Application Research Of Fractal Theory In Microcosmic Image Processing

In this thesis, the author tried to use fractal dynamics to research the relationshipbetween the macroscopic mechanical properties and microstructure morphology ofthe polymer material. The emphasis of the research is the characterization anddescription of microstucture and morphology in the polymer meterial, the fractaltheory was applied to describe and characterize the scanning electron microscopeimages, then brought in the fractal interpolation to process image data. The fractalinterpolation image processing is another main content in this research.Canny operator was chosen for edge extraction, associated with the original images,according to the description of fractal by K.Falconner, the existence of fractalcharacteristics in the microscopic images was discussed, the result shows that theself-similarity is existed, but exists regionally and in a certain limitted scale.Thefractal interpolation was applied in the digital image processing, contrasting theresults which was obtained by traditional interpolation, the key point of research wasput in its application in the image sacaling, the results show that in the polymermaterial microstructure images which have self-similarity feature, the fractalinterpolation magnification can well retain the fractal information of the originalimage. Based on the comparation of the calculation result and the actual dimension inthe classic2d images and typical fractal images, the the accuracy of the proposedbox-dimension algorithm was demonstrated, by adjusting the algorithm parameter andcontrasting analysis of the result in the microscopic image processing, the relativelyaccurate box counting dimension was obtained.The macroscopic mechanical properties of polymer material can be characterizedby fractal dynamics fractional order constitutive equation. The study shows that, thereis obvious inner relationship between the fractal dimension which characterizingmaterial’s microstructure morphology and the fractional differentiation order offractional constitutive equations which describing material’s macroscopic properties,and preliminarily validated the assumption about the physical interpretation offractional differential constitutive law proposed by Rouse and some other famousscholars in early period.