多重分形及其在图像识别中的应用研究

【作者】 王瑞；

【导师】 赵健；

【作者基本信息】 西北大学 ， 通信与信息系统， 2010， 硕士

【摘要】 多重分形分析是分形理论的深入研究,分形中用单一维数来描述自然界中的几何体,而多重分形则将其扩展至用多个维数来描述自然界中的复杂几何体。多重分形分析作为分形几何领域中的一个重要发展方向,近年来在材料学、地质学、图像处理等学科领域有着广泛的应用。多重分形分析充分考虑了几何体在形成过程中不同层次的分形特征,从而能够比较全面有效地描述物体的分形结构。图像识别是图像处理的重要内容之一,以图像的分类和描述为主要研究内容,也是当今不断发展的重要应用学科。多重分形用于图像处理,已经成为一些科学工作者解决复杂图像处理问题的重要研究手段。本论文在深入讨论基于多重分形分析的图像去噪和图像边缘提取方法的基础上,进一步分析了图像识别时分形特征应满足的条件,既而提出了基于多重分形分析的图像特征提取算法,利用计算出的多个多重分形谱特征,对四类图像进行了有效的分类识别。实验结果证明,将经过多重分形分析方法提取的图像特征用于图像识别,可以取得较好的识别效果,能够获得较高的识别率。多重分形图像特征为图像识别的研究带来了新的思路,也扩展了多重分形分析在图像处理中的应用,具有一定的理论意义和应用价值。更多还原

【Abstract】 Multifractal analysis is a further research of the fractal theory. It uses multiple dimensions to descripe the complex geometry of the nature, instead of one dimension in fractal theory. Recently, as a important reseach area of fractal geometry, multifractal analysis is applied widely into many fields of science such as materialogy, geology, image processing and so on. It can fully consider the fractal features of different levels in the forming process of the geometry, and thus, describe the fractal structure of the geometry effectively. Image recognition, which is one of the most important contents of image processing, takes image classification and description as the main research contents, also becoming an applied science with continuous development. Applying multifractal, has become an important reseach method which some scientists use to solve complex problems of image processing.This thesis first introduces image denoising and image edge extraction methods based on multifractal analysis, and analyses the conditions that fractal features should be met in image recognition. Afterwards a multifractal analysis-based image feature extraction algorithm is proposed, which can calculate sevral multifractal spectrum features of the image. Then the experiment recognize four types of images effectively with the multifractal spectrum features. Experiment result shows that, with the image features extracted by multifactual analysis method, image recognition could get better effect and higher recognition rate. In conclusion, image feature extracted by multifractal analysis method brings new ideas for research of image recognition, and extends the applied range of multifractal analysis in image processing, which shows its theoretical significance and application value.更多还原