A monocular visual servo system for a target with variable shape has been developed in this paper. It consists of two parts: an image-processing unit and a servo control unit. For the image-processing unit, the motion between the target and image center is determined by a template match approach. The image is grabbed by the camera equipped on a Pan-Tilt robot and the robot is controlled to track the target by maintaining the target on the image center. However, the template needs to be updated when the target deforms. For the servo control unit, the movement is estimated by the Kalman filter technique to enhance the tracking performance of the visual servo system.

<p>Robotic platforms have several characteristics such as speed and precision that make them enticing for use in medical procedures. Companies such as Intuitive Medical and Titan Medical have taken advantage of these features to introduce surgical robots for minimally invasive procedures. Such robots aim to reduce procedure and patient recovery times. Current technology requires platforms to be master-slave manipulators controlled by a surgeon, effectively converting the robot into an expensive surgical tool. Research into the interaction between robotic platforms and deformable objects such as human tissue is necessary in the development of autonomous and semi-autonomous surgical systems. This thesis investigates a class of robust linear controllers based on a worst case performance measure known as the $H_{\infty}$ norm, for the purpose of performing so called Indirect Deformable Object Manipulation (IDOM). This task allows positional regulation of regions of interest in a deformable object without directly interacting with them, enabling tasks such as stabilization of tumors during biopsies or automatic suturing. A complete approach to generating linear $H_{\infty}$ based controllers is presented, from derivation of a plant model to the actual synthesis of the controller. The introduction of model uncertainty requires $\mu$ synthesis techniques, which extend $H_{\infty}$ designs to produce highly robust controller solutions. In addition to $H_{\infty}$ and $\mu$ synthesis designs, the thesis presents an approach to design an optimal PID controller with gains that minimize the $H_{\infty}$ norm of a weighted plant. The three control approaches are simulated performing set point regulation in $\text{MATLAB}^{TM}$'s $simulink$. Simulations included disturbance inputs and noises to test stability and robustness of the approaches. $H_{\infty}$ controllers had the best robust performance of the controllers simulated, although all controllers simulated were stable. The $H_{\infty}$ and PID controllers were validated in an experimental setting, with experiments performed on two different deformable synthetic materials. It was found that $H_{\infty}$ techniques were highly robust and provided good tracking performance for a material that behaved in a relatively elastic manner, but failed to track well when applied to a highly nonlinear rubber compound. PID based control was outperformed by $H_{\infty}$ control in experiments performed on the elastic material, but proved to be superior when faced with the nonlinear material. These experimental findings are discussed and a linear $H_{\infty}$ control design approach is proposed.</p> / Master of Applied Science (MASc)

Nonrigid deformation modeling and estimation from images is a technically challenging task due to its nonlinear, nonconvex and high-dimensional nature. Traditional optimization procedures often rely on good initializations and give locally optimal solutions. On the other hand, learning-based methods that directly model the relationship between deformed images and their parameters either cannot handle complicated forms of mapping, or suffer from the Nyquist Limit and the curse of dimensionality due to high degrees of freedom in the deformation space. In particular, to achieve a worst-case guarantee of ∈ error for a deformation with d degrees of freedom, the sample complexity required is O(1/∈d). In this thesis, a generative model for deformation is established and analyzed using a unified theoretical framework. Based on the framework, three algorithms, Data-Driven Descent, Top-down and Bottom-up Hierarchical Models, are designed and constructed to solve the generative model. Under Lipschitz conditions that rule out unsolvable cases (e.g., deformation of a blank image), all algorithms achieve globally optimal solutions to the specific generative model. The sample complexity of these methods is substantially lower than that of learning-based approaches, which are agnostic to deformation modeling. To achieve global optimality guarantees with lower sample complexity, the structureembedded in the deformation model is exploited. In particular, Data-driven Descentrelates two deformed images that are far away in the parameter space by compositionalstructures of deformation and reduce the sample complexity to O(Cd log 1/∈).Top-down Hierarchical Model factorizes the local deformation into patches once theglobal deformation has been estimated approximately and further reduce the samplecomplexity to O(Cd/1+C2 log 1/∈). Finally, the Bottom-up Hierarchical Model buildsrepresentations that are invariant to local deformation. With the representations, theglobal deformation can be estimated independently of local deformation, reducingthe sample complexity to O((C/∈)d0) (d0 ≪ d). From the analysis, this thesis showsthe connections between approaches that are traditionally considered to be of verydifferent nature. New theoretical conjectures on approaches like Deep Learning, arealso provided. practice, broad applications of the proposed approaches have also been demonstrated to estimate water distortion, air turbulence, cloth deformation and human pose with state-of-the-art results. Some approaches even achieve near real-time performance. Finally, application-dependent physics-based models are built with good performance in document rectification and scene depth recovery in turbulent media.

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<p>This thesis presents a computational model of the surgical stitching tasks and a path planning algorithm for robotic assisted stitching. The overall goal of the research is to enable surgical robots to perform automatic suturing. Suturing comprises several distinct steps, one of them is the stitching. During stitching, reaching the desired exit point is difficult because it must be accomplished without direct visual feedback. Moreover, the stitching is a time consuming procedure repeated multiple times during suturing. Therefore, it would be desirable to enhance the surgical robots with the ability of performing automatic suturing. The focus of this work is on the automation of the stitching task. The thesis presents a model based path planning algorithm for the autonomous stitching. The method uses a nonlinear model for the curved needle - soft tissue interaction. The tissue is modeled as a deformable object using continuum mechanics tools. This thesis uses a mesh free deformable tissue model namely, Reproducing Kernel Particle Method (RKPM). RKPM was chosen as it has been proven to accurately handle large deformation and requires no re-meshing algorithms. This method has the potential to be more realistic in modeling various material characteristics by using appropriate strain energy functions. The stitching task is simulated using a constrained deformable model; the deformable tissue is constrained by the interaction with the curved needle. The stitching model was used for needle trajectory path planning during stitching. This new path planning algorithm for the robotic stitching was developed, implemented, and evaluated. Several simulations and experiments were conducted. The first group of simulations comprised random insertions from different insertion points without planning to assess the modeling method and the trajectory of the needle inside the tissue. Then the parameters of the simulations were set according to the measured experimental parameters. The proposed path planning method was tested using a surgical ETHICON needle of type SH 1=2 Circle with the radius of 8:88mm attached to a robotic manipulator. The needle was held by a grasper which is attached to the robotic arm. The experimental results illustrate that the path planned curved needle insertions are fifty percent more accurate than the unplanned ones. The results also show that this open loop approach is sensitive to model parameters.</p> / Master of Applied Science (MASc)

Les Graphes sont des structures mathématiques puissantes constituant un outil de modélisation universel utilisé dans différents domaines de l'informatique, notamment dans le domaine de la reconnaissance de formes. L'appariement de graphes est l'opération principale dans le processus de la reconnaissance de formes à base de graphes. Dans ce contexte, trouver des solutions d'appariement de graphes, garantissant l'optimalité en termes de précision et de temps de calcul est un problème de recherche difficile et d'actualité. Dans cette thèse, nous nous intéressons à la résolution de ce problème dans deux domaines : la reconnaissance de formes 2D et 3D. Premièrement, nous considérons le problème d'appariement de graphes géométriques et ses applications sur la reconnaissance de formes 2D. Dance cette première partie, la reconnaissance des Kites (structures archéologiques) est l'application principale considérée. Nous proposons un "framework" complet basé sur les graphes pour la reconnaissance des Kites dans des images satellites. Dans ce contexte, nous proposons deux contributions. La première est la proposition d'un processus automatique d'extraction et de transformation de Kites a partir d'images réelles en graphes et un processus de génération aléatoire de graphes de Kites synthétiques. En utilisant ces deux processus, nous avons généré un benchmark de graphes de Kites (réels et synthétiques) structuré en 3 niveaux de bruit. La deuxième contribution de cette première partie, est la proposition d'un nouvel algorithme d'appariement pour les graphes géométriques et par conséquent pour les Kites. L'approche proposée combine les invariants de graphes au calcul de l'édition de distance géométrique. Deuxièmement, nous considérons le problème de reconnaissance des formes 3D ou nous nous intéressons à la reconnaissance d'objets déformables représentés par des graphes c.à.d. des tessellations de triangles. Nous proposons une décomposition des tessellations de triangles en un ensemble de sous structures que nous appelons triangle-étoiles. En se basant sur cette décomposition, nous proposons un nouvel algorithme d'appariement de graphes pour mesurer la distance entre les tessellations de triangles. L'algorithme proposé assure un nombre minimum de structures disjointes, offre une meilleure mesure de similarité en couvrant un voisinage plus large et utilise un ensemble de descripteurs qui sont invariants ou au moins tolérants aux déformations les plus courantes. Finalement, nous proposons une approche plus générale de l'appariement de graphes. Cette approche est fondée sur une nouvelle formalisation basée sur le problème de mariage stable. L'approche proposée est optimale en terme de temps d'exécution, c.à.d. la complexité est quadratique O(n2), et flexible en terme d'applicabilité (2D et 3D). Cette approche se base sur une décomposition en sous structures suivie par un appariement de ces structures en utilisant l'algorithme de mariage stable. L'analyse de la complexité des algorithmes proposés et l'ensemble des expérimentations menées sur les bases de graphes des Kites (réelle et synthétique) et d'autres bases de données standards (2D et 3D) attestent l'efficacité, la haute performance et la précision des approches proposées et montrent qu'elles sont extensibles et générales / Graphs are powerful mathematical modeling tools used in various fields of computer science, in particular, in Pattern Recognition. Graph matching is the main operation in Pattern Recognition using graph-based approach. Finding solutions to the problem of graph matching that ensure optimality in terms of accuracy and time complexity is a difficult research challenge and a topical issue. In this thesis, we investigate the resolution of this problem in two fields: 2D and 3D Pattern Recognition. Firstly, we address the problem of geometric graphs matching and its applications on 2D Pattern Recognition. Kite (archaeological structures) recognition in satellite images is the main application considered in this first part. We present a complete graph based framework for Kite recognition on satellite images. We propose mainly two contributions. The first one is an automatic process transforming Kites from real images into graphs and a process of generating randomly synthetic Kite graphs. This allowing to construct a benchmark of Kite graphs (real and synthetic) structured in different level of deformations. The second contribution in this part, is the proposition of a new graph similarity measure adapted to geometric graphs and consequently for Kite graphs. The proposed approach combines graph invariants with a geometric graph edit distance computation. Secondly, we address the problem of deformable 3D objects recognition, represented by graphs, i.e., triangular tessellations. We propose a new decomposition of triangular tessellations into a set of substructures that we call triangle-stars. Based on this new decomposition, we propose a new algorithm of graph matching to measure the distance between triangular tessellations. The proposed algorithm offers a better measure by assuring a minimum number of triangle-stars covering a larger neighbourhood, and uses a set of descriptors which are invariant or at least oblivious under most common deformations. Finally, we propose a more general graph matching approach founded on a new formalization based on the stable marriage problem. The proposed approach is optimal in term of execution time, i.e. the time complexity is quadratic O(n2) and flexible in term of applicability (2D and 3D). The analyze of the time complexity of the proposed algorithms and the extensive experiments conducted on Kite graph data sets (real and synthetic) and standard data sets (2D and 3D) attest the effectiveness, the high performance and accuracy of the proposed approaches and show that the proposed approaches are extensible and quite general