Journal of Mathematical Imaging and Vision

, Volume 61, Issue 9, pp 1243–1257

# Image Processing Algorithm Based on Bi-dimensional Local Mean Decomposition

• Feng-Ping An
• Zhi-Wen Liu
Article

## Abstract

Because images contain rich characteristic information, adaptive image decomposition algorithms are necessary to achieve multi-scale extraction of image information in multi-scale image decomposition processing. For this reason, based on local mean decomposition (LMD), which has good self-adaptive characteristics, this paper proposes a new adaptive image processing algorithm, bi-dimensional local mean decomposition (BLMD). BLMD can decompose the original image into multiple bi-dimensional product functions (BPFs). Aiming at the decomposition of BLMD, this paper proposes targeted solutions and designs for the extraction of extremum points, screening process interpolation methods, and decomposition and stop conditions involved in BLMD. After fully recognizing the self-adaptive and multi-scale characteristics of BLMD, this paper proposes a variable neighborhood window method to obtain the extreme points in the decomposition process and uses fractal theory to interpolate the image and obtain the corresponding mean surface and other information. Then, the number of non-coincident extreme points on the zero-valued plane projection between adjacent surfaces in the screening process is counted and analyzed, and a stop condition that matches the characteristics of the image is given to ensure the BPF component obtained by decomposition accurately reflects certain feature information of an image. Finally, the BLMD proposed in this paper is formed. Empirical analysis shows this method can quickly decompose and maintain the characteristics of data-drivenness, adaptability and scale consistency of LMD; it can also avoid the disadvantages of other adaptive processing algorithms, such as the bi-dimensional intrinsic mode function obtained by the decomposition of bi-dimensional empirical mode decomposition and the residual failing to completely contain the feature information of the original image.

## Keywords

Bi-dimensional empirical mode decomposition Local mean decomposition Bi-dimensional local mean decomposition Fractal interpolation Stop condition

## Notes

### Acknowledgements

This paper is supported by National Natural Science Foundation of China (No. 61701188).

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## Authors and Affiliations

• Feng-Ping An
• 1
• 2
• Zhi-Wen Liu
• 2
1. 1.School of Physics and Electronic Electrical EngineeringHuaiyin Normal UniversityHuai’anChina
2. 2.Beijing Institute of TechnologyBeijingChina