FPGA-Based Hardware Architecture for Fuzzy Homomorphic Enhancement Based on Partial Differential Equations

Abstract

This paper presents an efficient, high speed hardware architecture for a PDE-based variational fuzzy homomorphic color image enhancement algorithm for both RGB and HSI/HSV color space variants. The developed architecture avoids the use of filters either in the spatial or frequency domain, utilizing an easily implementable fuzzy membership function with a high boost emphasis filter characteristic. This eliminates multiply-accumulate (MAC) operations, which result in increased usage of hardware resources, especially in smaller FPGA devices where multipliers are costly. The resulting implemented multiplier-less architecture yields a soft filtering effect due to the fuzzy evaluation when compared with the hard and crisp homomorphic filters based in the frequency and spatial domain. Based on the device utilization information obtained from hardware synthesis, the fuzzy homomorphic algorithm is shown to be the least computationally complex and faster algorithm. Additionally, the proposed architecture consumes the least amount of hardware resources on the target FPGA when compared with the spatial domain homomorphic filter. This reduced hardware structural and computational complexity makes the system easily incorporated within a PDE-based framework for improved results, which enables gradual but controlled illumination correction. The results show that the proposed system is a more effective and versatile enhancement system than those found in the literature.