High-speed Robert’s Cross edge detector using residue number system

Abstract

Digital image processing is one of the high demands in the market that is targeted from a variety of fields. This demand has arisen because of the introduction of applications for editing and capturing images in the market. In image processing, the Robert's Cross Detector (RCD) is a detector that conducts median reordering, picture smoothing, and quick 2-D convolution on an image to discover edge pixels. This approach is based on noise reduction and gradient-based edge detection algorithms. RCD is designed to avoid creating statistics that are artificial while highlighting changes in intensity that occur in a diagonal direction. When it comes to speed, power consumption, and throughput rate application, having a mathematical arithmetic process with a high throughput is always one of the most important factors to attain. Positional number system requires large bit width to process the data which slows down the computation and becomes the major issue while processing the edge detection. On the other hand, the complexity of this implementation's design and the amount of computing it requires make it expensive to implement. Therefore, Residue Number System (RNS) architecture is implemented to replace normal PNS architecture. The RNS represents binary numbers using a set of residue numbers. Each modulus in the moduli set transforms enormous numbers into a collection of small residue numbers without requiring the full propagation chain length of adders and multipliers. Due to the carry free characteristic of residue numbers, the calculation on the set of residue numbers can be performed in parallel. As a result, RNS outperforms conventional positional number systems in mathematical computations. This study aims to create an RNS-based RCD with a high computing speed and throughput for processing picture data. In Gaussian filter and Robert Cross Operator (RCO) functional blocks, arithmetic units are implemented in Positional Number System and Residue Number System. Those units are replaced with smaller bit width of modulo adder and multiplier in residue number system. Simulation is carried out in Quartus Prime 21.1 and compiled in Synopsys Design Compiler. The Signal Noise Ratio, Peak Signal Noise Ratio, and absolute percentage error show better results in the RNS-based Gaussian Filter functional block. The results are similar for both the PNS and RNS-based RCO functional blocks. From the result of Synopsys Design Compiler, the operating frequency and throughput of RNS-based RCD are 282MHz and 3384MHz, whereas for PNS-based RCD, they are 151MHz and 2416MHz. The area of the RNS-based RCD and PNS-based RCD is 1187212.12um and 1143353.53um, respectively. For power analysis, RNS-based RCD consumed more power, which is 299.138mW, whereas PNS-based RCD consumed 290.646mW. In conclusion, the RNS-based RCD outperforms the PNS-based RCD by 86.75% and 40.10% from the speed perspective, but it traded off and required higher area and power, with a percentage of 3.83% and 2.92%, respectively.