¡@¡@It has been for a long time to develop systems of eye control, which are related to a variety of techniques, such as signal/image processing, characteristics of face identifying/tracking, action-mappings, etc. In terms of implementations, the acquisition of data can be done by either special instruments or by general devices. Such systems can be applied to many fields, for instance, military, medicine, entertainments, and other tasks that are fitted. And for the similar system, the performance differs due to the disparity of distinct situations and the way to use it. ¡@¡@In this thesis, we present a system that takes a sequence of images of a user as inputs, and then integrates methods of elliptical model of head, dual states of eyes, deformable templates, and the most yield filter to track the user¡¦s eyes. A coarse-to-fine strategy is used to rapidly locate the region of eyes and to get the information of eyes in order to translate into corresponding operations on machines. The experiment shows that our system is quite robust and fast so that it can help people who are unable to use physical body well.

Simulating blood flow in microvessels is a major challenge because of the numerous blood cells suspended in the blood. Furthermore, red blood cells (RBCs), which constitute 45% of the total blood volume, are highly deformable. RBCs deformation and RBC-RBC interactions determine the complex rheology of the blood. In this research, we simulate the blood flow in periodic two dimensional channels and conduct numerical experiments on the cell-free layer which appears near the wall. We use the boundary integral method and the smooth particle mesh Ewald method to represent the blood flow, and cells are modeled as deformable capsules. In the numerical experiments, we examine four possible mechanisms that may contribute to the cell-free layer: RBC deformation, RBC aggregation, configuration constraint, and the lubrication mechanism. Our simulations correctly represent hemodynamic phenomena such as the blunt velocity profile and the Fåhræus effect. We observed that more deformable RBCs migrate more away from the wall, and, consequently, the thickness of the cell-free layer increases. However, RBC aggregation increased the cell-free layer thickness by only 5%. In the experiment on the configuration constraint, no cell-free "layer" was detected when we removed cells which intersected an artificial constraint in the microvessel. In the last experiment on the lubrication mechanism, the cell-free layer disappeared at a no-shear stress boundary, and the hematocrit profile was similar to that in the constraint test. Therefore, this research clearly shows that the cell-free layer is generated by the lateral migration of deformable RBCs due to the lubrication mechanism. / text

Deformable modeling of facial soft tissues have found use in application domains such as human-machine interaction for facial expression recognition. More recently, such modeling techniques have been used for tasks like age estimation and person identification. This dissertation is focused on development of novel image analysis algorithms to follow facial strain patterns observed through video recording of faces in expressions. Specifically, we use the strain pattern extracted from non-rigid facial motion as a simplified and adequate way to characterize the underlying material properties of facial soft tissues. Such an approach has several unique features. Strain pattern instead of the image intensity is used as a classification feature. Strain is related to biomechanical properties of facial tissues that are distinct for each individual. Strain pattern is less sensitive to illumination differences (between enrolled and query sequences) and face camouflage because the strain pattern of a face remains stable as long as reliable facial deformations are captured. A finite element modeling based method enforces regularization which mitigates issues (such as temporal matching and noise sensitivity) related to automatic motion estimation. Therefore, the computational strategy is accurate and robust. Images or videos of facial deformations are acquired with video camera and without special imaging equipment. Experiments using range images on a dataset consisting of 50 subjects provide the necessary proof of concept that strain maps indeed have a discriminative value. On a video dataset containing 60 subjects undergoing a particular facial expression, experimental results using the computational strategy presented in this work emphasize the discriminatory and stability properties of strain maps across adverse data conditions (shadow lighting and face camouflage). Such properties make it a promising feature for image analysis tasks that can benefit from such auxiliary information about the human face. Strain maps add a new dimension in our abilities to characterize a human face. It also fosters newer ways to capture facial dynamics from video which, if exploited efficiently, can lead to an improved performance in tasks involving the human face. In a subsequent effort, we model the material constants (Young's modulus) of the skin in sub-regions of the face from the motion observed in multiple facial expressions. On a public database consisting of 40 subjects undergoing some set of facial motions, we present an expression invariant strategy to matching faces using the Young's modulus of the skin. Such an efficient way of describing underlying material properties from the displacements observed in video has an important application in deformable modeling of physical objects which are usually gauged by their simplicity and adequacy. The contributions through this work will have an impact on the broader vision community because of its highly novel approaches to the long-standing problem of motion analysis of elastic objects. In addition, the value is the cross disciplinary nature and its focus on applying image analysis algorithms to the rather difficult and important problem of material property characterization of facial soft tissues and their applications. We believe this research provides a special opportunity for the utilization of video processing to enhance our abilities to make unique discoveries through the facial dynamics inherent in video.

We first describe the methodology for a two-dimensional, elastic deformable microplate modeling approach for continental plate boundaries. Deformable microplate models combine discrete slip on microplate boundaries (faults) with continuous deformation in block interiors. Two idealized models simulating continental collision are presented, one with two microplates and one with four microplates. / Earth and Planetary Sciences

Methods of component mode synthesis, such as Craig and Bampton reduction, are known to generally yield more accurate results in deformable multibody dynamics. The main shortcoming of those methods is that they are intuitively based. Recently Nikravesh developed a reduction method called mode condensation which is derived from the equations of motion and yields the same results as Craig and Bampton reduction. In this dissertation, it is proven that these two methods span the same column space; therefore, they should yield identical results. We propose that mode condensation provides an analytical justification for Craig and Bampton reduction. Test results suggest that Craig and Bampton reduction and mode condensation are appropriate for a broader range of applications because their column space matches up well with the conditions under which the deformable body is restrained. Although Guyan reduction preserves exact solutions for static problems, its applications shall be limited to low frequency excitation because of raised eigen-frequencies. Modal truncation is not recommended for use in multibody dynamic settings because it lacks the ability to receive forces and displacements at the moving boundary. Another issue addressed in this dissertation is the misconception that if mean axes are adopted as the moving reference frame, only free-free modes should be used for model reduction. It was not clear how a restrained deformable body with mean axes can be condensed properly. We have shown that the conventional (nodal-fixed) mode shapes can be used with mean axes as long as the transformation matrix has full rank and contains complete rigid-body mode shapes.

Non-rigid shapes are generally known as objects whose three dimensional geometry may deform by internal and/or external forces. Deformable shapes are all around us, ranging from protein molecules, to natural objects such as the trees in the forest or the fruits in our gardens, and even human bodies. Two deformable shapes may be related by isometry, which means their intrinsic geometries are preserved, even though their extrinsic geometries are dissimilar. An important problem in the analysis of the deformable shapes is to identify the three-dimensional correspondence between two isometric shapes, given that the two shapes may be deviated from isometry by intrinsic distortions. A major challenge is that non-rigid shapes have large degrees of freedom on how to deform. Nevertheless, irrespective of how they are deformed, they may be aligned such that the geodesic distance between two arbitrary points on two shapes are nearly equal. Such alignment may be expressed by a permutation matrix (a matrix with binary entries) that corresponds to every paired geodesic distance in between the two shapes. The alignment involves searching the space over all possible mappings (that is all the permutations) to locate the one that minimizes the amount of deviation from isometry. A brute-force search to locate the correspondence is not computationally feasible. This thesis introduces a novel approach created to locate such correspondences, in spite of the large solution space that encompasses all possible mappings and the presence of intrinsic distortion. In order to find correspondences between two shapes, the first step is to create a suitable descriptor to accurately describe the deformable shapes. To this end, we developed deformation-invariant metric descriptors. A descriptor constitutes pair-wise geodesic distances among arbitrary number of discrete points that represent the topology of the non-rigid shape. Our descriptor provides isometric-invariant representation of the shape irrespective of its circumstantial deformation. Two isometric-invariant descriptors, representing two candidate deformable shapes, are the input parameters to our optimization algorithm. We then proceed to locate the permutation matrix that aligns the two descriptors, that minimizes the deviation from isometry. Once we have developed such a descriptor, we turn our attention to finding correspondences between non deformable shapes. In this study, we investigate the use of both classical and quantum particle swarm optimization (PSO) algorithms for this task. To explore the merits of variants of PSO, integer optimization involving test functions with large dimensions were performed, and the results and the analysis suggest that quantum PSO is more effective optimization method than its classical PSO counterpart. Further, a scheme is proposed to structure the solution space, composed of permutation matrices, in lexicographic ordering. The search in the solution space is accordingly simplified to integer optimization to find the integer rank of the targeted permutation matrix. Empirical results suggest that this scheme improves the scalability of quantum PSO across large solution spaces. Yet, quantum PSO's global search capability requires assistance in order to more effectively manoeuvre through the local extrema prevalent in the large solution spaces. A mutation based genetic algorithm (GA) is employed to augment the search diversity of quantum PSO when/if the swarm stagnates among the local extrema. The mutation based GA instantly disengages the optimization engine from the local extrema in order to reorient the optimization energy to the trajectories that steer to the global extrema, or the targeted permutation matrix. Our resultant optimization algorithm combines quantum Particle Swarm Optimization (PSO) and mutation based Genetic Algorithm (GA). Empirical results show that the optimization method presented is scalable and efficient on standard hardware across different solution space sizes. The performance of the optimization method, in simulations and on various near-isometric shapes, is discussed. In all cases investigated, the method could successfully identify the correspondence among the non-rigid deformable shapes that were related by isometry.

Three problems are being investigated in this thesis. The first two relate to the modelling and analysis of martensitic phase transitions, while the third is concerned with some mathematical tools used in this setting. After a short introduction (Chapter 1) and overviews of the calculus of variations and martensitic phase transformations (Chapter 2), the research part of this thesis is divided into three chapters. We show in Chapter 3 that for the two wells $\mathrm{SO}(3)U$ and $\mathrm{SO}(3)V$ to be rank-one connected, where the $3\times 3$ symmetric positive definite $U$ and $V$ have the same eigenvalues, it is necessary and sufficient that $\mathrm{det}(U-V)=0$, a result that does not hold in higher dimensions. Using this criterion and a result of Gurtin, formulae for the twinning plane and the shearing vector are obtained, which yield an extremely simple condition for the occurrence of so-called compound twins. Our results also provide a simple classification of the twinning mode of the two wells by looking at the crystallographic properties of the eigenvectors of the difference $U-V$. As an illustration, we apply our results to cubic-to-tetra gonal,tetragonal-to-monoclinic and cubic-to-monoclinic transitions. Chapter 4 focuses on the mathematical analysis of biaxial loading experiments in martensite, more particularly on how hysteresis relates to metastability. These experiments were carried out by Chu and James and their mathematical treatment was initiated by Ball, Chu and James. Experimentally it is observed that a homogeneous deformation $y_1(x)= U_1x$ is the stable state for `small' loads while $y_2(x)=U_2x$ is stable for `large' loads. A model was proposed by Ball, Chu and James which, for a certain intermediate range of loads, predicts crucially that $y_1(x)=U_1x$ remains metastable i.e., a local - as opposed to global - minimiser of the energy). This result explains convincingly the hysteresis that is observed experimentally. It is easy to get an upper bound for when metastability finishes. However, it was also noticed that this bound (the Schmid Law) may not be sharp, though this required some geometric conditions on the sample. In this chapter, we rigorously justify the Ball-Chu-James model by means of De Giorgi's $\Gamma$-convergence, establish some properties of local minimisers of the (limiting) energy and prove the metastability result mentioned above. An important part of the chapter is then devoted to establishing which geometric conditions are necessary and sufficient for the counter-example to the Schmid Law to apply. Finally, Chapter 5 investigates the structure of the solutions to the two-well problem. Restricting ourselves to the subset $K=\{H\}\cup \mathrm{SO}(2)V \subset\mathrm{SO}(2)U\cup\mathrm{SO}(2)V$ and assuming the two wells to be compatible, we let $T_1$ and $T_2$ denote the two (not necessarily distinct) twins of $H$ on $\mathrm{SO}(2)V$ and ask the following question: if $\nu_x$ is a non-trivial gradient Young measure almost everywhere supported on $K$, does its support necessarily contain a pair of rank-one connected matrices on a set of positive measure? Although we do not provide a solution for the general case, we show that this is true whenever (a) $\nu_x\equiv \nu$ is homogeneous and $\mathrm{supp}\nu\cap \mathrm{SO}(2)V$ is connected, (b) $\nu_x\equiv \nu$ is homogeneous and $T_1=T_2$ i.e., when the two wells are trivially rank-one connected) or (c) $\mathrm{supp}\nu_x \subset F$ a.e., for some finite set $F$. We also establish a more general case provided a strong `rigidity' conjecture holds.

Carding is an essential pre-spinning process whereby masses of dirty tufted fibres are cleaned, disentangled and refined into a smooth coherent web. Research and development in this `low-technology' industry have hitherto depended on empirical evidence. In collaboration with the School of Textile Industries at the University of Leeds, a mathematical theory has been developed that describes the passage of fibres through the carding machine. The fibre dynamics in the carding machine are posed, modelled and simulated by three distinct physical problems: the journey of a single fibre, the extraction of fibres from a tuft or tufts and many interconnecting, entangled fibres. A description of the life of a single fibre is given as it is transported through the carding machine. Many fibres are sparsely distributed across machine surfaces, therefore interactions with other neighbouring fibres, either hydrodynamically or by frictional contact points, can be neglected. The aerodynamic forces overwhelm the fibre's ability to retain its crimp or natural curvature, and so the fibre is treated as an inextensible string. Two machine topologies are studied in detail, thin annular regions with hooked surfaces and the nip region between two rotating drums. The theoretical simulations suggest that fibres do not transfer between carding surfaces in annular machine geometries. In contrast to current carding theories, which are speculative, a novel explanation is developed for fibre transfer between the rotating drums. The mathematical simulations describe two distinct mechanisms: strong transferral forces between the taker-in and cylinder and a weaker mechanism between cylinder and doffer. Most fibres enter the carding machine connected to and entangled with other fibres. Fibres are teased from their neighbours and in the case where their neighbours form a tuft, which is a cohesive and resistive fibre structure, a model has been developed to understand how a tuft is opened and broken down during the carding process. Hook-fibre-tuft competitions are modelled in detail: a single fibre extracted from a tuft by a hook and diverging hook-entrained tufts with many interconnecting fibres. Consequently, for each scenario once fibres have been completely or partially extracted, estimates can be made as to the degree to which a tuft has been opened-up. Finally, a continuum approach is used to simulate many interconnected, entangled fibre-tuft populations, focusing in particular on their deformations. A novel approach describes this medium by density, velocity, directionality, alignment and entanglement. The materials responds to stress as an isotropic or transversely isotropic medium dependent on the degree of alignment. Additionally, the material's response to stress is a function of the degree of entanglement which we describe by using braid theory. Analytical solutions are found for elongational and shearing flows, and these compare very well with experiments for certain parameter regimes.

Over the past 30 years the study of free boundary problems has stimulated much work. However, there exists a widely occurring, but little studied subclass of free boundary problems in which the free boundary has dimension two fewer than that of the underlying space rather than the more commonly studied case of one less. These problems are called `codimension-two' free boundary problems. In Chapter 1 the typical geometries required for such problems, the main mathematical techniques and the methodology used are discussed. Then, in Chapter 2, the techniques required to solve them are demonstrated using the particular example of the water entry problem. Further results for the water entry problem are then derived including an analysis of the relatively poorly understood water exit problem. In Chapter 3 a review is given of some classical contact and crack problems in solid mechanics. The inclusion of a cohesive zone in a dynamic type-III crack problem is considered. The Muskhelishvili potential method is presented and used to solve both a contact and crack problem. This enables the solution of a type-I crack problem relating to an ink delivery system to be found. In Chapter 4 a problem posed by car windscreen forming is addressed. A local solution near a corner is analysed to explain when and how point forces occur at the corners of the frame on which the simply supported windscreen rests. Then the full problem is solved numerically for different types of boundary condition. Chapters 5 and 6 deal with several sintering problems in viscous flow highlighting the value of the methodology introduced in Chapter 1. It will be shown how the Muskhelishvili potential method also carries over to Stokes flow problems. The difficulties of matching to an inner as opposed to an outer region are investigated. Last two interface problems between immiscible liquids are considered which show how the solution procedure is adapted when the field equation in the thin region is non-trivial. In the final chapter results are summarised, open problems listed and conclusions drawn.

In brachytherapy, radiation therapy is performed by placing the radiation source into or very close to the tumour. When calculating the absorbed dose, water is often used as the radiation transport and dose scoring medium for soft tissues and this leads to inaccuracies. The iterative reconstruction algorithm DIRA is under development at the Center for Medical Imaging Science and Visualization, Linköping University. DIRA uses dual-energy CT to decompose tissues into different doublets and triplets of base components for a better absorbed dose estimation. To accurately determine mass fractions of these base components for different tissues, the tissues needs to be identified in the image. The aims of this master thesis are: (i) Find an automated segmentation algorithm in CT that best segments the male pelvis. (ii) Implement a segmentation algorithm that can be used in DIRA. (iii) Implement a fully automatic segmentation algorithm. Seven segmentation methods were tested in Matlab using images obtained from Linköping University Hospital. The methods were: active contours, atlas based registration, graph cuts, level set, region growing, thresholding and watershed. Four segmentation algorithms were selected for further analysis: phase based atlas registration, region growing, thresholding and active contours without edges. The four algorithms were combined and supplemented with other image analysis methods to form a fully automated segmentation algorithm that was implemented in DIRA. The newly developed algorithm (named MK2014) was sufficiently stable for pelvic image segmentation with a mean computational time of 45.3 s and a mean Dice similarity coefficient of 0.925 per 512×512 image. The performance of MK2014 tested on a simplified anthropomorphic phantom in DIRA gave promising result. Additional tests with more realistic phantoms are needed to confirm the general applicability of MK2014 in DIRA.