It is well known that biological structures such as human brains, although may contain the same global structures, differ in shape, orientation, and fine structures across individuals and at different times. Such variabilities during registration are usually represented by nonrigid transformations. This research seeks to address this issue by developing physically based models in which transformations are constructed to obey certain physical laws. <br /><br /> In this thesis, a novel registration technique is presented based on the physical behavior of particles. Regarding the image as a particle system without mutual interaction, we simulate the registration process by a set of free particles moving toward the target positions under applied forces. The resulting partial differential equations are a nonlinear hyperbolic system whose solution describes the spatial transformation between the images to be registered. They can be numerically solved using finite difference methods. <br /><br /> This technique extends existing physically based models by completely excluding mutual interaction and highly localizing image deformations. We demonstrate its performance on a variety of images including two-dimensional and three-dimensional, synthetic and clinical data. Deformable images are achieved with sharper edges and clearer texture at less computational cost.

It is well known that biological structures such as human brains, although may contain the same global structures, differ in shape, orientation, and fine structures across individuals and at different times. Such variabilities during registration are usually represented by nonrigid transformations. This research seeks to address this issue by developing physically based models in which transformations are constructed to obey certain physical laws. <br /><br /> In this thesis, a novel registration technique is presented based on the physical behavior of particles. Regarding the image as a particle system without mutual interaction, we simulate the registration process by a set of free particles moving toward the target positions under applied forces. The resulting partial differential equations are a nonlinear hyperbolic system whose solution describes the spatial transformation between the images to be registered. They can be numerically solved using finite difference methods. <br /><br /> This technique extends existing physically based models by completely excluding mutual interaction and highly localizing image deformations. We demonstrate its performance on a variety of images including two-dimensional and three-dimensional, synthetic and clinical data. Deformable images are achieved with sharper edges and clearer texture at less computational cost.

The main topic of this thesis is nonrigid image registration for medical applications. We start with an overview and classification of existing registration techniques. We develop a general nonrigid image registration algorithm. It uses spline functions to describe the deformation and uses multi-scale strategy to search for the optimal transformation. Then we present a new registration operator that is transitive and symmetric. We investigate the theoretical implication of these properties and apply this operator to the registration of sequences of MR cardiac images. In the second part of the thesis, two methods, one 2D and one 3D, for validation of nonrigid image registration algorithms are proposed and compared to a manual validation strategy. Both methods provide pairs of deformed images as well as corresponding true displacement fields with known accuracy. Nonrigid registration algorithms can be run on the pairs of images and their outputs can be compared to the true displacement fields that were generated manually by five observers. While these phantom validation studies do not provide physically correct deformations, they are certainly a useful way to test the algorithm's ability to recover various deformation patterns.

Estimating the dense image motion or optical flow on a real-world nonrigid surface is a fundamental research issue in computer vision, and is applicable to a wide range of fields, including medical imaging, computer animation and robotics. However, nonrigid surface tracking is a difficult challenge because complex nonrigid deformation, accompanied by image blur and natural noise, may lead to severe intensity changes to pixels through an image sequence. This violates the basic intensity constancy assumption of most visual tracking methods. In this thesis, we show that local geometric constraints and long term feature matching techniques can improve local motion preservation, and reduce error accumulation in optical flow estimation. We also demonstrate that combining RGB data with additional information from other sensing channels, can improve tracking performance in blurry scenes as well as allow us to create nonrigid ground truth from real world scenes. First, we introduce a local motion constraint based on a laplacian mesh representation of nonrigid surfaces. This additional constraint term encourages local smoothness whilst simultaneously preserving nonrigid deformation. The results show that our method outperforms most global constraint based models on several popular benchmarks. Second, we observe that the inter-frame blur in general video sequences is near linear, and can be roughly represented by 3D camera motion. To recover dense correspondences from a blurred scene, we therefore design a mechanical device to track camera motion and formulate this as a directional constraint into the optical flow framework. This improves optical flow in blurred scenes. Third, inspired by recent developments in long term feature matching, we introduce an optimisation framework for dense long term tracking -- applicable to any existing optical flow method -- using anchor patches. Finally, we observe that traditional nonrigid surface analysis suffers from a lack of suitable ground truth datasets given real-world noise and long image sequences. To address this, we construct a new ground truth by simultaneously capturing both normal RGB and near-infrared images. The latter spectrum contains dense markers, visible only in the infrared, and represents ground truth positions. Our benchmark contains many real-world scenes and properties absent in existing ground truth datasets.

Much of what is known about how we process faces comes from research using static stimuli. Thus, the primary goal of the present series of studies was to compare the processing of more naturalistic, dynamic face stimuli to the processing of static face stimuli. A second goal of the present series of studies was to provide insight into the development of attentional mechanisms that underlie perception of faces. Results from the eye-tracking study (Chapter 2) indicated that viewers attended to faces more than to other parts of the static or dynamic social scenes. Importantly, motion cues were associated with a reduction in the number, but an increase in the average duration of fixations on faces. Children showed the largest effects related to the introduction of motion cues, suggesting that they find dynamic faces difficult to process. Then using selective attention tasks (Chapters 3-5), interactions between the processing of facial expression and identity while participants viewed static and dynamic faces were examined. When processing static faces, viewers experienced significant interference from task-irrelevant cues (expression or identity) while processing the relevant cues (identity or expression). Age-related differences in interference effects were not evident (Chapter 3); however, biological sex and perceptual biases did contribute to the levels of interference seen with static faces (Chapters 4-5). During dynamic trials, however, viewers (regardless of age, sex, or perceptual bias) experienced negligible interference from task-irrelevant facial cues. Taken together, these findings stress the importance of using dynamic displays when characterizing typical face processing mechanisms, using the same methods across development, and of considering individual differences when examining various face processing abilities.

Résumé : En dépit des nombreuses recherches pour réduire le coût d'inspection des pièces à l'aide d'outils numériques, l'inspection de pièces souples demeure un défi. La raison est que les pièces souples peuvent prendre à l'état libre une forme substantiellement différente de leur géométrie nominale. Il en résulte que l'inspection de ce type de pièces nécessite des outils dédiés et coûteux, comme un gabarit d'inspection. Cette thèse détaille les défis associés au contrôle de ces pièces, pour proposer ensuite une méthode permettant l'inspection à l'état libre de pièces souples ayant une spécification limitant les forces de montage. L'approche proposée combine la méthode par éléments finis, les méthodes de traitement d'images ainsi que les démarches du domaine de l'optimisation. Essentiellement, la méthode proposée transpose (maps) le nuage de points représentant la pièce à l'état libre dans une configuration correspondant à sa géométrie installée sur son gabarit d'inspection. La méthode n'exige pas la conversion du nuage de points en modèle d'éléments finis, et veille à ce que les forces de montage ne dépassent pas leurs limites spécifiées, tout en tolérant des incertitudes dans la position des points de fixation simulant l'interface de montage. Ceci est accompli par le biais d'une optimisation par contrainte des déplacements des points de fixation. La contrainte de l'optimisation limite l'étendue des valeurs des forces de montage. La performance de la méthode d'inspection numérique proposée est évaluée à partir de cas d'études simulés, ainsi qu'à partir de deux pièces réelles du secteur de l'aéronautique. // Abstract : Despite extensive research to reduce the cost of inspection of parts using computational tools, inspection of compliant parts remains a challenge. The reason is that in a free-state, compliant parts can take on different shapes compared to their design model. It follows that the inspection of such parts requires dedicated and expensive inspectionfixtures. This thesis details the challenges associated with the inspection of these partsto then propose a fixetureless inspection method for compliant parts for which theirfunctional requirements mandate to limit the restraining forces imposed during assembly. The proposed approach combines the finite element method, image processing andoptimization techniques. Essentially, the proposed method maps the point cloud, representing the part in a free-state, to a configuration corresponding to its shape mounted onto its inspection fixture. The method does not necessitate the conversion of the point cloud into a finite element model, ensures that restraining forces do not exceed their specified limits, and accepts uncertainties in the position of features simulating the mounting interface. This is done through an constrained optimization on the displacements of the fixing points. The optimization constraint bounds the restraining forces values. The performance of the proposed computational inspection method is evaluated on simulated case studies, as well as on two aeronautics workpiece.

The past two decades has witnessed growing interest in physics based techniques in computer vision, computer graphics and medical imaging. The main advantage of a physical model is its mathematical rigor and physical soundness, which makes it an ideal tool to study complex nonrigid motion. However, since a model based on continuum mechanics is computationally demanding, an idealized framework is often adopted where physical motion parameters are significantly simplified, which inevitably affects the accuracy and reliability of modeling results. In this study, a new modeling approach is developed that features the reconstruction of actual material properties such as the Young's modulus and the Poisson's ratio. Justified by the constitutive law and mathematical considerations, the Young's modulus is identified as a unique physical motion parameter. By imposing an adaptive smoothness constraint, the Young's modulus helps preserve the local characteristics (discontinuity) of an object's deformation, a role similar to the weighting coefficient in the study of edge-preserving visual surface reconstruction. The contribution of this work is fourfold: (1) two recovery algorithms are developed to solve the inverse elastic problem: A deterministic algorithm that is based on the Gauss-Newton method and the general cross validation, and a stochastic algorithm that is based on the constrained genetic evolution; (2) a new modeling approach is proposed that has the ability to recover nonrigid motion in terms of the physical parameters. The use of recovered parameters can be implemented within a boundary-driven motion synthesis scheme; (3) A sensitivity method is proposed to evaluate the impact of different parameters. The method uses the adjoint state equation and hence is suitable for large scale models. (4) the proposed modeling approach has been applied to burn scar assessment and face recognition.

Geometric morphometry serves biologists and anthropologists to rigorously and quantitatively describe shapes. These representations can be treated as a statistical sample, allowing the researchers to study its variability within groups and correlate it to other features. Geometric morphometry uses landmarks as the proxy for shape, with consistent semantics in each specimen. General triangle meshes do not have this property, and as such, semantically consistent remeshes must be created artificially. This thesis deals with the design of an algorithm that consistently resamples a set of surface models for the purpose of statistical analysis. Coherent point drift was employed to perform nonrigid registration, whose result is then used to generate a semantically consistent remeshes. This approach was successfully applied in a number of studies. As CPD is compute-intensive, we propose methods of accelerating both its initialization and processing phases. Also, an extension was introduced, that can map the deviation of the surfaces from perfect bilateral symmetry and analyze it in a sample, which is significant, among others, for quantification of pathologies. Manual trimming of the surfaces and merging datasets results in outlier regions in the individual surfaces and potentially large differences in their vertex...

This thesis deals with a nonrigid image registration for movement correction in thoracic dynamic contrast CT data. The deformation field is initialized by the analysis of disparities based on nonlinear matched filter, which defines local movement deformation. The values of control points are optimized by the Nelder-Mead method. The transformation model is based on a 4D (3D + time) free-form B-spline deformation for feature of movement distortion. The first part of the thesis briefly discusses the theory of image registration. Knowledge of this theory is necessary for understanding the remaining chapters, which describe the proposed method and its realization. The large part of this thesis is devoted to the geometrical image transformations, that is very important for the image registration. The thesis also describes a simplex method for function minimization. Three publicated methods of registration of medical 4D CT data are given. In the following chapter are individual parts of the purposed nonrigid registration including possible problems and their solution described.

Dans ce manuscrit, nous avons l’intention d’une part d’étudier les effets isotopiques dans les spectres infrarougesde la phosphine et de l’éthylène et d’autre part de contribuer au développement d’un modèle théoriquepour les molécules non-rigides. La finalité de ce travail est la construction de listes spectroscopiques complètesen lien avec les applications planétologiques et astrophysiques à partir de calculs variationnels. La premièrepartie de ce travail de thèse concerne l’étude des 2 espèces deutérées de la molécule de phoshine et des 10 espècesisotopiques de l’éthylène enrichies par 13C et/ou D, le tout à partir de surfaces ab initio. Pour cela, nous avonsutilisé une procédure systématique permettant de propager l’information de l’isotope principal vers des espècesmoins abondantes à partir de considérations de symétrie et de transformations entre les coordonnées normales.Finalement, les spectres infrarouges ont été modélisés et confrontés aux données observées. La deuxième partiede ce travail porte sur l’étude des molécules non-rigides présentant un ou plusieurs mouvements de largeamplitude. Dans ce contexte, nous sommes partis du formalisme proposé par Hougen, Bunker et Johns. Afinde pouvoir réutiliser une grande partie des outils déjà existants, nous avons choisi une formulation algébriquedu problème. Ce modèle a d’abord été validé sur des molécules rigides connues pour lesquelles nous avions descalculs de référence. Concernant les systèmes non-rigides, des résultats préliminaires ont été obtenus pour lesmolécules d’ammoniac et d’éthane. De manière plus générale, ce travail offre également des solutions concrètesà des problèmes allant au-delà de l’approche HBJ en proposant différentes méthodes de calcul de la matrice derotation permettant de tourner le repère afin de minimiser le couplage entre la rotation et les mouvements degrande amplitude. / This thesis is devoted to the study of the isotopic effects in infrared spectra of the phosphine and ethylenemolecules as well as to the development of a theoretical model for treating nonrigid polyatomic molecules. Thefinal goal of this work is to build complete theoretical line lists for planetological and astrophysical applicationsby using ab initio surfaces and variational calculations. In a first part, a systematic procedure allowing to propagateinformation from the main isotopolog to the less abundant «daughter» species has been developed fromsymmetry considerations and normal coordinate transformations. Finally, the infrared spectra predictions havebeen carried out and compared to the experimental available data. The second part focuses on the treatment ofnonrigid molecules possessing one or more large amplitude motions. In this context, the Hougen-Bunker-Johnsformalism was used. The particularity of our algebraic model consists in the possibility of using most of thetools previously developed in the group. Our model has been first validated on semirigid systems for whichthere exist reference calculations. Some preliminary results concerning nonrigid molecules have been obtainedfor ammonia and ethane. In addition, we have proposed different methods for computing the rotation matrixallowing to take place in a frame minimizing couplings between rotation and large amplitude motions.