| With the development of data science and information technology,research related to image processing has become a rapidly growing and emerging cross-cutting sub-discipline.Among them,image enhancement and image segmentation tasks are of practical interest in many application areas,such as locating cracked edges in brain images,texture analysis of fabrics,fingerprint recognition in biology,and analysis of impressionistic paintings.The image acquisition is often disturbed by external factors such as acquisition equipment,light temperature,noise and time,resulting in blurred or even misaligned edges,interrupted lines,unrecognized fine structures and reduced contrast,which severely degrade the image quality and greatly hinder image analysis studies.Therefore,for image enhancement and image segmentation,this thesis proposes some models based on anisotropic diffusion equations(systems)from several aspects such as designing nonlinear structure tensors,changing diffusion types and adding source terms.The main research is as follows:First,for the image enhancement and image segmentation problems in scalar images,the linear structure tensor has no memory and the pure diffusion model degrades the recovered image contrast and blurs the edges.Therefore,a coupled nonlinear timedelay anisotropic diffusion system model is proposed in this thesis.The model evolves a nonlinear structure tensor using the isotropic diffusion equation and is normalized by the time-delay regularization.This makes the structure tensor nonlocal and nonlinear in nature.Adding source terms to the anisotropic diffusion equation of the image can change the nature of the solution of the model.It not only enhances the contrast of the image but also makes the image converge to a binary image for the purpose of image segmentation.The existence and uniqueness of weak solution of the anisotropic diffusion system are proved by theoretically separating the time and space variables.Numerically the model is discretized using a finite difference approach and the specific forms of the source terms in the image enhancement and image segmentation tasks are given,respectively.Image enhancement and segmentation experiments on degraded fingerprint images,geometric images,and crop images demonstrate the effectiveness of the model.Then,for the image segmentation problem of scalar-value and vector-value images,the conventional methods are not ideal for segmenting the fine structure of the image and guiding the vector image segmentation with insufficient features.This thesis proposes an anisotropic diffusion equation model of the level set function.The model constructs a new anisotropic diffusion principal part using gradient and structure tensor based on texture details and local geometric features.For different types of images to be segmented,the corresponding color features and texture features are obtained and a normalized feature vector is constructed.This approach ensures the diversity of features while eliminating the singularity between features.The probability density functions on the normalized feature vector are added to the source term of the model,which is used to guide the level set function to complete the image segmentation.For numerical simulations,four different eigenvalues are used to construct the diffusion tensor in the model,and the texture features are obtained using the additive operator splitting algorithm.The proposed segmentation model takes the form of a variational level set,which allows the use of larger time steps and eliminates the need for a reinitialization procedure.The efficiency of the proposed method and its improvement in segmenting fine features are verified by experimental results on some medical images and natural images.Finally,to address the problem of constructing a generalized model framework that can fulfill a variety of image tasks,this thesis proposes a generalized anisotropic diffusion equation model with non-standard growth conditions.The diffusion terms in the model use the higher-level structural descriptor,i.e.,it contains diffusion coefficients and diffusion exponents with non-standard growth conditions,allowing the model to obtain more local structural information and preserve or even enhance fine features.The source term of the anisotropic diffusion equation model involves prior knowledge of different image tasks and images to be processed.By selecting different source terms and diffusion coefficients,the proposed anisotropic diffusion model can be extended as a general framework to many different image tasks,such as image enhancement,image segmentation,and image deblurring,among others.Theoretically,the Banach spaces with variable exponents are constructed to define the weak solution of the anisotropic diffusion equation with nonstandard growth conditions,and the Galerkin method is applied to prove the existence and the uniqueness of its weak solution.In numerical simulations,the construction methods of edge enhancement diffusion tensor and coherence enhancement diffusion tensor are given,and the way and rate of diffusion at different structures are analyzed.Numerical experiments demonstrate the advantages of the model in enhancing small detail structures and being able to adapt to the complexity of image tasks and image structures. |
