Constructal Design of Energy Systems

This dissertation shows the use of Constructal law to find the relation between the morphing of the system configuration and the improvements in the global performance of the complex flow system. It shows that the better features of both flow and heat transfer architecture can be found and predicted by using the constructal law in energy systems. Chapter 2 shows the effect of flow configuration on the heat transfer performance of a spiral shaped pipe embedded in a cylindrical conducting volume. Several configurations were considered. The optimal spacings between the spiral turns and spire planes exist, such that the volumetric heat transfer rate is maximal. The optimized features of the heat transfer architecture are robust. Chapter 3 shows the heat transfer performance of a helically shaped pipe embedded in a cylindrical conducting volume. It shows that the optimized features of the heat transfer architecture are robust with respect to changes in several physical parameters. Chapter 4 reports analytically the formulas for effective permeability in several configurations of fissured systems, using the closed-form description of tree networks designed to provide flow access. The permeability formulas do not vary much from one tree design to the next, suggesting that similar formulas may apply to naturally fissured porous media with unknown precise details, which occur in natural reservoirs. Chapter 5 illustrates a counterflow heat exchanger consists of two plenums with a core. The results show that the overall flow and thermal resistance are lowest when the core is absent. Overall, the constructal design governs the evolution of flow configuration in nature and energy systems.

Learning and Exploiting Camera Geometry for Computer Vision

This work explores the use of statistical methods in describing and estimating camera poses, as well as the information feedback loop between camera pose and object detection. Surging development in robotics and computer vision has pushed the need for algorithms that infer, understand, and utilize information about the position and orientation of the sensor platforms when observing and/or interacting with their environment.

The first contribution of this thesis is the development of a set of statistical tools for representing and estimating the uncertainty in object poses. A distribution for representing the joint uncertainty over multiple object positions and orientations is described, called the mirrored normal-Bingham distribution. This distribution generalizes both the normal distribution in Euclidean space, and the Bingham distribution on the unit hypersphere. It is shown to inherit many of the convenient properties of these special cases: it is the maximum-entropy distribution with fixed second moment, and there is a generalized Laplace approximation whose result is the mirrored normal-Bingham distribution. This distribution and approximation method are demonstrated by deriving the analytical approximation to the wrapped-normal distribution. Further, it is shown how these tools can be used to represent the uncertainty in the result of a bundle adjustment problem.

Another application of these methods is illustrated as part of a novel camera pose estimation algorithm based on object detections. The autocalibration task is formulated as a bundle adjustment problem using prior distributions over the 3D points to enforce the objects' structure and their relationship with the scene geometry. This framework is very flexible and enables the use of off-the-shelf computational tools to solve specialized autocalibration problems. Its performance is evaluated using a pedestrian detector to provide head and foot location observations, and it proves much faster and potentially more accurate than existing methods.

Finally, the information feedback loop between object detection and camera pose estimation is closed by utilizing camera pose information to improve object detection in scenarios with significant perspective warping. Methods are presented that allow the inverse perspective mapping traditionally applied to images to be applied instead to features computed from those images. For the special case of HOG-like features, which are used by many modern object detection systems, these methods are shown to provide substantial performance benefits over unadapted detectors while achieving real-time frame rates, orders of magnitude faster than comparable image warping methods.

The statistical tools and algorithms presented here are especially promising for mobile cameras, providing the ability to autocalibrate and adapt to the camera pose in real time. In addition, these methods have wide-ranging potential applications in diverse areas of computer vision, robotics, and imaging.