In this work the problem of calibrating Flush Air Data Sensing (FADS) has been addressed. The inverse problem of extracting freestream wind speed and angle of attack from pressure measurements has been solved. The aim of this work was to develop machine learning and statistical tools to optimize design and calibration of FADS systems. Experimental and Computational Fluid Dynamics (EFD and CFD) solve the forward problem of determining the pressure distribution given the wind velocity profile and bluff body geometry. In this work three ways are presented in which machine learning techniques can improve calibration of FADS systems. First, a scattered data approximation scheme, called Sequential Function Approximation (SFA) that successfully solved the current inverse problem was developed. The proposed scheme is a greedy and self-adaptive technique that constructs reliable and robust estimates without any user-interaction. Wind speed and direction prediction algorithms were developed for two FADS problems. One where pressure sensors are installed on a surface vessel and the other where sensors are installed on the Runway Assisted Landing Site (RALS) control tower. Second, a Tikhonov regularization based data-model fusion technique with SFA was developed to fuse low fidelity CFD solutions with noisy and sparse wind tunnel data. The purpose of this data model fusion approach was to obtain high fidelity, smooth and noiseless flow field solutions by using only a few discrete experimental measurements and a low fidelity numerical solution. This physics based regularization technique gave better flow field solutions compared to smoothness based solutions when wind tunnel data is sparse and incomplete. Third, a sequential design strategy was developed with SFA using Active Learning techniques from the machine learning theory and Optimal Design of Experiments from statistics for regression and classification problems. Uncertainty Sampling was used with SFA to demonstrate the effectiveness of active learning versus passive learning on a cavity flow classification problem. A sequential G-optimal design procedure was also developed with SFA for regression problems. The effectiveness of this approach was demonstrated on a simulated problem and the above mentioned FADS problem.

Analysis and visualization of dynamic scenes is often constrained by the amount of spatio-temporal information available from the environment. In most scenarios, we have to account for incomplete information and sparse motion data, requiring us to employ interpolation and approximation methods to fill for the missing information. Scattered data interpolation and approximation techniques have been widely used for solving the problem of completing surfaces and images with incomplete input data. We introduce approaches for such data interpolation and approximation from limited sensors, into the domain of analyzing and visualizing dynamic scenes. Data from dynamic scenes is subject to constraints due to the spatial layout of the scene and/or the configurations of video cameras in use. Such constraints include: (1) sparsely available cameras observing the scene, (2) limited field of view provided by the cameras in use, (3) incomplete motion at a specific moment, and (4) varying frame rates due to different exposures and resolutions. In this thesis, we establish these forms of incompleteness in the scene, as spatio-temporal uncertainties, and propose solutions for resolving the uncertainties by applying scattered data approximation into a spatio-temporal domain. The main contributions of this research are as follows: First, we provide an efficient framework to visualize large-scale dynamic scenes from distributed static videos. Second, we adopt Radial Basis Function (RBF) interpolation to the spatio-temporal domain to generate global motion tendency. The tendency, represented by a dense flow field, is used to optimally pan and tilt a video camera. Third, we propose a method to represent motion trajectories using stochastic vector fields. Gaussian Process Regression (GPR) is used to generate a dense vector field and the certainty of each vector in the field. The generated stochastic fields are used for recognizing motion patterns under varying frame-rate and incompleteness of the input videos. Fourth, we also show that the stochastic representation of vector field can also be used for modeling global tendency to detect the region of interests in dynamic scenes with camera motion. We evaluate and demonstrate our approaches in several applications for visualizing virtual cities, automating sports broadcasting, and recognizing traffic patterns in surveillance videos.