Fractal Geometry On Image Information Representation And Its Application

In recently years, nonlinar science has been widely applied in image processing area, especially in image information representation. Nonlinear method solves the problems which can not be conquered by linear way for a long time and it becomes one of the hotspot of this area. Fractal Theory is a novel theory in nonlinear science with important theoretical significance and practical application prospect. It supplies a novel method for image information representation.On the basis of fractal geometry, this thesis is organized in the clue as "fractal→image modeling and representation→application". The image information representation framework based on fractal is built which includes image shape, texture information and internal structure information of image manifold. Under this framework, some key applications, such as image coding, texture image segmentation and image recognition are researched.The principle work of the thesis includes:1. The developing history, research status, theoretical background and application in image processing of fractal geometry are elaborated. Then image information representation methods are summarized. According to this, the image information representation framework based on fractal is proposed2. The image information representation framework based on fractal is built which includes image shape, texture information and internal structure information of image manifold. Theoretical tools of image representation based on Fractal are addressed, and the fractal parameter characteristics of image information representation are analyzed by experiments.3. Image shape information representation based on Fractal and its application in image coding is researched. Aiming at solving the speed problem, a generative sparse fractal image coding framework is proposed. On the basis of constructing an over-complete vocabulary of fractal building blocks, a novel fractal image coding method based on primitive vocabulary is proposed.4. Image texture information representation based on Fractal Geometry and its application in texture image segmentation is researched. Aiming at the problem that single fractal dimension could not descript texture feature adequately, a novel multi-scale, multi-orientation texture feature extraction method based on fractal theory is proposed by combining the fractal dimension and multi-scale, multi-resolution method.5. Internal information representation of image manifold based on Fractal Geometry and its application in image recognition is researched. Aiming at solving the problem of image recognition method based on fractal. Geometrical shape of image manifold and internal structure information embedding in the manifold are researched. A novel image recognition method based on fractal dimension estimation of point set in high dimension space is proposed.