PROPAGATION OF SONIC BOOMS THROUGH A REAL, STRATIFIED ATMOSPHERE

Sonic boom propagation in a quiet) stratified) lossy atmosphere is the subject of this dissertation. Two questions are considered in detail: (1) Does waveform freezing occur? (2) Are sonic booms shocks in steady state? Both assumptions have been invoked in the past to predict sonic boom waveforms at the ground. A very general form of the Burgers equation is derived and used as the model for the problem. The derivation begins with the basic conservation equations. The effects of nonlinearity) attenuation and dispersion due to multiple relaxations) viscosity) and heat conduction) geometrical spreading) and stratification of the medium are included. When the absorption and dispersion terms are neglected) an analytical solution is available. The analytical solution is used to answer the first question. Geometrical spreading and stratification of the medium are found to slow down the nonlinear distortion of finite-amplitude waves. In certain cases the distortion reaches an absolute limit) a phenomenon called waveform freezing. Judging by the maturity of the distortion mechanism, sonic booms generated by aircraft at 18 km altitude are not frozen when they reach the ground. On the other hand, judging by the approach of the waveform to its asymptotic shape, N waves generated by aircraft at 18 km altitude are frozen when they reach the ground. To answer the second question we solve the full Burgers equation and for this purpose develop a new computer code, THOR. The code is based on an algorithm by Lee and Hamilton (J. Acoust. Soc. Am. 97, 906-917, 1995) and has the novel feature that all its calculations are done in the time domain, including absorption and dispersion. Results from the code compare very well with analytical solutions. In a NASA exercise to compare sonic boom computer programs, THOR gave results that agree well with those of other participants and ran faster. We show that sonic booms are not steady state waves because they travel through a varying medium, suffer spreading, and fail to approximate step shocks closely enough. Although developed to predict sonic boom propagation, THOR can solve other problems for which the extended Burgers equation is a good propagation model.

Automated Placement of Cameras in a Floorplan to Satisfy Task-Specific Constraints

In many multi-camera vision systems the effect of camera locations on the task-specific quality of service is ignored. Researchers in Computational Geometry have proposed elegant solutions for some sensor location problem classes. Unfortunately, these solutions utilize unrealistic assumptions about the cameras' capabilities that make these algorithms unsuitable for many real-world computer vision applications: unlimited field of view, infinite depth of field, and/or infinite servo precision and speed. In this paper, the general camera placement problem is first defined with assumptions that are more consistent with the capabilities of real-world cameras. The region to be observed by cameras may be volumetric, static or dynamic, and may include holes that are caused, for instance, by columns or furniture in a room that can occlude potential camera views. A subclass of this general problem can be formulated in terms of planar regions that are typical of building floorplans. Given a floorplan to be observed, the problem is then to efficiently compute a camera layout such that certain task-specific constraints are met. A solution to this problem is obtained via binary optimization over a discrete problem space. In preliminary experiments the performance of the resulting system is demonstrated with different real floorplans.

Automated Camera Layout to Satisfy Task-Specific and Floorplan-Specific Coverage Requirements

In many multi-camera vision systems the effect of camera locations on the task-specific quality of service is ignored. Researchers in Computational Geometry have proposed elegant solutions for some sensor location problem classes. Unfortunately, these solutions utilize unrealistic assumptions about the cameras' capabilities that make these algorithms unsuitable for many real-world computer vision applications: unlimited field of view, infinite depth of field, and/or infinite servo precision and speed. In this paper, the general camera placement problem is first defined with assumptions that are more consistent with the capabilities of real-world cameras. The region to be observed by cameras may be volumetric, static or dynamic, and may include holes that are caused, for instance, by columns or furniture in a room that can occlude potential camera views. A subclass of this general problem can be formulated in terms of planar regions that are typical of building floorplans. Given a floorplan to be observed, the problem is then to efficiently compute a camera layout such that certain task-specific constraints are met. A solution to this problem is obtained via binary optimization over a discrete problem space. In experiments the performance of the resulting system is demonstrated with different real floorplans.

3D Trajectory Recovery for Tracking Multiple Objects and Trajectory Guided Recognition of Actions

A mechanism is proposed that integrates low-level (image processing), mid-level (recursive 3D trajectory estimation), and high-level (action recognition) processes. It is assumed that the system observes multiple moving objects via a single, uncalibrated video camera. A novel extended Kalman filter formulation is used in estimating the relative 3D motion trajectories up to a scale factor. The recursive estimation process provides a prediction and error measure that is exploited in higher-level stages of action recognition. Conversely, higher-level mechanisms provide feedback that allows the system to reliably segment and maintain the tracking of moving objects before, during, and after occlusion. The 3D trajectory, occlusion, and segmentation information are utilized in extracting stabilized views of the moving object. Trajectory-guided recognition (TGR) is proposed as a new and efficient method for adaptive classification of action. The TGR approach is demonstrated using "motion history images" that are then recognized via a mixture of Gaussian classifier. The system was tested in recognizing various dynamic human outdoor activities; e.g., running, walking, roller blading, and cycling. Experiments with synthetic data sets are used to evaluate stability of the trajectory estimator with respect to noise.

Trajectory Guided Tracking and Recognition of Actions

A combined 2D, 3D approach is presented that allows for robust tracking of moving people and recognition of actions. It is assumed that the system observes multiple moving objects via a single, uncalibrated video camera. Low-level features are often insufficient for detection, segmentation, and tracking of non-rigid moving objects. Therefore, an improved mechanism is proposed that integrates low-level (image processing), mid-level (recursive 3D trajectory estimation), and high-level (action recognition) processes. A novel extended Kalman filter formulation is used in estimating the relative 3D motion trajectories up to a scale factor. The recursive estimation process provides a prediction and error measure that is exploited in higher-level stages of action recognition. Conversely, higher-level mechanisms provide feedback that allows the system to reliably segment and maintain the tracking of moving objects before, during, and after occlusion. The 3D trajectory, occlusion, and segmentation information are utilized in extracting stabilized views of the moving object that are then used as input to action recognition modules. Trajectory-guided recognition (TGR) is proposed as a new and efficient method for adaptive classification of action. The TGR approach is demonstrated using "motion history images" that are then recognized via a mixture-of-Gaussians classifier. The system was tested in recognizing various dynamic human outdoor activities: running, walking, roller blading, and cycling. Experiments with real and synthetic data sets are used to evaluate stability of the trajectory estimator with respect to noise.

An Invariant Representation for Matching Trajectories across Uncalibrated Video Streams

We introduce a view-point invariant representation of moving object trajectories that can be used in video database applications. It is assumed that trajectories lie on a surface that can be locally approximated with a plane. Raw trajectory data is first locally approximated with a cubic spline via least squares fitting. For each sampled point of the obtained curve, a projective invariant feature is computed using a small number of points in its neighborhood. The resulting sequence of invariant features computed along the entire trajectory forms the view invariant descriptor of the trajectory itself. Time parametrization has been exploited to compute cross ratios without ambiguity due to point ordering. Similarity between descriptors of different trajectories is measured with a distance that takes into account the statistical properties of the cross ratio, and its symmetry with respect to the point at infinity. In experiments, an overall correct classification rate of about 95% has been obtained on a dataset of 58 trajectories of players in soccer video, and an overall correct classification rate of about 80% has been obtained on matching partial segments of trajectories collected from two overlapping views of outdoor scenes with moving people and cars.

View Registration Using Interesting Segments of Planar Trajectories

We introduce a method for recovering the spatial and temporal alignment between two or more views of objects moving over a ground plane. Existing approaches either assume that the streams are globally synchronized, so that only solving the spatial alignment is needed, or that the temporal misalignment is small enough so that exhaustive search can be performed. In contrast, our approach can recover both the spatial and temporal alignment. We compute for each trajectory a number of interesting segments, and we use their description to form putative matches between trajectories. Each pair of corresponding interesting segments induces a temporal alignment, and defines an interval of common support across two views of an object that is used to recover the spatial alignment. Interesting segments and their descriptors are defined using algebraic projective invariants measured along the trajectories. Similarity between interesting segments is computed taking into account the statistics of such invariants. Candidate alignment parameters are verified checking the consistency, in terms of the symmetric transfer error, of all the putative pairs of corresponding interesting segments. Experiments are conducted with two different sets of data, one with two views of an outdoor scene featuring moving people and cars, and one with four views of a laboratory sequence featuring moving radio-controlled cars.