基于比尔朗伯定律的变分水平集模型

doi:10.12263/DZXB.20210214

摘要/Abstract

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.

关键词: 比尔朗伯定律, 变分法, 水平集, 图像分割, 图像修正

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.

Key words: Beer-Lambert law, variational, level set, image segmentation, image correction

中图分类号:

TP391.4

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(2): 416-426.

Li-ming TANG, Dian-hua XIONG, Zhuang FANG . A Variational Level Set Model Based on Beer-Lambert Law[J]. Acta Electronica Sinica, 2023, 51(2): 416-426.

图/表 12

参考文献 32

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图像	LBF模型		LIF模型		LGDF模型		本文模型
图像	Iter	Time	Iter	Time	Iter	Time	Iter	Time
合成图像A(图1)	130	8.23	130	6.43	150	9.42	50	2.52
合成图像B(图1)	120	7.62	110	5.46	150	9.36	40	2.02
汽车图像(图1)	60	3.70	60	2.87	70	4.41	50	2.51
脑MR图像(图1)	130	8.43	90	4.46	120	7.54	40	2.03
At本文图像(图4)	40	2.53	30	1.49	30	1.78	20	1.04
血管图像(图4)	1 420	89.90	860	42.24	1 530	96.28	148	7.32

图像	LBF模型		LIF模型		LGDF模型		本文模型
图像	Iter	Time	Iter	Time	Iter	Time	Iter	Time
合成图像A(图1)	130	8.23	130	6.43	150	9.42	50	2.52
合成图像B(图1)	120	7.62	110	5.46	150	9.36	40	2.02
汽车图像(图1)	60	3.70	60	2.87	70	4.41	50	2.51
脑MR图像(图1)	130	8.43	90	4.46	120	7.54	40	2.03
At本文图像(图4)	40	2.53	30	1.49	30	1.78	20	1.04
血管图像(图4)	1 420	89.90	860	42.24	1 530	96.28	148	7.32

图像	LIC模型		LSACM模型		本文模型
图像	Iter	Time	Iter	Time	Iter	Time
Horse(图5)	120	8.03	150	10.12	50	2.61
Plane(图5)	160	10.73	210	14.11	60	3.25
Wire(图5)	130	8.72	140	9.35	50	2.62
脑MR图像(图6)	90	6.12	110	7.46	40	2.09

图像	LIC模型		LSACM模型		本文模型
图像	Iter	Time	Iter	Time	Iter	Time
Horse(图5)	120	8.03	150	10.12	50	2.61
Plane(图5)	160	10.73	210	14.11	60	3.25
Wire(图5)	130	8.72	140	9.35	50	2.62
脑MR图像(图6)	90	6.12	110	7.46	40	2.09

数据集	指标	CV模型	LBF模型	LGDF模型	MCV模型	GLFIF模型	GLIF模型	本文模型
Image 1	JSI	0.732 5	0.704 3	0.713 9	0.638 6	0.711 1	0.650 6	0.743 2
	DSI	0.845 6	0.826 5	0.833 0	0.779 4	0.831 2	0.788 3	0.852 0
	VOE	0.294 1	0.287 4	0.293 2	0.210 4	0.329 0	0.234 7	0.128 1
Image 2	JSI	0.403 2	0.373 2	0.348 0	0.362 6	0.371 3	0.414 3	0.623 2
	DSI	0.465 3	0.429 1	0.291 6	0.416 0	0.426 8	0.478 3	0.732 1
	VOE	0.556 7	0.417 8	0.461 9	0.545 4	0.520 8	0.422 8	0.147 6
Image 3	JSI	0.732 5	0.704 3	0.713 9	0.638 6	0.711 1	0.650 6	0.753 4
	DSI	0.845 6	0.826 5	0.833 0	0.779 4	0.831 2	0.788 3	0.862 3
	VOE	0.294 1	0.287 4	0.293 2	0.210 4	0.329 0	0.134 7	0.119 8
Weizmann	JSI	0.563 5	0.439 6	0.399 0	0.521 8	0.570 2	0.548 5	0.603 2
	DSI	0.693 9	0.597 5	0.402 4	0.657 4	0.701 1	0.686 6	0.711 5
	VOE	0.402 2	0.288 5	0.318 1	0.418 6	0.369 8	0.336 3	0.276 5