Fractional-Order Retinex for Adaptive Contrast Enhancement of Under-Exposed Traffic Images

Yi-Fei Pu, Ni Zhang, Zhengning Wang, Jian Wang, Zhang Yi, Yan Wang, Jiliu Zhou

Abstract: In this paper, a Fractional-order Retinex (FR) for the adaptive contrast enhancement of Under-Exposed Traffic Images (UETI) is proposed to be achieved by the fractional-order variational method. The disposable reconstructive results of the contrast enhancement of UETI play a significant role in traffic safety and are often taken as intermediate results for the traffic virtual reality and augmented reality of intelligent transportation systems. To this end, this paper proposes a state-ofthe-art application of a promising mathematical method, fractional calculus, to extend the classic integer-order Retinex to the fractional-order one, a FR, which leads to a fractional-order algebraic regularization term and contributes to better conditioning of the reconstruction problem. At first, the fractional-order isotropic equation related to a FR is implemented by the Fractional-order Steepest Descent Method (FSDM). Secondly, the corresponding restrictive fractional-order optimization is achieved. Finally, the capability of a FR to non-linearly preserve complex textural details as well as desired contrast enhancing is validated by experimental analysis, which is a major advantage superior to conventional contrast enhancement algorithms, especially for UETI rich in textural details. The paper gives a novel mathematical approach, fractional calculus, to the family of Retinex algorithms that differs from most of the previous approaches and as such, it represents an interesting theoretical contribution.