RESEARCH ARTICLE Exposure and Median Based One-to-One Gray Level Mapping Transformation for Entropy Preservation and Contrast Enhancement M. Eswar Reddy 1 • Gudheti Ramachandra Reddy 1 Received: 17 December 2016 / Revised: 6 April 2017 / Accepted: 4 April 2018 Ó The National Academy of Sciences, India 2018 Abstract Many histogram equalization (HE) techniques have been proposed for the contrast enhancement in the past. In recent years clipped histogram equalization tech- niques are developed to control the degree of over enhancement and the noise. Yet these methods are not guaranteed to preserve the gray levels and thus the infor- mation in output image is less than that in the input image, even though it has been enhanced. We propose two new one-to-one gray level mapping (OGM) transformation methods, namely exposure based one-to-one gray level mapping (EOGM) transformation and median based one- to-one gray level mapping (MOGM) transformation. In EOGM and MOGM methods histogram is divided into two sub histograms based on exposure and median of the images respectively. Weights for these sub histograms are calculated and then OGM transformation function is applied to these sub histograms by using the derived weights. This transformation addresses both over enhancement and gray level loss effectively and also ensure uniform degree of enhancement. This preserves all the information content even after enhancement with all structural details, ensures no false contouring. Thus they are suitable for medical image applications, where infor- mation loss leads to wrong diagnosis. The experimental results show the supremacy of our methods over existing HE methods. Keywords Gray level loss  Over enhancement  Gray level mapping  Weights  Image information content 1 Introduction Simple and well known technique to achieve the contrast enhancement of the poor contrasted image is HE [1]. But major problem with HE is over enhancement of peaks in the histogram and thus enhancing the noise. Because of this image loses its natural look and also has large shift of mean brightness in the output image. Preservation of mean brightness is important in consumer electronic products such as TV, digital camera and camcoder etc. To preserve the mean brightness various histogram partition and equalization techniques viz, brightness preserving bi his- togram equalization (BBHE) [2], minimum mean bright- ness error bi histogram equalization (MMBEBHE) [3], Dualistic sub-image histogram equalization (DSIHE) [4], recursive mean separated histogram equalization (RMSHE) [5] and recursive sub image histogram equalization (RSIHE) [6] have been proposed. In BBHE histogram is divided into two parts and the separation gray level is mean of the image and these sub histograms are equalized independently by conventional HE. MMBEBHE is similar to BBHE but separation point is chosen in such a way that it produces smallest absolute mean brightness error (AMBE). Computational complexity is high in this method as it carries out BBHE from lowest nonzero frequency gray level to highest non zero frequency gray level, to find out the separation point. One more technique which is similar to BBHE is DSIHE, but separation intensity is based on median of the image. Recursive way of performing BBHE to each sub histogram is RMSHE. Recursive way of per- forming DSIHE to each sub histogram is RSIHE. Both Electronic supplementary material The online version of this article (https://doi.org/10.1007/s40010-018-0497-3) contains supple- mentary material, which is available to authorized users. & M. Eswar Reddy m.eswarreddypjm@gmail.com 1 VIT University, Vellore, Tamil Nadu, India 123 Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. https://doi.org/10.1007/s40010-018-0497-3