A Hardware Implementation for Colour Edge Detection Using Prewitt-Inspired Filters Based on Geometric Algebra

Abstract

Geometric algebra (GA) is a powerful mathematical tool that offers intuitive solutions for image-processing problems, including colour edge detection. Rotor-based and Prewitt-inspired Sangwine (RBS and PIS) filters are amongst the efficient algorithms based on GA operators for solving colour edge detection problem. Algorithms in GA framework have enormous computational load that limits the general-purpose processors’ ability to execute them in reasonable time. Recently, some specialized hardware architectures, called full-hardware implementations, are proposed. These architectures, such as ConformalALU co-processor, are able to execute GA algorithms in acceptable time with the moderate use of computational resources. So far, all colour edge detection hardwares in GA framework exploited RBS filters. Nevertheless, this novel work presents a full-hardware architecture for efficient execution of PIS filters. PIS filters consume less computational resources and are faster to execute. For comparison, the hardware obtained by Gaalop pre-compiler uses twice as much resources with the same speed as the proposed hardware. As an evidence of faster operation, the proposed hardware is able to execute the edge detection algorithm almost 315 times faster than a GA co-processor, with only 2.5 times of its resources.