifras aumenten en los próximos anos, ya que las tendencias indican que en el año 2030 las muertes por esta causa ascenderán a 53 millones de personas. La Organización Mundial de la Salud (OMS) considera importante buscar soluciones para afrontar esta situación y ha solicitado a los gobiernos del mundo la implementación de intervenciones para mejorar los hábitos de vida de las personas y reducir así el riesgo de desarrollo de enfermedades no trasmisibles. Cada año se producen 32 millones de infartos de miocardio y derrames celebrales, de los cuales 12.5 son mortales. En el mundo entre el 40% y 75% de la víctimas de un infarto de miocardio mueren antes de su ingreso en el hospital. En los casos que sobreviven, la adopción de un estilo de vida saludable puede evitar infartos sucesivo, y supone un ahorro potencial de 6 billones de euros al año. La rehabilitación cardiaca es un programa individualizado que aplica un método multidisciplinar para ayudar al paciente a recuperar su condición física, a gestionar la enfermedad cardiovascular y sus comorbilidades, a adoptar hábitos de vida saludables, y a promover su salud mental. La rehabilitación cardiaca requiere la total involucración y motivación del paciente, solo de esta manera se podrán promover hábitos saludables y mejorar la gestión y prevención de su enfermedad. Aunque la participación en los programas de rehabilitación cardiaca es baja, hoy en día existen programas de rehabilitación cardiaca que el paciente puede realizar en su casa. Estos suponen una solución prometedora para aumentar la participación. La rehabilitación cardiaca se considera una intervención integral donde los modelos de psicología de la salud son aplicados para promover un cambio en el estilo de vida de las personas así como para ayudarles a afrontar su propia enfermedad. Existen métodos para implementar cambios de hábitos y de aptitud, y también se considera muy relevante promover no solo el bienestar físico sino también el mental. Existen tecnologías que promueven los cambios de comportamientos en los seres humanos. En concreto, las tecnologías persuasivas y los sistemas de apoyo al cambio de comportamientos modelan las características, las estrategias y los métodos de diseño para promover cambios usando la tecnología. Pero estos modelos tienen algunas limitaciones: todavía no se ha definido que rol tienen las emociones en el cambio de comportamientos y como traducir los métodos de la psicología de la salud en la tecnología. Esta tesis se centra en tres elementos que tienen un rol clave en los cambios de hábitos y actitud: el estado físico, el estado mental, y la tecnología. -Estado de salud: un estado de salud critico puede modificar la actitud del ser humano respecto al cambio. A la vez un buen estado de salud hace que la necesidad del cambio sea menos percibida. -Estado emocional: la actitud tiene un componente afectivo. Los estados emocionales negativos pueden reducir la habilidad de una persona para adoptar nuevos comportamientos. La salud mental es la situación ideal donde los individuos tienen predisposición a los cambios. La tecnología puede ayudar a las personas a adoptar nuevos hábitos, así como a mantener una salud física y mental. Este trabajo de investigación se centra en el diseño de tecnologías para la mejora del estado físico y emocional de las personas. Se ha propuesto un marco de diseño llamado “Well.Be.Sign”. El marco se basa en tres aspectos: El marco teórico: representa los elementos que se tienen que definir para diseñar tecnologías para promover el bienestar de las personas. -El diagrama de influencia: presenta las fuerzas de ‘persuasión’ en el contexto de la salud. El rol de las tecnologías persuasivas ha sido contextualizado en una dimensión donde otros elementos influencian el usuario.  El proceso de diseño: describe el proceso de diseño utilizando una metodología iterativa e incremental que aplica una combinación de métodos de diseño existentes (Diseño Orientado a Objetivos, Diseño de Sistemas Persuasivos) así como elementos originales de este trabajo de investigación. Los métodos se han aplicados para diseñar un sistema que ofrezca un programa de tele-rehabilitación cardiaca. Inicialmente se ha diseñado un prototipo de acuerdo con las necesidades del usuario. En segundo lugar, el prototipo se ha extendido especificando la intervención requerida para al programa de rehabilitación cardiaca. Finalmente el sistema se ha desarrollado y validado en un ensayo clínico con grupo control, donde se observaron las variaciones del estado cardiovascular, el nivel de conocimiento acerca de la enfermedad, la percepción de la enfermedad, la persistencia de hábitos saludables, y la aceptabilidad del sistema. Los resultados muestran que el grupo de intervención tiene una superior capacidad cardiovascular, mejor conocimiento acerca de la enfermedad, y más percepción de control de la enfermedad. Asimismo, en algunos casos se ha registrado persistencia de los hábitos de ejercicios 6 meses después del uso del sistema. Otros dos estudios se han presentado para demonstrar la relevancia del estado emocional del usuario en el diseño de aplicaciones para la promoción del bienestar.  En personas con una grave enfermedad crónica como la insuficiencia cardiaca, donde se ha presentado las conexiones entre estado de salud y estado emocional. En el estudio se ensena la relaciones que tienen los síntomas y las emociones negativas y como un estado negativo emocional puede empeorar la condición física del paciente. -Personas con trastornos del humor: el estudio muestra como las emociones pueden tener un impacto en la percepción de la tecnología por parte del usuario. ABSTRACT Noncommunicable diseases (NCDs) cause the death of 38 million people every year. Four major NCDs are responsible for 82% of these deaths: cardio vascular disease, chronic respiratory disease, diabetes and cancer. These pandemic numbers are projected to raise to 53 million deaths in 2030, and for this reason the assembly of the World Health Organization (WHO) considers communicable diseases as an urgent need to be addressed. It is also a trend to advocate the adoption of mobile technology to deliver health services and to promote healthy behaviours among citizens, but adopting healthS promoting lifestyle is still a difficult task facing human tendencies. Within this context, there is a promising opportunity: persuasive technologies. These technologies are intentionally designed to change a person’s attitudes or behaviours; when applied in this context, than can be used to change health-related attitudes, beliefs, and behaviours. Each year there are 32 million heart attacks and strokes globally, of which about 12.5 million are fatal. Worldwide between 40 and 75% of all heart-attack victims die before reaching hospital. Avoiding a second heart attack by improving adherence to lifestyle and medication regimens has a cost saving potential of around €6 billion per year. In most of the cases the cardiovascular event has been provoked by unhealthy lifestyle. Furthermore, after an MI event the patient's decision to adopt or not healthier behaviour will influence the progress of the disease. Cardio-rehabilitation is an individualized program that follows a multidisciplinary approach to support the user to recover from the Myocardial Infarction, manage the Cardio Vascular Disease and the comorbidities, adopt healthy habits, and cope with any emotional distress. Cardio- rehabilitation requires patient participation and willingness to perform behavioral modifications and change the attitude toward the management and prevention of the disease. Participation in the Cardio Rehabilitation program is not high; the home-based rehabilitation program is a promising solution to increase participation. Nowadays cardio rehabilitation is considered a comprehensive intervention in which models of health psychology are applied to promote the behaviour change of the individuals. Relevant methods that have been successfully applied to foster healthy habits include the Health Belief Model and the Trans Theoretical Model. Studies also demonstrate the importance to promote not only the physical but also the mental well being of the individuals. The idea of also promoting behaviour change using technologies has been defined by the literature as persuasive technologies or behaviour change support systems, in which the features, the strategies and the design method have been modelled to foster the behaviour change using technology. Limitations have been found in this model: there is still research to be done on the role of the emotions and how psychological health intervention can be translated into computer methods. This research focuses on three elements that could foster behaviour change in individuals: the physical and emotional status of the person, and the technology. Every component can influence the user's attitude and behaviour in the following ways: ' Physical status: bad physical status could change human attitude toward the necessity to adopt health behaviours; at the same time, good health status reduces the need to adopt healthy habits. ' Emotional status: the attitude has an affective component, negative emotional state can reduce the ability of a person to adopt new behaviours, and mental well being is the ideal situation in which individuals have a predisposition to adopt healthy behaviours. ' Technology: it can help users to adopt new behaviours and can also be support to promote physical and emotional status. Following this approach the idea driven in this research is that technology that is designed to improve the physical status and the emotional status of the individual could better foster behaviour change. According to this principle, the Well.Be.Sign framework has been proposed. The framework is based on three views: ' The theoretical framework: it represents the patterns that have to be defined to design the technologies to promote well being. ' The influence diagram: it shows the persuasive forces in the context of health care. The role of the persuasive technologies is contextualized in a wider universe where other factors and persuasive forces influence a patient. ' The design process: it shows the process of design using an iterative, incremental methodology that applies a combination of existing methodologies (Goal Directed Design and Persuasive System Design) and others that are original to this research. The methods have been applied to design a system to deliver cardio rehabilitation at home: first a prototype has been defined according to the user’s needs, then it has been extended with the specific intervention required for the cardio–rehabilitation, finally the system has been developed and validated in a controlled clinical study in which the cardiovascular fitness, the level of knowledge, the perception of the illness, the persistence of healthy habits and the system acceptance (only the intervention group) were measured. The results show that the intervention group increased cardiovascular capacity, knowledge, feeling of control of illness and perceived benefits of exercise at the end of the study. After six months of the study, a followSup of the exercise habits was performed. Some individuals of the intervention group continued to be engaged in the running exercise sessions promoted in the designed system. Two other cases have been presented to demonstrate the foundations of the Well.Be.Sign’s approach to promote both physical and emotional status: ' People affected by Heart Failure, in which a bidirectional connection between health status and emotions has been discussed with patients. Two correlations were demonstrated: the relationship between symptoms and negative emotional response, and that negative emotional status is correlated with worsening of chronic conditions. ' People with mood disorders: the study shows that emotions could also impact how the user perceives the technology.