Analysis of Differential and Matching Methods for Optical Flow

Several algorithms for optical flow are studied theoretically and experimentally. Differential and matching methods are examined; these two methods have differing domains of application- differential methods are best when displacements in the image are small (<2 pixels) while matching methods work well for moderate displacements but do not handle sub-pixel motions. Both types of optical flow algorithm can use either local or global constraints, such as spatial smoothness. Local matching and differential techniques and global differential techniques will be examined. Most algorithms for optical flow utilize weak assumptions on the local variation of the flow and on the variation of image brightness. Strengthening these assumptions improves the flow computation. The computational consequence of this is a need for larger spatial and temporal support. Global differential approaches can be extended to local (patchwise) differential methods and local differential methods using higher derivatives. Using larger support is valid when constraint on the local shape of the flow are satisfied. We show that a simple constraint on the local shape of the optical flow, that there is slow spatial variation in the image plane, is often satisfied. We show how local differential methods imply the constraints for related methods using higher derivatives. Experiments show the behavior of these optical flow methods on velocity fields which so not obey the assumptions. Implementation of these methods highlights the importance of numerical differentiation. Numerical approximation of derivatives require care, in two respects: first, it is important that the temporal and spatial derivatives be matched, because of the significant scale differences in space and time, and, second, the derivative estimates improve with larger support.

Multiple-User Quantum Optical Communication

A fundamental understanding of the information carrying capacity of optical channels requires the signal and physical channel to be modeled quantum mechanically. This thesis considers the problems of distributing multi-party quantum entanglement to distant users in a quantum communication system and determining the ability of quantum optical channels to reliably transmit information. A recent proposal for a quantum communication architecture that realizes long-distance, high-fidelity qubit teleportation is reviewed. Previous work on this communication architecture is extended in two primary ways. First, models are developed for assessing the effects of amplitude, phase, and frequency errors in the entanglement source of polarization-entangled photons, as well as fiber loss and imperfect polarization restoration, on the throughput and fidelity of the system. Second, an error model is derived for an extension of this communication architecture that allows for the production and storage of three-party entangled Greenberger-Horne-Zeilinger states. A performance analysis of the quantum communication architecture in qubit teleportation and quantum secret sharing communication protocols is presented. Recent work on determining the channel capacity of optical channels is extended in several ways. Classical capacity is derived for a class of Gaussian Bosonic channels representing the quantum version of classical colored Gaussian-noise channels. The proof is strongly mo- tivated by the standard technique of whitening Gaussian noise used in classical information theory. Minimum output entropy problems related to these channel capacity derivations are also studied. These single-user Bosonic capacity results are extended to a multi-user scenario by deriving capacity regions for single-mode and wideband coherent-state multiple access channels. An even larger capacity region is obtained when the transmitters use non- classical Gaussian states, and an outer bound on the ultimate capacity region is presented