Hidden details and lack of image contrast can be attributed to limited user experience, poor device quality, environment settings during image acquisition, and illumination. To address these problems, techniques based on histogram equalization (HE) have been frequently used to reduce these problems and to improve image contrast. However, the resultant images obtained by techniques often appear unnatural possibly due to washed-out effects and unwanted artifacts. This study proposes a new technique called adaptive entropy index histogram equalization (AEIHE) that belongs to the local sub-class of HE-based contrast enhancement techniques. AEIHE initially divides the image into three sub-images to enhance and highlight its local details. Each of these sub-images uses a different contextual region and clip limit based on the richness of their information and their structure, both of which are adaptively determined by AEIHE. A new parameter called Entropy-Index is then used to ensure the high information richness of the resultant sub-image while preserving its structure. AEIHE guarantees the production of an excellent resultant image by combining enhanced sub-images. Quantitative evaluations of 819 images show that AEIHE has successfully produced excellent resultant images with improved contrast, highlighted local details, and minimized effects of artifacts and unwanted noise. Therefore, AEIHE has a high application potential in the medical imaging, machine vision, and industrial domains.