AHCI RESEARCH GROUP

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2015

Franchini, Silvia; Gentile, Antonio; Sorbello, Filippo; Vassallo, Giorgio; Vitabile, Salvatore

ConformalALU: A Conformal Geometric Algebra Coprocessor for Medical Image Processing Journal Article

In: IEEE Transactions on Computers, vol. 64, no. 4, pp. 955–970, 2015, ISSN: 0018-9340.

Abstract | Links | BibTeX | Tags: 3D modeling, Clifford algebra, Computational geometry, Conformal geometric algebra, Embedded coprocessors, Field Programmable Gate Arrays, FPGA prototyping, Geometric algebra, Growing Neural Gas, iterative closest point (ICP), marching spheres, Medical image registration, Medical Imaging, Segmentation, systems-on-programmable-chip, thin-plate spline robust point matching (TPS-RPM), Volume registration

@article{franchiniConformalALUConformalGeometric2015,

title = {ConformalALU: A Conformal Geometric Algebra Coprocessor for Medical Image Processing},

author = { Silvia Franchini and Antonio Gentile and Filippo Sorbello and Giorgio Vassallo and Salvatore Vitabile},

doi = {10.1109/TC.2014.2315652},

issn = {0018-9340},

year  = {2015},

date = {2015-01-01},

journal = {IEEE Transactions on Computers},

volume = {64},

number = {4},

pages = {955--970},

abstract = {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 scaling) aimed at a parallel hardware implementation. A specialized coprocessing architecture (ConformalALU) that offers direct hardware support to the new CGA operators, is also presented. The ConformalALU has been prototyped as a complete System-on-Programmable-Chip (SoPC) on the Xilinx ML507 FPGA board, containing a Virtex-5 FPGA device. Experimental results show average speedups of one order of magnitude for CGA rotations, translations, and dilations with respect to the geometric algebra software library Gaigen running on the general-purpose PowerPC processor embedded in the target FPGA device. A suite of medical imaging applications, including segmentation, 3D modeling and registration of medical data, has been used as testbench to evaluate the coprocessor effectiveness. textcopyright 2015 IEEE.},

keywords = {3D modeling, Clifford algebra, Computational geometry, Conformal geometric algebra, Embedded coprocessors, Field Programmable Gate Arrays, FPGA prototyping, Geometric algebra, Growing Neural Gas, iterative closest point (ICP), marching spheres, Medical image registration, Medical Imaging, Segmentation, systems-on-programmable-chip, thin-plate spline robust point matching (TPS-RPM), Volume registration},

pubstate = {published},

tppubtype = {article}

}