针对多模态图像的自适应引导形态学设计  

Design of guided adaptive mathematical morphology for multimodal images

作　　者：孙梦迪 孙忠贵[1] 孔旭 韩红燕[1] SUN Mengdi;SUN Zhonggui;KONG Xu;HAN Hongyan(College of Mathematical Sciences,Liaocheng University,Liaocheng Shandong 252000,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252000

出　　处：《计算机应用》2023年第2期560-566,共7页journal of Computer Applications

基　　金：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)。

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。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.

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 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术] TP751.1[自动化与计算机技术—计算机科学与技术]