ConformalALU: A Conformal Geometric Algebra Coprocessor for Medical Image Processing

PROJECT TITLE :

ConformalALU: A Conformal Geometric Algebra Coprocessor for Medical Image Processing

ABSTRACT:

Medical imaging involves important computational geometric problems, such as image segmentation and analysis, shape approximation, 3-dimensional (3D) modeling, and registration of volumetric data. In the previous few years, Conformal Geometric Algebra (CGA), primarily based on 5-dimensional (5D) Clifford Algebra, is rising as a brand new paradigm that offers simple and universal operators for the representation and resolution of advanced geometric issues. However, the widespread use of CGA has been thus so much 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 toward a parallel hardware implementation. A specialized coprocessing architecture (ConformalALU) that gives direct hardware support to the new CGA operators, is additionally 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 1 order of magnitude for CGA rotations, translations, and dilations with respect to the geometric algebra software library Gaigen running on the final-purpose PowerPC processor embedded in the target FPGA device. A suite of medical imaging applications, as well as segmentation, 3D modeling and registration of medical information, has been used as testbench to guage the coprocessor effectiveness.

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