Riesz fractional derivative based homomorphic filtering for image enhancement

The visual quality of images is the primary concern of the image enhancement approaches. There is a need to enhance the images visually due to loss of details or degradation in their quality during acquisition or transmission. This paper provides the Riesz Fractional Derivative (RFD) based Homomorphic Filtering (HF) in Fractional Fourier Transform (FrFT) for enhancing the non-uniformly illuminated images. In this method, the logarithm of the image is taken to convert it into illumination and reflectance components which are converted into fractional Fourier domain for performing the RFD filtering for enhancement. Then, the inverse FrFT and exponential are taken to obtain the enhanced image in the spatial domain. This approach provides more flexibility owing to two additional degrees of freedom for achieving better visual quality. The adequacy of the presented approach is evaluated by considering the qualitative and quantitative measures such as Information Entropy (IE), Peak-Signal-to-Noise-Ratio (PSNR), Universal Image Quality Index (UIQI), etc. by taking into consideration images from different datasets. The presented RFD approach outperforms the existing approaches as it shows a minimum improvement of 1.18 dB in average PSNR and 0.15% in average IE for considered test images. Even the other parameters show their superiority over the existing techniques.