An Optimized Architecture for CGA Operations and Its Application to a Simulated Robotic Arm

Conformal geometric algebra (CGA) is a new geometric computation tool that is attracting growing attention in many research fields, such as computer graphics, robotics, and computer vision. Regarding the robotic applications, new approaches based on CGA have been proposed to efficiently solve problems as the inverse kinematics and grasping of a robotic arm. The hardware acceleration of CGA operations is required to meet real-time performance requirements in embedded robotic platforms. In this paper, we present a novel embedded coprocessor for accelerating CGA operations in robotic tasks. Two robotic algorithms, namely, inverse kinematics and grasping of a human-arm-like kinematics chain, are used to prove the effectiveness of the proposed approach. The coprocessor natively supports the entire set of CGA operations including both basic operations (products, sums/differences, and unary operations) and complex operations as rigid body motion operations (reflections, rotations, translations, and dilations). The coprocessor prototype is implemented on the Xilinx ML510 development platform as a complete system-on-chip (SoC), integrating both a PowerPC processing core and a CGA coprocessing core on the same Xilinx Virtex-5 FPGA chip. Experimental results show speedups of 78x and 246x for inverse kinematics and grasping algorithms, respectively, with respect to the execution on the PowerPC processor

Implementation and evaluation of medical imaging techniques based on conformal geometric algebra

Medical imaging tasks, such as segmentation, 3D modeling, and registration of medical images, involve complex geometric problems, usually solved by standard linear algebra and matrix calculations. In the last few decades, conformal geometric algebra (CGA) has emerged as a new approach to geometric computing that offers a simple and efficient representation of geometric objects and transformations. However, the practical use of CGA-based methods for big data image processing in medical imaging requires fast and efficient implementations of CGA operations to meet both real-time processing constraints and accuracy requirements. The purpose of this study is to present a novel implementation of CGA-based medical imaging techniques that makes them effective and practically usable. The paper exploits a new simplified formulation of CGA operators that allows significantly reduced execution times while maintaining the needed result precision. We have exploited this novel CGA formulation to re-design a suite of medical imaging automatic methods, including image segmentation, 3D reconstruction and registration. Experimental tests show that the re-formulated CGA-based methods lead to both higher precision results and reduced computation times, which makes them suitable for big data image processing applications. The segmentation algorithm provides the Dice index, sensitivity and specificity values of 98.14%, 98.05% and 97.73%, respectively, while the order of magnitude of the errors measured for the registration methods is 10-5

Pattern Recognition

Pattern recognition is a very wide research field. It involves factors as diverse as sensors, feature extraction, pattern classification, decision fusion, applications and others. The signals processed are commonly one, two or three dimensional, the processing is done in real- time or takes hours and days, some systems look for one narrow object class, others search huge databases for entries with at least a small amount of similarity. No single person can claim expertise across the whole field, which develops rapidly, updates its paradigms and comprehends several philosophical approaches. This book reflects this diversity by presenting a selection of recent developments within the area of pattern recognition and related fields. It covers theoretical advances in classification and feature extraction as well as application-oriented works. Authors of these 25 works present and advocate recent achievements of their research related to the field of pattern recognition

Programmable Image-Based Light Capture for Previsualization

Previsualization is a class of techniques for creating approximate previews of a movie sequence in order to visualize a scene prior to shooting it on the set. Often these techniques are used to convey the artistic direction of the story in terms of cinematic elements, such as camera movement, angle, lighting, dialogue, and character motion. Essentially, a movie director uses previsualization (previs) to convey movie visuals as he sees them in his minds-eye . Traditional methods for previs include hand-drawn sketches, Storyboards, scaled models, and photographs, which are created by artists to convey how a scene or character might look or move. A recent trend has been to use 3D graphics applications such as video game engines to perform previs, which is called 3D previs. This type of previs is generally used prior to shooting a scene in order to choreograph camera or character movements. To visualize a scene while being recorded on-set, directors and cinematographers use a technique called On-set previs, which provides a real-time view with little to no processing. Other types of previs, such as Technical previs, emphasize accurately capturing scene properties but lack any interactive manipulation and are usually employed by visual effects crews and not for cinematographers or directors. This dissertation\u27s focus is on creating a new method for interactive visualization that will automatically capture the on-set lighting and provide interactive manipulation of cinematic elements to facilitate the movie maker\u27s artistic expression, validate cinematic choices, and provide guidance to production crews. Our method will overcome the drawbacks of the all previous previs methods by combining photorealistic rendering with accurately captured scene details, which is interactively displayed on a mobile capture and rendering platform. This dissertation describes a new hardware and software previs framework that enables interactive visualization of on-set post-production elements. A three-tiered framework, which is the main contribution of this dissertation is; 1) a novel programmable camera architecture that provides programmability to low-level features and a visual programming interface, 2) new algorithms that analyzes and decomposes the scene photometrically, and 3) a previs interface that leverages the previous to perform interactive rendering and manipulation of the photometric and computer generated elements. For this dissertation we implemented a programmable camera with a novel visual programming interface. We developed the photometric theory and implementation of our novel relighting technique called Symmetric lighting, which can be used to relight a scene with multiple illuminants with respect to color, intensity and location on our programmable camera. We analyzed the performance of Symmetric lighting on synthetic and real scenes to evaluate the benefits and limitations with respect to the reflectance composition of the scene and the number and color of lights within the scene. We found that, since our method is based on a Lambertian reflectance assumption, our method works well under this assumption but that scenes with high amounts of specular reflections can have higher errors in terms of relighting accuracy and additional steps are required to mitigate this limitation. Also, scenes which contain lights whose colors are a too similar can lead to degenerate cases in terms of relighting. Despite these limitations, an important contribution of our work is that Symmetric lighting can also be leveraged as a solution for performing multi-illuminant white balancing and light color estimation within a scene with multiple illuminants without limits on the color range or number of lights. We compared our method to other white balance methods and show that our method is superior when at least one of the light colors is known a priori

The Coherent Parity Check Framework for Quantum Error Correction

Quantum error correction protocols are an essential element in the design of any circuit-model quantum computer. In this thesis, I introduce the coherent parity check (CPC) framework for quantum error correction. CPC codes have a fundamental structure in which quantum parity check measurements are stored coherently and compared over time. The specific advantage of the CPC code structure is that it provides a way of creating new stabilizer codes from the starting point of any sequence of parity checks. I show that this freedom in the choice of parity checks can be used to derive methods for the construction of distance-three quantum codes based on almost any distance-three classical code. The CPC framework has further applications in machine search routines for code discovery, as well as in the design of bespoke codes tailored for the demands of a given device. Another feature of CPC codes is that they can be represented as factor graphs of the type commonly seen in classical error correction and machine learning. I outline a procedure for this mapping, and demonstrate how a quantum code can be derived by manipulating its factor graph representation. The aim of the factor graph mapping for CPC codes is to make it easier to adapt well-developed techniques from classical information theory for use with quantum codes. This will make the CPC framework a useful tool for the theoretical and practical study of quantum error correction codes as large-scale quantum computers move closer to becoming a reality