O crescente número de sistemas de animação que utilizam a cinemática para gerar movimento de objetos vem levando os pesquisadores a buscar outras alternativas para produzir resultados mais realistas. Com base nesta premissa, vários autores começaram a estudar a geração de movimento de objetos sintéticos através da aplicação da dinâmica. Assim surgiram os modelos baseados em leis físicas. Num primeiro momento foram abordados apenas objetos rígidos, passando-se mais tarde a considerar objetos articulados e, por fim, aqueles com características elásticas, também denominados de objetos flexíveis ou deformáveis. O objetivo principal do trabalho é a definição de um modelo para simulação de objetos deformáveis no espaço euclidiano. São abordados tanto o modelo geométrico utilizado como o modelo físico, sendo ressaltadas as forças aplicadas sobre o objeto e as restrições que podem ser impostas pelo mundo virtual no qual o mesmo está inserido. Dentre as forças descritas, pode-se destacar: força gravitacional, elasticidade, força de curvatura e torção, colisão e atrito. A fundamentação do trabalho desenvolvido é apresentada na forma de uma introdução aos sistemas de animação, enfatizando os sistemas baseados em leis físicas e de uma revisão bibliográfica dos métodos de deformação existentes. No que diz respeito à colisão de objetos elásticos, são descritos tanto os métodos estudados para a solução das mesmas, como as técnicas para detecção do choque. A simulação do movimento é descrita sob dois aspectos: o algoritmo utilizado para a geração do movimento e a integração numérica das equações diferenciais no tempo. É abordado ainda, em detalhe, o protótipo desenvolvido com o propósito de validar o modelo proposto, sendo descrita a linguagem criada a fim de permitir a especificação da animação e parâmetros diversos do modelo. Por fim, são apresentados e avaliados os resultados obtidos através do desenvolvimento do modelo proposto por intermédio do protótipo FLEX3D. É dedicada ainda especial atenção às perspectivas futuras deste trabalho. / The growing number of animation systems that use kinematics to generate the motion of objects have led to other alternatives to produce more realistic results. Some authors began to study the animation of synthetic objects through the application of the dynamic concepts, creating the modern physically based models. At first, only rigid objects were treated; later on articulated objects were considered. At last, those with elastic characteristics (called flexible or deformable objects) were taken into consideration. The main goal of this work is to define a simulation model for deformable objects in the euclidean space. Both the geometric and the physical models are presented, considering the forces applied to the object and the constraints defined by the virtual world. Described forces include gravity, elasticity, dumping force, collision and attrition. This work presents an introduction to animation systems focusing the physically based systems. After this, a bibliographic review of the existent deformation methods is made. Methods for detecting and solving the collision between two elastic objects are described. Two aspects of the motion simulation are described: the algorithm used to generate the motion and the numeric integration of the differential equations in time. A prototype named FLEX3D is presented to validate the proposed model. The language used for specifying the animation is described and results obtained through the use of FLEX3D are also presented. Special attention is given to the possible future works.

abstract: Human fingertips contain thousands of specialized mechanoreceptors that enable effortless physical interactions with the environment. Haptic perception capabilities enable grasp and manipulation in the absence of visual feedback, as when reaching into one's pocket or wrapping a belt around oneself. Unfortunately, state-of-the-art artificial tactile sensors and processing algorithms are no match for their biological counterparts. Tactile sensors must not only meet stringent practical specifications for everyday use, but their signals must be processed and interpreted within hundreds of milliseconds. Control of artificial manipulators, ranging from prosthetic hands to bomb defusal robots, requires a constant reliance on visual feedback that is not entirely practical. To address this, we conducted three studies aimed at advancing artificial haptic intelligence. First, we developed a novel, robust, microfluidic tactile sensor skin capable of measuring normal forces on flat or curved surfaces, such as a fingertip. The sensor consists of microchannels in an elastomer filled with a liquid metal alloy. The fluid serves as both electrical interconnects and tunable capacitive sensing units, and enables functionality despite substantial deformation. The second study investigated the use of a commercially-available, multimodal tactile sensor (BioTac sensor, SynTouch) to characterize edge orientation with respect to a body fixed reference frame, such as a fingertip. Trained on data from a robot testbed, a support vector regression model was developed to relate haptic exploration actions to perception of edge orientation. The model performed comparably to humans for estimating edge orientation. Finally, the robot testbed was used to perceive small, finger-sized geometric features. The efficiency and accuracy of different haptic exploratory procedures and supervised learning models were assessed for estimating feature properties such as type (bump, pit), order of curvature (flat, conical, spherical), and size. This study highlights the importance of tactile sensing in situations where other modalities fail, such as when the finger itself blocks line of sight. Insights from this work could be used to advance tactile sensor technology and haptic intelligence for artificial manipulators that improve quality of life, such as prosthetic hands and wheelchair-mounted robotic hands. / Dissertation/Thesis / Ph.D. Mechanical Engineering 2013

Dans cette thèse sont présentées deux méthodes visant à obtenir automatiquement une description tridimensionnelle des mouvements d'une main étant donnée une séquence vidéo monoculaire de cette main. En utilisant l'information fournie par la vidéo, l'objectif est de déterminer l'ensemble des paramètres cinématiques nécessaires à la description de la configuration spatiale des différentes parties de la main. Cet ensemble de paramètres est composé des angles de chaque articulation ainsi que de la position et de l'orientation globale du poignet. Ce problème est un problème difficile. La main a de nombreux degrés de liberté et les auto-occultations sont omniprésentes, ce qui rend difficile l'estimation de la configuration des parties partiellement ou totalement cachées. Dans cette thèse sont proposées deux nouvelles méthodes qui améliorent par certains aspects l'état de l'art pour ce problème. Ces deux méthodes sont basées sur un modèle de la main dont la configuration spatiale est ajustée pour que sa projection dans l'image corresponde au mieux à l'image de main observée. Ce processus est guidé par une fonction de coût qui définit une mesure quantitative de la qualité de l'alignement de la projection du modèle avec l'image observée. La procédure d'ajustement du modèle est réalisée grâce à un raffinement itératif de type descente de gradient quasi-newton qui vise à minimiser cette fonction de coût.Les deux méthodes proposées diffèrent principalement par le choix du modèle et de la fonction du coût. La première méthode repose sur un modèle de la main composé d'ellipsoïdes et d'une fonction coût utilisant un modèle de la distribution statistique de la couleur la main et du fond de l'image.La seconde méthode repose sur un modèle triangulé de la surface de la main qui est texturé est ombragé. La fonction de coût mesure directement, pixel par pixel, la différence entre l'image observée et l'image synthétique obtenue par projection du modèle de la main dans l'image. Lors du calcul du gradient de la fonction de coût, une attention particulière a été portée aux termes dûs aux changements de visibilité de la surface au voisinage des auto-occultations, termes qui ont été négligés dans les méthodes préexistantes.Ces deux méthodes ne fonctionnement malheureusement pas en temps réel, ce qui rend leur utilisation pour l'instant impossible dans un contexte d'interaction homme-machine. L'amélioration de la performance des ordinateur combinée avec une amélioration de ces méthodes pourrait éventuellement permettre d'obtenir un résultat en temps réel. / In this thesis we propose two methods that allow to recover automatically a full description of the 3d motion of a hand given a monocular video sequence of this hand. Using the information provided by the video, our aimto is to determine the full set of kinematic parameters that are required to describe the pose of the skeleton of the hand. This set of parameters is composed of the angles associate to each joint/articulation and the global position and orientation of the wrist. This problem is extremely challenging. The hand as many degrees of freedom and auto-occlusion are ubiquitous, which makes difficult the estimation of occluded or partially ocluded hand parts.In this thesis, we introduce two novel methods of increasing complexity that improve to certain extend the state-of-the-art for monocular hand tracking problem. Both are model-based methods and are based on a hand model that is fitted to the image. This process is guided by an objective function that defines some image-based measure of the hand projection given the model parameters. The fitting process is achieved through an iterative refinement technique that is based on gradient-descent and aims a minimizing the objective function. The two methos differ mainly by the choice of the hand model and of the cost function.The first method relies on a hand model made of ellipsoids and a simple discrepancy measure based on global color distributions of the hand and the background. The second method uses a triangulated surface model with texture and shading and exploits a robust distance between the synthetic and observed image as discrepancy measure.While computing the gradient of the discrepancy measure, a particular attention is given to terms related to the changes of visibility of the surface near self occlusion boundaries that are neglected in existing formulations. Our hand tracking method is not real-time, which makes interactive applications not yet possible. Increase of computation power of computers and improvement of our method might make real-time attainable.

Alors que la perspective de la fusion d’images médicales capturées par des systèmes d’imageries de type différent est largement contemplée, la mise en pratique est toujours victime d’un obstacle théorique : la définition d’une mesure de similarité entre les images. Des efforts dans le domaine ont rencontrés un certain succès pour certains types d’images, cependant la définition d’un critère de similarité entre les images quelle que soit leur origine et un des plus gros défis en recalage d’images déformables. Dans cette thèse, nous avons décidé de développer une approche générique pour la comparaison de deux types de modalités donnés. Les récentes avancées en apprentissage statistique (Machine Learning) nous ont permis de développer des solutions innovantes pour la résolution de ce problème complexe. Pour appréhender le problème de la comparaison de données incommensurables, nous avons choisi de le regarder comme un problème de plongement de données : chacun des jeux de données est plongé dans un espace commun dans lequel les comparaisons sont possibles. A ces fins, nous avons exploré la projection d’un espace de données image sur l’espace de données lié à la seconde image et aussi la projection des deux espaces de données dans un troisième espace commun dans lequel les calculs sont conduits. Ceci a été entrepris grâce à l’étude des correspondances entre les images dans une base de données images pré-alignées. Dans la poursuite de ces buts, de nouvelles méthodes ont été développées que ce soit pour la régression d’images ou pour l’apprentissage de métrique multimodale. Les similarités apprises résultantes sont alors incorporées dans une méthode plus globale de recalage basée sur l’optimisation discrète qui diminue le besoin d’un critère différentiable pour la recherche de solution. Enfin nous explorons une méthode qui permet d’éviter le besoin d’une base de données pré-alignées en demandant seulement des données annotées (segmentations) par un spécialiste. De nombreuses expériences sont conduites sur deux bases de données complexes (Images d’IRM pré-alignées et Images TEP/Scanner) dans le but de justifier les directions prises par nos approches. / Even though the prospect of fusing images issued by different medical imagery systems is highly contemplated, the practical instantiation of it is subject to a theoretical hurdle: the definition of a similarity between images. Efforts in this field have proved successful for select pairs of images; however defining a suitable similarity between images regardless of their origin is one of the biggest challenges in deformable registration. In this thesis, we chose to develop generic approaches that allow the comparison of any two given modality. The recent advances in Machine Learning permitted us to provide innovative solutions to this very challenging problem. To tackle the problem of comparing incommensurable data we chose to view it as a data embedding problem where one embeds all the data in a common space in which comparison is possible. To this end, we explored the projection of one image space onto the image space of the other as well as the projection of both image spaces onto a common image space in which the comparison calculations are conducted. This was done by the study of the correspondences between image features in a pre-aligned dataset. In the pursuit of these goals, new methods for image regression as well as multi-modal metric learning methods were developed. The resulting learned similarities are then incorporated into a discrete optimization framework that mitigates the need for a differentiable criterion. Lastly we investigate on a new method that discards the constraint of a database of images that are pre-aligned, only requiring data annotated (segmented) by a physician. Experiments are conducted on two challenging medical images data-sets (Pre-Aligned MRI images and PET/CT images) to justify the benefits of our approach.

O crescente número de sistemas de animação que utilizam a cinemática para gerar movimento de objetos vem levando os pesquisadores a buscar outras alternativas para produzir resultados mais realistas. Com base nesta premissa, vários autores começaram a estudar a geração de movimento de objetos sintéticos através da aplicação da dinâmica. Assim surgiram os modelos baseados em leis físicas. Num primeiro momento foram abordados apenas objetos rígidos, passando-se mais tarde a considerar objetos articulados e, por fim, aqueles com características elásticas, também denominados de objetos flexíveis ou deformáveis. O objetivo principal do trabalho é a definição de um modelo para simulação de objetos deformáveis no espaço euclidiano. São abordados tanto o modelo geométrico utilizado como o modelo físico, sendo ressaltadas as forças aplicadas sobre o objeto e as restrições que podem ser impostas pelo mundo virtual no qual o mesmo está inserido. Dentre as forças descritas, pode-se destacar: força gravitacional, elasticidade, força de curvatura e torção, colisão e atrito. A fundamentação do trabalho desenvolvido é apresentada na forma de uma introdução aos sistemas de animação, enfatizando os sistemas baseados em leis físicas e de uma revisão bibliográfica dos métodos de deformação existentes. No que diz respeito à colisão de objetos elásticos, são descritos tanto os métodos estudados para a solução das mesmas, como as técnicas para detecção do choque. A simulação do movimento é descrita sob dois aspectos: o algoritmo utilizado para a geração do movimento e a integração numérica das equações diferenciais no tempo. É abordado ainda, em detalhe, o protótipo desenvolvido com o propósito de validar o modelo proposto, sendo descrita a linguagem criada a fim de permitir a especificação da animação e parâmetros diversos do modelo. Por fim, são apresentados e avaliados os resultados obtidos através do desenvolvimento do modelo proposto por intermédio do protótipo FLEX3D. É dedicada ainda especial atenção às perspectivas futuras deste trabalho. / The growing number of animation systems that use kinematics to generate the motion of objects have led to other alternatives to produce more realistic results. Some authors began to study the animation of synthetic objects through the application of the dynamic concepts, creating the modern physically based models. At first, only rigid objects were treated; later on articulated objects were considered. At last, those with elastic characteristics (called flexible or deformable objects) were taken into consideration. The main goal of this work is to define a simulation model for deformable objects in the euclidean space. Both the geometric and the physical models are presented, considering the forces applied to the object and the constraints defined by the virtual world. Described forces include gravity, elasticity, dumping force, collision and attrition. This work presents an introduction to animation systems focusing the physically based systems. After this, a bibliographic review of the existent deformation methods is made. Methods for detecting and solving the collision between two elastic objects are described. Two aspects of the motion simulation are described: the algorithm used to generate the motion and the numeric integration of the differential equations in time. A prototype named FLEX3D is presented to validate the proposed model. The language used for specifying the animation is described and results obtained through the use of FLEX3D are also presented. Special attention is given to the possible future works.

Simulação computacional de ambientes cirúrgicos têm sido amplamente utilizados, normalmente para treinamentos, ajudando no desenvolvimento de habilidades essenciais e minimizando erros em procedimentos cirúrgicos. Para estes ambientes, é essencial a obtenção de um comportamento mais realista, sendo importante o uso de técnicas com alta precisão, além de uma simulação em tempo real. A fim de melhor controlar este trade-off entre eficiência e eficácia, apresentamos um ambiente híbrido e adaptativo que combina um conjunto de métodos para alcançar uma boa precisão e desempenho na simulação. Nosso sistema mescla métodos físicos de deformação (Método de Elementos Finitos e Mass-Mola) com um método não-físico que aproxima o comportamento dos primeiros (Green Coordinates), sendo capaz de utilizar o método apropriado dependendo da situação. Para melhor simular um ambiente cirúrgico completo, foram implementadas ferramentas adicionais para interação, permitindo pegar e manipular, queimar, e sentir os objetos do cenário. Nosso sistema proporciona grande imersão ao usuário, consumindo menos recursos computacionais e aumentando as taxas de atualização da simulação. / Computational simulation of surgical environments have been widely used usually for trainings, improving essential skills and minimizing errors in surgical procedures. As these environments are always looking for a more realistic behavior, it is important to use high-precision techniques while ensuring a real-time simulation. In order to better manage this trade-off between efficiency and effectiveness, we present a hybrid and adaptive environment that combines a set of methods to achieve good accuracy and performance for a simulation. Our system merges physically deformation methods (Finite Elements Method and Mass Spring Damper) with a non-physical method that approximates the formers behavior (Green Coordinates), being able to use the appropriate method depending on the situation. To simulate an approximation of a complete surgical environment, we also implement interaction tools, such as picking, burning, and haptic feedback. Our system provides great immersion for the user, consuming less computational resources and increasing update rates.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2016-09-27T15:30:53Z No. of bitstreams: 2 Dissertação - Halanna Cristina Barbosa Silva - 2016.pdf: 1692105 bytes, checksum: 1a6dba862cc9e4e590269d62f3d72bca (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-09-27T15:31:19Z (GMT) No. of bitstreams: 2 Dissertação - Halanna Cristina Barbosa Silva - 2016.pdf: 1692105 bytes, checksum: 1a6dba862cc9e4e590269d62f3d72bca (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-09-27T15:31:19Z (GMT). No. of bitstreams: 2 Dissertação - Halanna Cristina Barbosa Silva - 2016.pdf: 1692105 bytes, checksum: 1a6dba862cc9e4e590269d62f3d72bca (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-03-29 / Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG / Bexarotene is an agonist to retinoid X receptors (RXR) clinically used in cutaneous T cell lymphoma (CTCL). The oral bexaroteno therapy results in disagreeable side effects related to lipid metabolism, such that topical administration presents as an alternative to bexaroteno use increasing the drug concentration at the target site. Nanostructured systems, such as the deformable liposomes can be an interesting alternative to facilitate or promote increased cutaneous permeation of bexarotene. So, the aim of this study was the development and characterization of deformable bexarotene liposomes. Three surfactants were evaluated for composition of deformable liposomes (Span 80, Tween 80 and Span 85) in different concentrations (5, 10 and 15%). Liposomes were evaluated for average diameter, PdI and elasticity. And then a full factorial design with 3² triplicate central point was applied to analyze the influence of variables ethanol concentration and surfactant in the elasticity of the vesicles. A global solution was proposed by analyzing the Statistica 7.0 software applying the desirability tool and the deformable liposomes encapsulating bexarotene were prepared from the obtained response. Deformable liposomes were prepared by lipid film hydration and extrusion polycarbonate membrane (200 and 100 nm). The desirability function provided a global solution with 5.25% (v / v) ethanol and 5% (w / v) Span 80. Deformable liposomes had encapsulation efficiency of 99.67±3.4%, diameter average of 93.69±1.95 nm and PDI 0.092±0.02. Lyophilized liposomes showed higher elasticity parameters than non-lyophilized formulations, with elasticity up to 215.5±5.5 (mg.s-1.cm-2) for formulations with sucrose and 22.13±1.04 (mg. s-1.cm-2) for conventional liposomes. EPR studies demonstrated that lyophilized formulations presented higher molecular dynamics of lipids regarding the non lyophilized in all formulations, while the formulations without BXT was most dynamic in formulations in which sucrose was used as cryoprotectant, in formulations with BXT occurs the oposite. In vitro skin permeation studies, BXT deformable liposomes had a penetration rate EC about 5 times greater than the conventional liposomes. Thus, the developed deformable liposomes present as bexarotene the potential permeation enhancer on the skin. / O bexaroteno é um agonista dos receptores retinoides X (RXR) clinicamente utilizado no tratamento de linfoma cutâneo de células T (LCCT). A terapia oral do bexaroteno resulta em efeitos colaterais desagradáveis relacionados ao metabolismo de lipídios, de forma que a via tópica se apresenta como alternativa para administração do bexaroteno, aumentando a concentração de fármaco no sítio alvo. O uso de sistemas nanoestruturados, como por exemplo, os lipossomas deformáveis, pode ser uma alternativa interessante para facilitar ou promover maior permeação cutânea do bexaroteno. Assim, o objetivo deste trabalho foi o desenvolvimento e caracterização de lipossomas deformáveis de bexaroteno. Para selecionar os componentes da formulação foram avaliados três tensoativos (Span 80, Tween 80 e Span 85) em três concentrações diferentes (5, 10 e 15%). Os lipossomas foram avaliados quanto ao diâmetro médio, PdI e elasticidade. A seguir um planejamento fatorial completo 3² com triplicata do ponto central foi aplicado para analisar a influência das variáveis de concentração do etanol e do tensoativo na elasticidade das vesículas. Uma solução global foi proposta mediante análise pelo software Statistica 7.0 aplicando-se a ferramenta desejabilidade e, os lipossomas deformáveis encapsulando bexaroteno foram preparados a partir da resposta obtida. Lipossomas deformáveis foram preparados por hidratação do filme lipídico e extrusão em membrana de policarbonato (200 e 100 nm). A função desejabilidade ofereceu uma solução global com 5,25% (v/v) de etanol e 5% (p/v) de Span 80. Os lipossomas deformáveis obtidos apresentaram eficiência de encapsulação de 99,67±3,4 %, diâmetro médio de 93,69±1,95 nm e PdI 0,092±0,02. Os lipossomas liofilizados indicaram parâmetros de elasticidade superiores as formulações não liofilizadas, com elasticidade de até 215,5±5,5 (mg.s-1.cm-2) para formulações com sacarose e 22,13±1,04 (mg.s-1.cm-2) para lipossomas convencionais. Os estudos de RPE demonstraram que as formulações liofilizadas apresentaram maior dinâmica molecular dos lipídios em relação as não liofilizadas em todas as formulações, enquanto nas formulações sem BXT houve maior dinâmica nas formulações em que a sacarose foi utilizada como crioprotetor, nas formulações com BXT ocorre o contrário. Nos estudos de permeação cutânea in vitro, os lipossomas deformáveis de BXT tiveram uma taxa de penetração no EC cerca de 5 vezes superior aos lipossomas convencionais. Dessa forma, os lipossomas deformáveis desenvolvidos se apresentam como potencial promotor de permeação do bexaroteno na pele.

The Particle Level set method is a successful extension to Level set methods to improve thevolume preservation in fluid simulations. This thesis will analyze how sparse volume data structures can be used to store both the signed distance function and the particles in order to improve access speed and memory efficiency. This Particle Level set implementation will be evaluated against Digital Domains current Particle Level set implementation. Different degrees of quantization will be used to implement particle representations with varying accuracy. These particles will be tested and both visual results and error measurments will be presented. The sparse volume data structures DB-Grid and Field3D will be evaluated in terms of speed and memory efficiency.

A common co-pathology of large lung tumors located near the central airways is collapse of portions of lung due to blockage of airflow by the tumor. Not only does the lung volume decrease as collapse occurs, but fluid from capillaries also fills the space no longer occupied by air, greatly altering tissue appearance. During radiotherapy, typically administered to the patient over multiple weeks, the tumor can dramatically shrink in response to the treatment, restoring airflow to the lung sections which were collapsed when therapy began. While return of normal lung function is a positive development, the change in anatomy presents problems for future radiation sessions since the treatment was planned on lung geometry which is no longer accurate. The treatment must be adapted to the new lung state so that the radiation continues to accurately target the tumor while safely avoiding healthy tissue. However, to account for the dose delivered previously, correspondences of anatomy between the former image when the lung was collapsed and the re-expanded lung in a current image must be obtained. This process, known as deformable image registration, is performed by registration software. Most registration algorithms assume that identical anatomy is contained in the images and that intensities of corresponding image elements are similar; both assumptions are untrue when collapsed lung re-expands. This work was to develop an algorithm which accurately registers images in the presence of lung expansion. The lung registration method matched CT images of patients aided by vessel enhancement and information of individual lobe boundaries. The algorithm was tested on eighteen patients with lung collapse using physician-specified correspondences to measure registration error. The image registration algorithm developed in this work which was designed for challenging lung patients resulted in accuracy comparable to that of other methods when large lung changes are absent.

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.