Search results for " computational"
showing 10 items of 661 documents
Un metodo numerico incodizionatamente stabile mesh-free per l'analisi elettromagnetica
2012
ConformalALU: A Conformal Geometric Algebra Coprocessor for Medical Image Processing
2015
Medical imaging involves important computational geometric problems, such as image segmentation and analysis, shape approximation, three-dimensional (3D) modeling, and registration of volumetric data. In the last few years, Conformal Geometric Algebra (CGA), based on five-dimensional (5D) Clifford Algebra, is emerging as a new paradigm that offers simple and universal operators for the representation and solution of complex geometric problems. However, the widespread use of CGA has been so far hindered by its high dimensionality and computational complexity. This paper proposes a simplified formulation of the conformal geometric operations (reflections, rotations, translations, and uniform …
A Sliced Coprocessor for Native Clifford Algebra Operations
2007
Computer graphics applications require efficient tools to model geometric objects. The traditional approach based on compute-intensive matrix calculations is error-prone due to a lack of integration between geometric reasoning and matrix-based algorithms. Clifford algebra offers a solution to these issues since it permits specification of geometry at a coordinate-free level. The best way to exploit the symbolic computing power of geometric (Clifford) algebra is supporting its data types and operators directly in hardware. This paper outlines the architecture of S-CliffoSor (Sliced Clifford coprocessor), a parallelizable embedded coprocessor that executes native Clifford algebra operations. …
Design and implementation of an embedded coprocessor with native support for 5D, quadruple-based Clifford algebra
2013
Geometric or Clifford algebra (CA) is a powerful mathematical tool that offers a natural and intuitive way to model geometric facts in a number of research fields, such as robotics, machine vision, and computer graphics. Operating in higher dimensional spaces, its practical use is hindered, however, by a significant computational cost, only partially addressed by dedicated software libraries and hardware/software codesigns. For low-dimensional algebras, several dedicated hardware accelerators and coprocessing architectures have been already proposed in the literature. This paper introduces the architecture of CliffordALU5, an embedded coprocessing core conceived for native execution of up t…
TSVD as a Statistical Estimator in the Latent Semantic Analysis Paradigm
2015
The aim of this paper is to present a new point of view that makes it possible to give a statistical interpretation of the traditional latent semantic analysis (LSA) paradigm based on the truncated singular value decomposition (TSVD) technique. We show how the TSVD can be interpreted as a statistical estimator derived from the LSA co-occurrence relationship matrix by mapping probability distributions on Riemanian manifolds. Besides, the quality of the estimator model can be expressed by introducing a figure of merit arising from the Solomonoff approach. This figure of merit takes into account both the adherence to the sample data and the simplicity of the model. In our model, the simplicity…
An Embedded, FPGA-based Computer Graphics Coprocessor with Native Geometric Algebra Support
2009
The representation of geometric objects and their transformation are the two key aspects in computer graphics applications. Traditionally, computer-intensive matrix calculations are involved in modeling and rendering three-dimensional (3D) scenery. Geometric algebra (aka Clifford algebra) is attracting attention as a natural way to model geometric facts and as a powerful analytical tool for symbolic calculations. In this paper, the architecture of Clifford coprocessor (CliffoSor) is introduced. CliffoSor is an embedded parallel coprocessing core that offers direct hardware support to Clifford algebra operators. A prototype implementation on a programmable gate array (FPGA) board is detailed…
Fixed-size Quadruples for a New, Hardware-Oriented Representation of the 4D Clifford Algebra
2010
Clifford algebra (geometric algebra) offers a natural and intuitive way to model geometry in fields as robotics, machine vision and computer graphics. This paper proposes a new representation based on fixed-size elements (quadruples) of 4D Clifford algebra and demonstrates that this choice leads to an algorithmic simplification which in turn leads to a simpler and more compact hardware implementation of the algebraic operations. In order to prove the advantages of the new, quadruple-based representation over the classical representation based on homogeneous elements, a coprocessing core supporting the new fixed-size Clifford operands, namely Quad-CliffoSor (Quadruple-based Clifford coproces…
Design Space Exploration of Parallel Embedded Architectures for Native Clifford Algebra Operations
2012
In the past few decades, Geometric or Clifford algebra (CA) has received a growing attention in many research fields, such as robotics, machine vision and computer graphics, as a natural and intuitive way to model geometric objects and their transformations. At the same time, the high dimensionality of Clifford algebra and its computational complexity demand specialized hardware architectures for the direct support of Clifford data types and operators. This paper presents the design space exploration of parallel embedded architectures for native execution of four-dimensional (4D) and five-dimensional (5D) Clifford algebra operations. The design space exploration has been described along wit…
An FPGA Implementation of a Quadruple-Based Multiplier for 4D Clifford Algebra
2008
Geometric or Clifford algebra is an interesting paradigm for geometric modeling in fields as computer graphics, machine vision and robotics. In these areas the research effort is actually aimed at finding an efficient implementation of geometric algebra. The best way to exploit the symbolic computing power of geometric algebra is to support its data types and operators directly in hardware. However the natural representation of the algebra elements as variable-length objects causes some problems in the case of a hardware implementation. This paper proposes a 4D Clifford algebra in which the variable-length elements are mapped into fixed-length elements (quadruples). This choice leads to a s…
Cloaking In-Plane Elastic Waves with Swiss Rolls
2020
We propose a design of cylindrical cloak for coupled in-plane shear waves consisting of concentric layers of sub-wavelength resonant stress-free inclusions shaped as Swiss rolls. The scaling factor between inclusions&rsquo