FPGA-Accelerated Color Edge Detection Using a Geometric-Algebra-To-Verilog Compiler

Abstract — Geometric Algebra (GA) is a branch of mathematics that generalizes complex numbers and quaternions. One of the advantages of the framework is, that it allows intuitive description and manipulation of geometric objects. While even complex operations can be described concisely, the actual evaluation of these GA expressions is extremely compute intensive. However, it has significant fine-grained parallelism, which makes it a profitable target for hardware implementation. In this paper, we present the automatic acceleration of a color edge-detection algorithm from a GA description. Using our Gaalop GA compiler with its Verilog back-end, we can show speed-ups of over 1000x even compared to a recent GA processor ASIC. I