【作者】 甘龙；

【导师】 潘孟贤； 高隽；

【作者基本信息】 合肥工业大学 ， 信号与信息处理， 2003， 硕士

【摘要】 分形概念的提出及分形几何学的创立，为人们描述客观世界提供了更准确的数学模型，引起了自然科学领域和社会科学领域的普遍关注，并在化学、生物学、天文学等诸多领域中得到了广泛的应用。由于分形集可以用简单的迭代方法生成复杂的自然景物、用分数维有效度量物体的复杂性，因此分形与图像之间存在着一种自然联系，而正是这种联系，奠定了分形理论用于图像处理的基础，开辟了分形理论在图像处理中应用的新领域。目前分形在图像中的应用大致可以概括为两类：一类是利用分形的自相似特性，采用映射变换的方法对自然界景物进行仿真，对图像进行压缩编码；另一类是根据分形及分数维的特征参量来建立模型，通过对模型参数的研究，有效地进行图像分析和处理。本文在对分形理论及其在图像边缘检测中的应用进行了研究，主要工作如下： 1．通过对近年来国内外学术界对分形理论及其在图像处理领域相关应用问题的研究成果和最新进展的搜集、整理和总结，对分形及分形维数的定义、原理、算法以及在图像处理上的应用进行了较为系统的研究和探讨； 2．针对基于DFBR场边缘检测典型算法的缺点，采用了一种基于分形截距特征的图像边缘检测算法，取得了较为满意的结果；并针对传统方法抗噪性能差的缺点，引入一种基于参照图的边缘评价方法，并对此算法性能与传统Sobel算法进行定量分析对比，实验证明该算法是有效的； 3．在基于分形截距特征方法的基础上，提出了一种基于斜率和截距两种分形特征的边缘检测算法，并将其性能与截距算法进行了定量的分析比较，实验证明该算法的性能要略优于截距算法； 4．利用分形检测算法对噪声不敏感的优点，对传统边缘检测算法进行改进，提出了一种将传统方法与分形方法相结合的算法，实验证明改进后方法的抗噪性能要明显优于传统方法，且能检测到丰富的边缘细节。更多还原

【Abstract】 Fractal and fractal geometry provide a more exact mathematical model to describe the external world, which broke though the situation limited to Euclid geometry and have drawn much attention from chemists, mathematicians, physicists in various disciplines. Fractal sets can be iterated to produce complex nature objects and fractal dimension can be used to measure the complexity of objects, so between fractal and image there lies a natural relation, which make it possible to process image based on fractal theory. At present the fractal based applications in image domain are approximately classified into two categories: according to the characteristic of self-similar of fractal, people imitate and compress the natural image using mapping transformation method. This is one category. The other is according to the features of fractal and fractal dimension, people set up image models, investigate the main geometric features of the images and process them effectively. This thesis has studied the fractal theory and its applications in image edge detection. The main works are described as follows:(1) We have summarized the latest research achievements and development of fractal theory and the applications in image processing domain and discussed and studied the definition, principle and algorithm of fractal and fractal dimension;(2) Aiming at the disadvantages of DFBR based edge detection method, an algorithm based on fractal intercept feature was put forward; Moreover, aiming at the bad anti-noise performance of traditional methods, a edge evaluation method was introduced to evaluate the performance of the algorithm and that of Sobel-based algorithm quantificationally;(3) Furthermore, we proposed a novel method based on slope feature and intercept feature, then compared the performance with that of intercept-based method. The experiment results shows that the performance of this algorithm are better than that of intercept-based method;(4) Taking advantages of good anti-noise performance of fractal-based method, we improved the traditional methods and proposed a algorithm which combined the traditional method with fractal theory achieved a better anti-noise performance.更多还原