La reconnaissance du comportement et la prédiction des activités des personnes depuis la vidéo sont des préoccupations majeures dans le domaine de la vision par ordinateur. L'objectif principal de mon travail de thèse est de proposer des algorithmes qui permettent d'analyser des objets en mouvement à partir de la vidéo pour extraire des comportements humains. Cette analyse est effectuée dans des environnements intérieurs ou extérieurs filmés par des simples webcams ou par des caméras plus sophistiquée. La scène analysée peut être de deux types en fonction du nombre de personnes présentes. On distingue les scènes de foule où le nombre de personnes est important. Dans ce type de scène, nous nous intéressons aux problèmes de la détection d'évènements de foule, à l'analyse des flux et à l'extraction des motifs de mouvement. Le deuxième type de scène se caractérise par la présence d'une seule personne à la fois dans le champ de la caméra. Elle est appelée scène individuelle. Nous y traitons le problème de reconnaissance d'actions humaines. Pour atteindre ces objectifs, nous proposons une approche basée sur trois niveaux d'analyse. Le premier est l'extraction des caractéristiques de bas niveau récupérés les images constituant un flux vidéo (ex. les zones en mouvement). Le deuxième construit des descripteurs pour l’analyse du comportement humain (ex. la direction et la vitesse de mouvement moyennes). Le niveau le plus haut se sert des descripteurs de l'étape intermédiaire afin de fournir aux utilisateurs des résultats concrets sur l'analyse du comportement humain (ex. telle personne marche, une autre court, etc.). Des expérimentations sur des benchmarks connus ont validé nos approches, avec un positionnement très intéressant par rapport à l'état de l'art. / The recognition and prediction of people activities from videos are major concerns in the field of computer vision. The main objective of my thesis is to propose algorithms that analyze human behavior from video. This problem is also called video content analysis or VCA. This analysis is performed in outdoor or indoor environments using simple webcams or more sophisticated surveillance cameras. The video scene can be of two types depending on the number of people present. The first type is characterized by the presence of only one person at a time in the video. We call this an individual scene where we will tackle the problem of human action recognition. The second type of scene contains a large number of persons. This is called a crowd scene where we will address the problems of motion pattern extraction, crowd event detection and people counting. To achieve our goals, we propose an approach based on three levels of analysis. The first level is the detection of low-level descriptors retrieved from the images of the video (e.g. areas in motion). The second level retrieves descriptors for modeling human behavior (e.g. average speed and direction of movement). The top level uses the descriptors of the intermediate step to provide users with concrete results on the analysis of behavior (e.g. this person is running, that one is walking, etc.). Experimentation on well-known benchmarks have validated our approaches, with very satisfying results compared to the state of the art.

Class of 2006 Abstract / Objectives: To develop a new equation to predict creatinine clearance specific for cystic fibrosis patients. Methods: A literature review was performed to capture data on the daily creatinine excretion in CF patients in relation to age, weight, height, and other physiologic variables. Nonlinear mixed effect modeling was then used to develop an equation to estimate creatinine clearance using individual covariates. The performance of the new equation developed was compared to the Cockcroft and Gault method in a CF population (age > 16 years). Results: A database of individual patient data from a previously published study of 19 patients was created. Significant covariates for model development included actual body weight, sex, and serum creatinine. The final candidate model was: 5.62× ABW0.67 CrCl = sCr(mg / dl) × 0.649( female) Conclusions: The results of the mean absolute error and root mean squared error calculations show that the new equation resulted in less bias and better precision than Cockcroft-Gault, Jeliffe I, and Jeliffe II based on the limited data available. However, these conclusions are limited in that the only evaluation data available was the same data that was used for model development.

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In this thesis we study the problem of estimation of parametric covariance and variogram functions for spatial and spatio- temporal random processes. It has the following principal parts. Variogram Estimation: We consider the "weighted" least squares criterion of fitting a parametric variogram function to second order stationary geo-statistical processes. Two new weight functions are investigated as alternative to the commonly used weight function proposed by Cressie (1985). We discuss asymptotic convergence properties of the sample variogram estimator and estimators of unknown parameters of parametric variogram functions, under a "mixed increasing domain" sampling design as proposed by Lahiriet al. While empirical results of Mean Square Errors, for parameter estimation, obtained using both the proposed functions are found to be comparatively better, we also theoretically establish that under general conditions one of the proposed weight functions give estimates with better asymptotic effciency. Spatio-Temporal Covariance Estimation: Over the past decade, there have been some important advances in methods for constructing valid spatiotemporal covariance functions; but not much attention has been given - so far - on methods of parameter estimation. In this thesis we propose a new frequency domain approach to estimating parameters of spatio-temporal covariance functions. We derive asymptotic strong consistency properties of the estimators using the concept of stochastic equicontinuity. The theory is illustrated with a simulation. Non-Linearity of Geostatistical Data: Linear prediction theory for spatial data is well established and substantial literature is available on the subject. Relatively less is known about non-linearity. In our final and ongoing, research problem we propose a non-linear predictor for geostatistical data. We demonstrate that the predictor is a function of higher order moments. This leads us to construct spatial bispectra for parametric third order moments.

Partial Differential Equations (PDEs) are commonly used to model complex systems that arise for example in biology, engineering, chemistry, and elsewhere. The parameters (or coefficients) and the source of PDE models are often unknown and are estimated from available measurements. Despite its importance, solving the estimation problem is mathematically and numerically challenging and especially when the measurements are corrupted by noise, which is often the case. Various methods have been proposed to solve estimation problems in PDEs which can be classified into optimization methods and recursive methods. The optimization methods are usually heavy computationally, especially when the number of unknowns is large. In addition, they are sensitive to the initial guess and stop condition, and they suffer from the lack of robustness to noise. Recursive methods, such as observer-based approaches, are limited by their dependence on some structural properties such as observability and identifiability which might be lost when approximating the PDE numerically. Moreover, most of these methods provide asymptotic estimates which might not be useful for control applications for example. An alternative non-asymptotic approach with less computational burden has been proposed in engineering fields based on the so-called modulating functions. In this dissertation, we propose to mathematically and numerically analyze the modulating functions based approaches. We also propose to extend these approaches to different situations. The contributions of this thesis are as follows. (i) Provide a mathematical analysis of the modulating function-based method (MFBM) which includes: its well-posedness, statistical properties, and estimation errors. (ii) Provide a numerical analysis of the MFBM through some estimation problems, and study the sensitivity of the method to the modulating functions' parameters. (iii) Propose an effective algorithm for selecting the method's design parameters. (iv) Develop a two-dimensional MFBM to estimate space-time dependent unknowns which is illustrated in estimating the source term in the damped wave equation describing the physiological characterization of brain activity. (v) Introduce a moving horizon strategy in the MFBM for on-line estimation and examine its effectiveness on estimating the source term of a first order hyperbolic equation which describes the heat transfer in distributed solar collector systems.

Partial differential equations (PDEs) are used to describe multi-dimensional physical phenomena. However, some of these phenomena are described by a more general class of systems called fractional systems. Indeed, fractional calculus has emerged as a new tool for modeling complex phenomena thanks to the memory and hereditary properties of fraction derivatives. In this thesis, we explore a class of controllers and estimators that respond to some control and estimation challenges for both PDE and FPDE. We first propose a backstepping controller for the flow control of a first-order hyperbolic PDE modeling the heat transfer in parabolic solar collectors. While backstepping is a well-established method for boundary controlled PDEs, the process is less straightforward for in-domain controllers. One of the main contributions of this thesis is the development of a new integral transformation-based control algorithm for the study of reference tracking problems and observer designs for fractional PDEs using the extended backstepping approach. The main challenge consists of the proof of stability of the fractional target system, which utilizes either an alternative Lyapunov method for time FPDE or a fundamental solution for the error system for reference tracking, and observer design of space FPDE. Examples of applications involving reference tracking of FPDEs are gas production in fractured media and solute transport in porous media. The designed controllers, require knowledge of some system’s parameters or the state. However, these quantities may be not measurable, especially, for space-evolving PDEs. Therefore, we propose a non-asymptotic and robust estimation algorithm based on the so-called modulating functions. Unlike the observers-based methods, the proposed algorithm has the advantage that it converges in a finite time. This algorithm is extended for the state estimation of linear and non-linear PDEs with general non-linearity. This algorithm is also used for the estimation of parameters and disturbances for FPDEs. This thesis aims to design an integral transformation-based algorithm for the control and estimation of PDEs and FDEs. This transformation is defined through a suitably designed function that transforms the identification problem into an algebraic system for non-asymptotic estimation purposes. It also maps unstable systems to stable systems to achieve control goals.

Concrete compressive strength is one of the most important material properties affectingthe design of concrete structures. Strength that will be achieved once the concrete sets should be correctly predicted prior to pouring the concrete. Regression techniques can be used to calculate the 28-day concrete strength with a level of certainty. This thesis deals with the data modelling and analysis of 28-day compressive strength of high-performance concrete. Historical data on various mix compositions of high-performance concrete was obtained from University of California, Irvine repository. The data had 8 predictors and 1 response variable. In this thesis, three penalized regression approaches, namely, ridge, lasso, and elastic net were used to create a predictive model for compressive strength, and the performance of these model were compared to the traditional multiple linear regression model. Holdout sets from 2% to 40% at an increment of 2% were taken. Every regression algorithm was designed to conduct regression on 30 sets of randomly partitioned data. The performance of models was assessed using coefficient of multiple determination, RMSE, and residual plots. All regression techniques were able to predict the concrete strength with about 75% accuracy level.

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Human pose estimation represents the skeleton of a person in color or depth images to improve a machine’s understanding of human movement. 3D human pose estimation uses a three-dimensional skeleton to represent the human body posture, which is more stereoscopic than a two-dimensional skeleton. Therefore, 3D human pose estimation can enable machines to play a role in physical education and health recovery, reducing labor costs and the risk of disease transmission. However, the existing datasets for 3D pose estimation do not involve fast motions that would cause optical blur for a monocular camera but would allow the subjects’ limbs to move in a more extensive range of angles. The existing models cannot guarantee both real-time performance and high accuracy, which are essential in physical education and health recovery applications. To improve real-time performance, researchers have tried to minimize the size of the model and have studied more efficient deployment methods. To improve accuracy, researchers have tried to use heat maps or point clouds to represent features, but this increases the difficulty of model deployment. To address the lack of datasets that include fast movements and easy-to-deploy models, we present a human kinetic dataset called the Kivi dataset and a hybrid model that combines the benefits of a heat map-based model and an end-to-end model for 3D human pose estimation. We describe the process of data collection and cleaning in this thesis. Our proposed Kivi dataset contains large-scale movements of humans. In the dataset, 18 joint points represent the human skeleton. We collected data from 12 people, and each person performed 38 sets of actions. Therefore, each frame of data has a corresponding person and action label. We design a preliminary model and propose an improved model to infer 3D human poses in real time. When validating our method on the Invariant Top-View (ITOP) dataset, we found that compared with the initial model, our improved model improves the mAP@10cm by 29%. When testing on the Kivi dataset, our improved model improves the mAP@10cm by 15.74% compared to the preliminary model. Our improved model can reach 65.89 frames per second (FPS) on the TensorRT platform.

Conditional coding is an application of Markov Chain Monte Carlo methods for sampling from conditional distributions. It is applied here to the problem of estimating the parameters of a computer-simulated pattern of fractures in an isomorphic, homotropic material under plane strain. We investigate the theory and procedures of conditional coding and show the viability of the technique by its application.