Search results for "Geometric"

showing 10 items of 652 documents

Graphic Coprocessors with Native Clifford Algebra Support

2009

Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniClifford Algebra Geometric Algebra Embedded Coprocessors Application-specific Processors FPGA Prototyping
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A brief introduction to Clifford algebra

2010

Geometric algebra (also known as Clifford algebra) is a powerful mathematical tool that offers a natural and direct way to model geometric objects and their transformations. It is gaining growing attention in different research fields as physics, robotics, CAD/CAM and computer graphics. Clifford algebra makes geometric objects (points, lines and planes) into basic elements of computation and defines few universal operators that are applicable to all types of geometric elements. This paper provides an introduction to Clifford algebra elements and operators.

Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniClifford algebra Geometric algebra
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4D Clifford algebra based on fixed-size representation

2008

Geometric algebra (also known as Clifford algebra) is a powerful mathematical tool that offers a natural and direct way to model geometric objects and their transformations. It is gaining growing attention in different research fields as physics, robotics, CAD/CAM and computer graphics. In particular, 4D geometric algebra implements homogeneous coordinates, which are used to model 3D scenery in most computer graphics applications. The research work on Clifford algebra is actually aimed at finding efficient implementations of the algebra. This paper wants to give a contribution to this research effort by proposing a direct hardware support for geometric algebra operators. The paper introduce…

Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniClifford algebra Geometric algebra Homogeneous model Fixed-size representation
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A brief introduction to Clifford algebra

2010

Geometric algebra (also known as Clifford algebra) is a powerful mathematical tool that offers a natural and direct way to model geometric objects and their transformations. It is gaining growing attention in different research fields as physics, robotics, CAD/CAM and computer graphics. Clifford algebra makes geometric objects (points, lines and planes) into basic elements of computation and defines few universal operators that are applicable to all types of geometric elements. This paper provides an introduction to Clifford algebra elements and operators.

Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniClifford algebrageometric algebra
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Real-time estimation of geometrical transformation between views in distributed smart-cameras systems

2008

In this paper, we present a method to automatically estimate the geometric relations among the different views of cameras with partially overlapping fields of view in a wireless video-surveillance system. The method uses the locations of the detected moving objects visible at the same time in two or more views. The correspondences among objects are found by comparing their appearance models based on dominant colour descriptors while the geometric transformation are computed iteratively and may be used to solve the consistent labelling problem. As a significant part of the processing is performed on the smart cameras, the method has been conceived by taking into account the limited resources…

Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniComputer sciencebusiness.industryGeometric transformationMotion detectiondistributed video surveillanceObject detectionData modelingTransformation (function)Computer visionSmart cameraArtificial intelligenceImage sensorbusinessHomography (computer vision)2008 Second ACM/IEEE International Conference on Distributed Smart Cameras
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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 …

Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniCoprocessorComputer scienceClifford algebraConformal geometric algebraConformal mapImage processingParallel computingImage segmentationComputational geometryTheoretical Computer ScienceGeometric algebraOperator (computer programming)Computational Theory and MathematicsConformal geometric algebra five-dimensional clifford algebra computational geometry embedded coprocessors systems-on-programmable-chip FPGA-based prototyping medical imaging segmentation 3D modeling Volume registration Growing Neural Gas marching spheres iterative closest point (ICP) thin-plate spline robust point matching (TPS-RPM)Hardware and ArchitectureScalingSoftwareIEEE Transactions on Computers
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A New Embedded Coprocessor for Clifford Algebra based Software Intensive Systems

2011

Computer graphics applications require efficient tools to model geometric objects and their transformations. Clifford algebra (also known as geometric algebra) is receiving a growing attention in many research fields, such as computer graphics, machine vision and robotics, as a new, interesting computational paradigm that offers a natural and intuitive way to perform geometric calculations. At the same time, compute-intensive graphics algorithms require the execution of million Clifford operations. Clifford algebra based software intensive systems need therefore the support of specialized hardware architectures capable of accelerating Clifford operations execution. In this paper the archite…

Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniCoprocessorSpeedupComputer sciencebusiness.industryembedded coprocessorsClifford algebraParallel computingcomputer graphicComputer graphicsGeometric algebracompute-intensive algorithmSoftwaresoftware intensive systemComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONcomputational geometryGraphicsClifford algebraField-programmable gate arraybusiness
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GAPPCO: An Easy to Configure Geometric Algebra Coprocessor Based on GAPP Programs

2017

Because of the high numeric complexity of Geometric Algebra, its use in engineering applications relies heavily on tools and devices for efficient implementations. In this article, we present a novel hardware design for a Geometric Algebra coprocessor, called GAPPCO, which is based on Geometric Algebra Parallelism Programs (GAPP). GAPPCO is a design for a coprocessor combining the advantages of optimizing software with a configurable hardware able to implement arbitrary Geometric Algebra algorithms. The idea is to have a fixed hardware easily and fast to be configured for different algorithms. We describe the new hardware design together with the complete tool chain for its configuration.

Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniCoprocessorTheoretical computer sciencebusiness.industryApplied MathematicsConfigurable hardware02 engineering and technologyParallel computing01 natural sciences020202 computer hardware & architectureComputer Science::Hardware ArchitectureGeometric algebraSoftwareChain (algebraic topology)0103 physical sciencesGeometric Algebra Geometric Algebra computing Gaalop GAPP GAPPCO0202 electrical engineering electronic engineering information engineeringParallelism (grammar)GapP010307 mathematical physicsbusinessImplementationMathematicsAdvances in Applied Clifford Algebras
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Clifford Rotors for Conceptual Representation in Chatbots

2013

In this abstract we introduce an unsupervised sub-symbolic natural language sentences encoding procedure aimed at catching and representing into a Chatbot Knowledge Base (KB) the concepts expressed by an user interacting with a robot. The chatbot KB is coded in a conceptual space induced from the application of the Latent Semantic Analysis (LSA) paradigm on a corpus of documents. LSA has the effect of decomposing the original relationships between elements into linearly-independent vectors. Each basis vector can be considered therefore as a "conceptual coordinate", which can be tagged by the words which better characterize it. This tagging is obtained by performing a (TF-IDF)-like weighting…

Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniDiscrete mathematicsComputer sciencebusiness.industryLatent semantic analysisInformationSystems_INFORMATIONSTORAGEANDRETRIEVALRepresentation (systemics)computer.software_genreChatbotGeometric algebraKnowledge baseArtificial IntelligenceEncoding (semiotics)chatbot clifford algebraArtificial intelligenceDialog systembusinesscomputerNatural language processingNatural language
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A Family of Embedded Coprocessors with Native Geometric Algebra Support

2015

Clifford Algebra or Geometric Algebra (GA) is a simple and intuitive way to model geometric objects and their transformations. Operating in high-dimensional vector spaces with significant computational costs, the practical use of GA requires, however, dedicated software and/or hardware architectures to directly support Clifford data types and operators. In this paper, a family of embedded coprocessors for the native execution of GA operations is presented. The paper shows the evolution of the coprocessor family focusing on the latest two architectures that offer direct hardware support to up to five-dimensional Clifford operations. The proposed coprocessors exploit hardware-oriented represe…

Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniGeometric Algebra Embedded Coprocessors Application- Specic Processors FPGA-based Prototyping
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