Abstract
This paper describes advancement in color edge detection, using a dedicated Geometric Algebra (GA) co-processor implemented on an Application Specific Integrated Circuit (ASIC). GA provides a rich set of geometric operations, giving the advantage that many signal and image processing operations become straightforward and the algorithms intuitive to design. The use of GA allows images to be represented with the three R, G, B color channels defined as a single entity, rather than separate quantities. A novel custom ASIC is proposed and fabricated that directly targets GA operations and results in significant performance improvement for color edge detection. Use of the hardware described in this paper also shows that the convolution operation with the rotor masks within GA belongs to a class of linear vector filters and can be applied to image or speech signals. The contribution of the proposed approach has been demonstrated by implementing three different types of edge detection schemes on the proposed hardware. The overall performance gains using the proposed GA Co-Processor over existing software approaches are more than 3.2× faster than GAIGEN and more than 2800× faster than GABLE. The performance of the fabricated GA co-processor is approximately an order of magnitude faster than previously published results for hardware implementations.
Highlights
With the pervasive nature of computing devices that use increasingly complex video processing, there is becoming an ever greater need for faster and more efficient processing of image and video data.One of the key areas in this field is edge detection, in color images, and while it is possible to carry out image processing using software, often it is too slow
In order to address this key issue of performance we have designed and implemented a Geometric Algebra Co-Processor that can be applied to image processing, in particular edge detection
Each color pixel is treated as a vector and each convolution operation consists of 12 geometric product multiplications (GP mul) and four geometric product additions (GP add)
Summary
One of the key areas in this field is edge detection, in color images, and while it is possible to carry out image processing using software, often it is too slow. Edge detection is one of the most basic operations in image processing and can be applied to both gray scale and color images. Traditional color edge detection involves applying the uncorrelated monochrome or scalar based technique to three correlated color channels. The techniques of convolution and correlation are quite common to image processing algorithms for scalar fields. Previous work [33] has already reported the usefulness of hypercomplex masks for edge detection and this was extended to rotor convolution by Corrochano-Flores in [8]. The rotor convolution works exactly the same way as the hypercomplex convolution and operates on the color vectors of the image.
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