Iterative exact global histogram specification and SSIM gradient ascent: a proof of convergence, step size and parameter selection

The SSIM-optimized exact global histogram specification (EGHS) is shown to converge in the sense that the first order approximation of the result's quality (i.e., its structural similarity with input) does not decrease in an iteration, when the step size is small. Each iteration is composed of SSIM gradient ascent and basic EGHS with the specified target histogram. Selection of step size and other parameters is also discussed.

Over-enhancement Reduction in Local Histogram Equalization using its Degrees of Freedom

A well-known issue of local (adaptive) histogram equalization (LHE) is over-enhancement (i.e., generation of spurious details) in homogenous areas of the image. In this paper, we show that the LHE problem has many solutions due to the ambiguity in ranking pixels with the same intensity. The LHE solution space can be searched for the images having the maximum PSNR or structural similarity (SSIM) with the input image. As compared to the results of the prior art, these solutions are more similar to the input image while offering the same local contrast. Index Terms: histogram modification or specification, contrast enhancement

Exact Histogram Specification Optimized for Structural Similarity

An exact histogram specification (EHS) method modifies its input image to have a specified histogram. Applications of EHS include image (contrast) enhancement (e.g., by histogram equalization) and histogram watermarking. Performing EHS on an image, however, reduces its visual quality. Starting from the output of a generic EHS method, we maximize the structural similarity index (SSIM) between the original image (before EHS) and the result of EHS iteratively. Essential in this process is the computationally simple and accurate formula we derive for SSIM gradient. As it is based on gradient ascent, the proposed EHS always converges. Experimental results confirm that while obtaining the histogram exactly as specified, the proposed method invariably outperforms the existing methods in terms of visual quality of the result. The computational complexity of the proposed method is shown to be of the same order as that of the existing methods. Index terms: histogram modification, histogram equalization, optimization for perceptual visual quality, structural similarity gradient ascent, histogram watermarking, contrast enhancement.