Aims: The manuscript aims at designing and developing a model for optimum contrast enhancement of an input image. The output image of model ensures the minimum noise, the maximum brightness and the maximum entropy preservation. Objectives: * To determine an optimal value of threshold by using the concept of entropy maximization for segmentation of all types of low contrast images. * To minimize the problem of over enhancement by using a combination of weighted distribution and weighted constrained model before applying histogram equalization process. * To provide an optimum contrast enhancement with minimum noise and undesirable visual artefacts. * To preserve the maximum entropy during the contrast enhancement process and providing detailed information recorded in an image. * To provide the maximum mean brightness preservation with better PSNR and contrast. * To effectively retain the natural appearance of an images. * To avoid all unnatural changes that occur in Cumulative Density Function. * To minimize the problems such as noise, blurring and intensity saturation artefacts. Methods: 1. Histogram Building. 2. Segmentation using Shannon’s Entropy Maximization. 3. Weighted Normalized Constrained Model. 4. Histogram Equalization. 5. Adaptive Gamma Correction Process. 6. Homomorphic Filtering. Results: Experimental results obtained by applying the proposed technique MEWCHE-AGC on the dataset of low contrast images, prove that MEWCHE-AGC preserves the maximum brightness, yields the maximum entropy, high value of PSNR and high contrast. This technique is also effective in retaining the natural appearance of an images. The comparative analysis of MEWCHE-AGC with existing techniques of contrast enhancement is an evidence for its better performance in both qualitative as well as quantitative aspects. Conclusion: The technique MEWCHE-AGC is suitable for enhancement of digital images with varying contrasts. Thus useful for extracting the detailed and precise information from an input image. Thus becomes useful in identification of a desired regions in an image.