ANALYSIS AND VISUALIZATION OF FLOW FIELDS USING INFORMATION-THEORETIC TECHNIQUES AND GRAPH-BASED REPRESENTATIONS

Three-dimensional flow visualization plays an essential role in many areas of science and engineering, such as aero- and hydro-dynamical systems which dominate various physical and natural phenomena. For popular methods such as the streamline visualization to be effective, they should capture the underlying flow features while facilitating user observation and understanding of the flow field in a clear manner. My research mainly focuses on the analysis and visualization of flow fields using various techniques, e.g. information-theoretic techniques and graph-based representations. Since the streamline visualization is a popular technique in flow field visualization, how to select good streamlines to capture flow patterns and how to pick good viewpoints to observe flow fields become critical. We treat streamline selection and viewpoint selection as symmetric problems and solve them simultaneously using the dual information channel [81]. To the best of my knowledge, this is the first attempt in flow visualization to combine these two selection problems in a unified approach. This work selects streamline in a view-independent manner and the selected streamlines will not change for all viewpoints. My another work [56] uses an information-theoretic approach to evaluate the importance of each streamline under various sample viewpoints and presents a solution for view-dependent streamline selection that guarantees coherent streamline update when the view changes gradually. When projecting 3D streamlines to 2D images for viewing, occlusion and clutter become inevitable. To address this challenge, we design FlowGraph [57, 58], a novel compound graph representation that organizes field line clusters and spatiotemporal regions hierarchically for occlusion-free and controllable visual exploration. We enable observation and exploration of the relationships among field line clusters, spatiotemporal regions and their interconnection in the transformed space. Most viewpoint selection methods only consider the external viewpoints outside of the flow field. This will not convey a clear observation when the flow field is clutter on the boundary side. Therefore, we propose a new way to explore flow fields by selecting several internal viewpoints around the flow features inside of the flow field and then generating a B-Spline curve path traversing these viewpoints to provide users with closeup views of the flow field for detailed observation of hidden or occluded internal flow features [54]. This work is also extended to deal with unsteady flow fields. Besides flow field visualization, some other topics relevant to visualization also attract my attention. In iGraph [31], we leverage a distributed system along with a tiled display wall to provide users with high-resolution visual analytics of big image and text collections in real time. Developing pedagogical visualization tools forms my other research focus. Since most cryptography algorithms use sophisticated mathematics, it is difficult for beginners to understand both what the algorithm does and how the algorithm does that. Therefore, we develop a set of visualization tools to provide users with an intuitive way to learn and understand these algorithms.

Supersymmetric Mode Converters

Originally developed in the context of quantum field theory, the concept of supersymmetry can be used to systematically design a new class of optical structures. In this work, we demonstrate how key features arising from optical supersymmetry can be exploited to control the flow of light for mode division multiplexing applications. Superpartner configurations are experimentally realized in coupled optical networks, and the corresponding light dynamics in such systems are directly observed. We show that supersymmetry can be judiciously utilized to remove the fundamental mode of a multimode optical structure, while establishing global phase matching conditions for the remaining set of modes. Along these lines, supersymmetry may serve as a promising platform for versatile optical components with desirable properties and functionalities.

Comparison of Computer-Based and Optical Face Recognition Paradigms

The main objectives of this thesis are to validate an improved principal components analysis (IPCA) algorithm on images; designing and simulating a digital model for image compression, face recognition and image detection by using a principal components analysis (PCA) algorithm and the IPCA algorithm; designing and simulating an optical model for face recognition and object detection by using the joint transform correlator (JTC); establishing detection and recognition thresholds for each model; comparing between the performance of the PCA algorithm and the performance of the IPCA algorithm in compression, recognition and, detection; and comparing between the performance of the digital model and the performance of the optical model in recognition and detection. The MATLAB © software was used for simulating the models. PCA is a technique used for identifying patterns in data and representing the data in order to highlight any similarities or differences. The identification of patterns in data of high dimensions (more than three dimensions) is too difficult because the graphical representation of data is impossible. Therefore, PCA is a powerful method for analyzing data. IPCA is another statistical tool for identifying patterns in data. It uses information theory for improving PCA. The joint transform correlator (JTC) is an optical correlator used for synthesizing a frequency plane filter for coherent optical systems. The IPCA algorithm, in general, behaves better than the PCA algorithm in the most of the applications. It is better than the PCA algorithm in image compression because it obtains higher compression, more accurate reconstruction, and faster processing speed with acceptable errors; in addition, it is better than the PCA algorithm in real-time image detection due to the fact that it achieves the smallest error rate as well as remarkable speed. On the other hand, the PCA algorithm performs better than the IPCA algorithm in face recognition because it offers an acceptable error rate, easy calculation, and a reasonable speed. Finally, in detection and recognition, the performance of the digital model is better than the performance of the optical model.