【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征,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。更多还原

【Abstract】 Fractal and fractal gometry 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 domain are approximately classifiec into two categories:according to the characteristic of self-similat 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.更多还原