Design of guided adaptive mathematical morphology for multimodal images

doi:10.11772/j.issn.1001-9081.2021122168

Journal of Computer Applications ›› 2023, Vol. 43 ›› Issue (2): 560-566.DOI: 10.11772/j.issn.1001-9081.2021122168

Special Issue: 多媒体计算与计算机仿真

• Multimedia computing and computer simulation • Previous Articles Next Articles

Design of guided adaptive mathematical morphology for multimodal images

Mengdi SUN, Zhonggui SUN(), Xu KONG, Hongyan HAN

College of Mathematical Sciences，Liaocheng University，Liaocheng Shandong 252000，China

Received:2021-12-29 Revised:2022-04-14 Accepted:2022-04-19 Online:2022-05-16 Published:2023-02-10
Contact: Zhonggui SUN
About author:SUN Mengdi， born in 1997， M. S. candidate. Her research interests include image processing， machine learning.
KONG Xu， born in 1981， Ph. D.， associate professor. His research interests include image processing， machine learning， applied mathematics.
HAN Hongyan， born in 1976， M. S.， associate professor. Her research interests include intelligent computation， image processing.
Supported by:
National Natural Science Foundation of China(11801249);Natural Science Foundation of Shandong Province(ZR2020MF040)

针对多模态图像的自适应引导形态学设计

孙梦迪, 孙忠贵(), 孔旭, 韩红燕

聊城大学数学科学学院，山东聊城 252000

通讯作者: 孙忠贵
作者简介:孙梦迪（1997—），女，山东滨州人，硕士研究生，主要研究方向：图像处理、机器学习
孔旭（1981—），男，山东曲阜人，副教授，博士，主要研究方向：图像处理、机器学习、应用数学
韩红燕（1976—），女，山东茌平人，副教授，硕士，主要研究方向：智能计算、图像处理。
基金资助:
国家自然科学基金资助项目(11801249);山东省自然科学基金资助项目(ZR2020MF040)

Abstract

Abstract:

Traditional Mathematical Morphology （TMM） is not well in structure-preserving， and the existing adaptive modified methods usually miss mathematical properties. To address the problems， a Guided Adaptive Mathematical Morphology （GAMM） for multimodal images was proposed. Firstly， the structure elements were constructed by considering the joint information of the input and the guidance images， so that the corresponding operators were more robust to the noise. Secondly， according to 3σ rule， the selected members of structure elements were able to be adapted to image contents. Finally， by using the Hadamard product of sparse matrices， the structure elements were imposed with a symmetry constraint. Both of the theoretical verification and simulation show that the corresponding operators of the proposed mathematical morphology can have important mathematical properties， such as order preservation and adjunction， at the same time. Denoising experimental results on multimodal images show that the Peak Signal-to-Noise Ratio （PSNR） of GAMM is 2 to 3 dB higher than those of TMM and Robust Adaptive Mathematical Morphology （RAMM）. Meanwhile， comparison of subjective visual effect shows that GAMM significantly outperforms TMM and RAMM in noise removal and structure preservation.

Key words: Guided Adaptive Mathematical Morphology (GAMM), multimodal image, mathematical property, robustness, sparse matrix

摘要：

针对传统数学形态学（TMM）细节保持能力较差，以及现有自适应改进方法数学性质丢失的问题，提出了一种针对多模态图像的自适应引导形态学（GAMM）。首先，通过考虑输入图像和引导图像的联合信息进行结构元素的构建，从而在一定程度上增强了相应算子对噪声的鲁棒性；其次，借助3σ原则，使结构元素成员的选取能够自适应于图像内容；最后，利用稀疏矩阵的哈达玛积对结构元素施加一个对称性约束。理论证明和仿真实验均表明所提形态学的相应算子能够同时具备保序性和附益性等重要数学性质。在多模态图像上进行去噪实验，结果表明GAMM比TMM以及近年所提出的鲁棒自适应形态学（RAMM）在峰值信噪比（PSNR）上高出约2~3 dB；同时，主观视觉效果对比表明了GAMM在噪声去除、结构保持方面明显优于TMM和RAMM。

关键词: 自适应引导形态学, 多模态图像, 数学性质, 鲁棒性, 稀疏矩阵

CLC Number:

TP391.4

Mengdi SUN, Zhonggui SUN, Xu KONG, Hongyan HAN. Design of guided adaptive mathematical morphology for multimodal images[J]. Journal of Computer Applications, 2023, 43(2): 560-566.

孙梦迪, 孙忠贵, 孔旭, 韩红燕. 针对多模态图像的自适应引导形态学设计[J]. 《计算机应用》唯一官方网站, 2023, 43(2): 560-566.

Figures/Tables 8

Fig. 1 Flowchart for GAMM

Fig. 2 Verification of properties

Fig. 3 RGB-depth image test set

Tab. 1 Results of PSNR in RGB-depth image denoising

图像	滤波窗口	输入			TMM			RAMM			GAMM
图像	滤波窗口	$δ = 10$	$δ = 30$	$δ = 50$	$δ = 10$	$δ = 30$	$δ = 50$	$δ = 10$	$δ = 30$	$δ = 50$	$δ = 10$	$δ = 30$	$δ = 50$
Art	$3 × 3$	28.08	18.66	14.55	30.59	28.14	24.80	29.38	27.63	24.65	32.70	28.23	24.81
	$5 × 5$				28.77	27.75	25.91	28.87	27.60	25.93	31.21	27.86	25.93
	$7 × 7$				27.37	27.07	25.51	27.57	27.12	25.68	30.33	27.57	25.73
Book	$3 × 3$	28.09	18.63	14.53	31.60	27.63	24.64	31.41	27.54	24.65	33.66	27.63	24.67
	$5 × 5$				30.53	27.70	26.20	30.47	27.65	26.03	33.66	27.75	26.29
	$7 × 7$				30.11	27.57	26.37	30.26	27.58	26.42	33.64	27.96	26.42
Doll	$3 × 3$	28.11	18.64	14.53	32.65	27.93	25.00	32.35	27.91	25.05	33.87	27.94	25.95
	$5 × 5$				31.98	28.68	26.78	32.06	28.64	26.67	34.19	28.69	26.79
	$7 × 7$				31.62	28.79	26.86	31.67	28.79	27.04	34.26	28.92	27.96
Laundry	$3 × 3$	28.09	18.73	14.48	33.90	28.95	25.35	33.21	28.83	25.31	34.07	29.01	25.41
	$5 × 5$				31.91	29.78	26.67	32.02	29.71	26.64	33.62	29.82	26.83
	$7 × 7$				31.41	29.33	26.04	31.42	29.46	26.21	32.59	29.84	26.36
Moebius	$3 × 3$	28.11	18.64	14.47	31.80	27.98	24.91	31.42	27.79	24.91	33.44	28.08	24.93
	$5 × 5$				30.40	28.32	26.32	30.48	28.20	26.24	32.91	28.82	26.55
	$7 × 7$				29.94	24.97	26.36	30.02	27.91	26.46	32.79	28.12	27.10
Reindeer	$3 × 3$	28.15	18.65	14.57	33.46	28.74	25.12	30.95	28.10	24.96	33.93	28.81	25.18
	$5 × 5$				29.98	29.24	26.98	30.26	28.99	26.75	33.57	30.01	27.86
	$7 × 7$				28.00	29.02	26.95	28.20	28.78	26.95	30.83	29.26	26.95

Tab. 1 Results of PSNR in RGB-depth image denoising

图像	滤波窗口	输入			TMM			RAMM			GAMM
图像	滤波窗口	$δ = 10$	$δ = 30$	$δ = 50$	$δ = 10$	$δ = 30$	$δ = 50$	$δ = 10$	$δ = 30$	$δ = 50$	$δ = 10$	$δ = 30$	$δ = 50$
Art	$3 × 3$	28.08	18.66	14.55	30.59	28.14	24.80	29.38	27.63	24.65	32.70	28.23	24.81
	$5 × 5$				28.77	27.75	25.91	28.87	27.60	25.93	31.21	27.86	25.93
	$7 × 7$				27.37	27.07	25.51	27.57	27.12	25.68	30.33	27.57	25.73
Book	$3 × 3$	28.09	18.63	14.53	31.60	27.63	24.64	31.41	27.54	24.65	33.66	27.63	24.67
	$5 × 5$				30.53	27.70	26.20	30.47	27.65	26.03	33.66	27.75	26.29
	$7 × 7$				30.11	27.57	26.37	30.26	27.58	26.42	33.64	27.96	26.42
Doll	$3 × 3$	28.11	18.64	14.53	32.65	27.93	25.00	32.35	27.91	25.05	33.87	27.94	25.95
	$5 × 5$				31.98	28.68	26.78	32.06	28.64	26.67	34.19	28.69	26.79
	$7 × 7$				31.62	28.79	26.86	31.67	28.79	27.04	34.26	28.92	27.96
Laundry	$3 × 3$	28.09	18.73	14.48	33.90	28.95	25.35	33.21	28.83	25.31	34.07	29.01	25.41
	$5 × 5$				31.91	29.78	26.67	32.02	29.71	26.64	33.62	29.82	26.83
	$7 × 7$				31.41	29.33	26.04	31.42	29.46	26.21	32.59	29.84	26.36
Moebius	$3 × 3$	28.11	18.64	14.47	31.80	27.98	24.91	31.42	27.79	24.91	33.44	28.08	24.93
	$5 × 5$				30.40	28.32	26.32	30.48	28.20	26.24	32.91	28.82	26.55
	$7 × 7$				29.94	24.97	26.36	30.02	27.91	26.46	32.79	28.12	27.10
Reindeer	$3 × 3$	28.15	18.65	14.57	33.46	28.74	25.12	30.95	28.10	24.96	33.93	28.81	25.18
	$5 × 5$				29.98	29.24	26.98	30.26	28.99	26.75	33.57	30.01	27.86
	$7 × 7$				28.00	29.02	26.95	28.20	28.78	26.95	30.83	29.26	26.95

Tab. 2 Results of SSIM in RGB-depth image denoising

图像	滤波窗口	输入			TMM			RAMM			GAMM
图像	滤波窗口	$δ = 10$	$δ = 30$	$δ = 50$	$δ = 10$	$δ = 30$	$δ = 50$	$δ = 10$	$δ = 30$	$δ = 50$	$δ = 10$	$δ = 30$	$δ = 50$
Art	$3 × 3$	0.576	0.155	0.080	0.891	0.678	0.473	0.871	0.664	0.468	0.896	0.678	0.481
	$5 × 5$				0.871	0.801	0.678	0.872	0.795	0.665	0.873	0.857	0.679
	$7 × 7$				0.845	0.821	0.651	0.844	0.817	0.639	0.846	0.821	0.691
Book	$3 × 3$	0.468	0.103	0.050	0.906	0.656	0.439	0.900	0.649	0.432	0.934	0.657	0.439
	$5 × 5$				0.924	0.818	0.700	0.923	0.807	0.676	0.973	0.872	0.754
	$7 × 7$				0.924	0.871	0.805	0.926	0.865	0.786	0.951	0.874	0.836
Doll	$3 × 3$	0.484	0.106	0.048	0.885	0.650	0.445	0.878	0.644	0.442	0.895	0.655	0.446
	$5 × 5$				0.893	0.806	0.686	0.900	0.797	0.666	0.900	0.815	0.692
	$7 × 7$				0.887	0.854	0.789	0.888	0.848	0.775	0.895	0.891	0.797
Laundry	$3 × 3$	0.480	0.107	0.050	0.911	0.662	0.461	0.902	0.658	0.454	0.946	0.662	0.471
	$5 × 5$				0.923	0.825	0.697	0.920	0.815	0.678	0.972	0.869	0.751
	$7 × 7$				0.918	0.865	0.776	0.916	0.862	0.767	0.949	0.890	0.775
Moebius	$3 × 3$	0.482	0.106	0.050	0.898	0.659	0.449	0.891	0.652	0.443	0.943	0.659	0.453
	$5 × 5$				0.909	0.815	0.688	0.910	0.806	0.666	0.969	0.865	0.696
	$7 × 7$				0.900	0.858	0.777	0.901	0.853	0.766	0.949	0.887	0.782
Reindeer	$3 × 3$	0.497	0.113	0.057	0.918	0.669	0.458	0.905	0.661	0.450	0.951	0.675	0.459
	$5 × 5$				0.920	0.826	0.704	0.922	0.814	0.685	0.981	0.882	0.767
	$7 × 7$				0.900	0.870	0.807	0.903	0.863	0.790	0.953	0.874	0.842

Tab. 2 Results of SSIM in RGB-depth image denoising

图像	滤波窗口	输入			TMM			RAMM			GAMM
图像	滤波窗口	$δ = 10$	$δ = 30$	$δ = 50$	$δ = 10$	$δ = 30$	$δ = 50$	$δ = 10$	$δ = 30$	$δ = 50$	$δ = 10$	$δ = 30$	$δ = 50$
Art	$3 × 3$	0.576	0.155	0.080	0.891	0.678	0.473	0.871	0.664	0.468	0.896	0.678	0.481
	$5 × 5$				0.871	0.801	0.678	0.872	0.795	0.665	0.873	0.857	0.679
	$7 × 7$				0.845	0.821	0.651	0.844	0.817	0.639	0.846	0.821	0.691
Book	$3 × 3$	0.468	0.103	0.050	0.906	0.656	0.439	0.900	0.649	0.432	0.934	0.657	0.439
	$5 × 5$				0.924	0.818	0.700	0.923	0.807	0.676	0.973	0.872	0.754
	$7 × 7$				0.924	0.871	0.805	0.926	0.865	0.786	0.951	0.874	0.836
Doll	$3 × 3$	0.484	0.106	0.048	0.885	0.650	0.445	0.878	0.644	0.442	0.895	0.655	0.446
	$5 × 5$				0.893	0.806	0.686	0.900	0.797	0.666	0.900	0.815	0.692
	$7 × 7$				0.887	0.854	0.789	0.888	0.848	0.775	0.895	0.891	0.797
Laundry	$3 × 3$	0.480	0.107	0.050	0.911	0.662	0.461	0.902	0.658	0.454	0.946	0.662	0.471
	$5 × 5$				0.923	0.825	0.697	0.920	0.815	0.678	0.972	0.869	0.751
	$7 × 7$				0.918	0.865	0.776	0.916	0.862	0.767	0.949	0.890	0.775
Moebius	$3 × 3$	0.482	0.106	0.050	0.898	0.659	0.449	0.891	0.652	0.443	0.943	0.659	0.453
	$5 × 5$				0.909	0.815	0.688	0.910	0.806	0.666	0.969	0.865	0.696
	$7 × 7$				0.900	0.858	0.777	0.901	0.853	0.766	0.949	0.887	0.782
Reindeer	$3 × 3$	0.497	0.113	0.057	0.918	0.669	0.458	0.905	0.661	0.450	0.951	0.675	0.459
	$5 × 5$				0.920	0.826	0.704	0.922	0.814	0.685	0.981	0.882	0.767
	$7 × 7$				0.900	0.870	0.807	0.903	0.863	0.790	0.953	0.874	0.842

Fig. 4 Visual effect of RGB-depth image denoising

Fig. 5 Visual effect of flash-flash-free image restoration

Fig. 6 Visual effect of NIR-RGB image denoising

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Design of guided adaptive mathematical morphology for multimodal images

针对多模态图像的自适应引导形态学设计

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