摘 要：传统直方图均衡在保持图像亮度，避免过增强方面表现不佳。为了克服上述缺点，提出了一种基于亮度保持 S 型函数变换的双直方图均衡方法。首先用输入图像的灰度均值对直方图进行分割，然后根据子直方图的信息自适应地调整 S 型函数的参数，将子直方图的灰度均值变为其不动点，同时调整 S 型函数曲线的倾斜程度，最后用调整参数后的 S 型函数代替子直方图的累积分布函数进行双直方图均衡。通过对 USC-SIPI 数据库中的灰度图像进行试验，该算法在亮度保持和图像保真方面均取得较好的效果。
关键词：图像增强；双直方图均衡；S 型函数；亮度保持；峰值信噪比
DOI:10.19850/j.cnki.2096-4706.2021.16.019
基金项目：南京信息职业技术学院博士专 项基金资助项目（YB20180901）
中图分类号：TP391 文献标识码：A 文章编号：2096-4706（2021）16-0073-06
Bi-Histogram Equalization Method Based on Brightness Preserving Sigmoid Function
WANG Gang1 , BAI Jiejing1 , ZHANG Zhengjun2
(1. Department of Quality Education, Nanjing Vocational College of Information Technology, Nanjing 210023, China; 2. College of Science, Nanjing University of Science and Technology, Nanjing 210094, China)
Abstract:Traditional histogram equalization performs poorly in maintaining image brightness and avoiding over enhancement. In order to overcome the above shortcomings, a bi-histogram equalization method based on the brightness preserving sigmoid function transformation is proposed. First, the gray mean of the input image is used to segment the histogram. Secondly, the parameters of the sigmoid function are adjusted adaptively according to the information of the sub-histogram, then the gray mean of the sub-histogram is changed to its fixed point, and the steepness of the sigmoid function curve is adjusted. Finally, the sigmoid function after adjusting the parameters is used to replace the cumulative distribution function of sub-histogram for bi-histogram equalization. By testing the grayscale images taken from the USC-SIPI database, the proposed method has achieved good effects in terms of brightness preserving and image fidelity.
Keywords: image enhancement; bi-histogram equalization; sigmoid function; brightness preserving; Peak Signal-to-Noise Ratio(PSNR)
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作者简介：王罡（1983—），男，汉族，江苏南京人，讲师，硕士，主要研究领域：数字图像处理、模式识别；白洁净（1981—），女， 汉族，江苏南京人，副教授，博士，主要研究领域：数值算法、微分方程数值解；张正军（1965—），男，汉族，江苏南京人，副教授， 硕士研究生导师，博士，主要研究领域：图形图像技术，数据挖掘。