基于比尔朗伯定律的变分水平集模型

唐利明; 熊点华; 方壮

doi:10.12263/DZXB.20210214

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基于比尔朗伯定律的变分水平集模型

学术论文 | 更新时间：2025-12-08

- 基于比尔朗伯定律的变分水平集模型
- A Variational Level Set Model Based on Beer-Lambert Law
- 电子学报 2023年51卷第2期页码：416-426
- 作者机构：
  
  1.湖北民族大学数学与统计学院, 湖北恩施 445000
  2.阿坝师范学院数学学院, 四川汶川 623002
- 作者简介：
  
  [ "唐利明男，1978年出生，湖北恩施人．博士，湖北民族大学数学与统计学院教授.主要研究方向为数字图像处理、机器学习等．E-mail: tlmcs78@foxmail.com" ]
  [ "熊点华男，1995年出生，贵州黔西人．阿坝师范学院数学学院助教.主要研究方向为数字图像处理．E-mail: xdhzx37@163.com" ]
  [ "方壮男，1980年出生，湖北孝感人．博士，湖北民族大学数学与统计学院副教授.主要研究方向为数字图像处理、数学建模等．E-mail: wdfangzhuang@163.com" ]
- 基金信息：
  
  国家自然科学基金(62061016;61561019)
- DOI：10.12263/DZXB.20210214
  中图分类号： TP391.4;
- 收稿：2021-02-03，
  
  修回：2022-05-05，
  
  纸质出版：2023-02-25
- 稿件说明：
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唐利明,熊点华,方壮.基于比尔朗伯定律的变分水平集模型[J].电子学报,2023,51(02):416-426.

TANG Li-ming,XIONG Dian-hua,FANG Zhuang.A Variational Level Set Model Based on Beer-Lambert Law[J].ACTA ELECTRONICA SINICA,2023,51(02):416-426.
唐利明,熊点华,方壮.基于比尔朗伯定律的变分水平集模型[J].电子学报,2023,51(02):416-426. DOI： 10.12263/DZXB.20210214.

TANG Li-ming,XIONG Dian-hua,FANG Zhuang.A Variational Level Set Model Based on Beer-Lambert Law[J].ACTA ELECTRONICA SINICA,2023,51(02):416-426. DOI： 10.12263/DZXB.20210214.

摘要

图像成像过程中，由于空气消光性的影响，获取的数字图像质量会退化，包括灰度不均，对比度下降等，给图像分割或者目标的识别带来困难.为解决此问题，本文提出了一个基于比尔朗伯光吸收定律的变分水平集模型以实现此类退化图像的分割和修正.首先基于比尔朗伯定律，将观测图像建模为一个退化场和真实图像的乘积.然后对退化场进行Markov随机场正则化，对真实图像实施分片Gaussian分布拟合建模，结合水平集函数正则项，建立变分水平集模型.最后采用结合梯度下降的交替迭代算法对模型进行数值求解.实验结果表明，本文模型可以很好地排除退化场的影响，得到满意的图像分割和修正效果.和几个经典的变分图像分割模型相比，本文模型展示出较好的实验效果，具有最优的JSI，DSI和VOE指标值.

Abstract

The intensity inhomogeneity and low contrast caused by air extinction significantly reduce image quality and affect the subsequent image segmentation and target recognition. To solve this problem

a variational level set model based on Beer-Lambert law is proposed for image segmentation and inhomogeneity correction. Firstly

the observed image is modeled by a product of a degradation field and a real image based on Beer-Lambert law

in which the degradation field is regularized by a Markov random field

and the real image is represented by a piecewise Gaussian distribution. And then

using maximum a posterior probability (MAP) criterion

and incorporating a regularization term

we propose a variational level set model. Finally

an alternating iteration algorithm combining with gradient descent is developed to numerically solve the model. The experimental results validate the proposed model and algorithm

which can eliminate the effects of the intensity inhomogeneity

and obtain satisfactory results of image segmentation and correction. Compared with several state-of-the-art variational models

the proposed model shows the best performance in terms of the JSI

DSI and VOE indexes.

关键词

Keywords

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