Application Research Of Partial Differential Equation In Image Segmentation

Image segmentation is a procedure to separate an image into homogeneous regions that are more meaningful and easier to analyze. There are many image segmentation/algorithms, for example, image segmentation based on partial differential equation is interactive imag segmentation, and it has strong local adaptability and high flexibility; clustering algorithm is automatic image segmentation, and it is suitable for image pre-segmentation.In recent years, many related papers have been published, which make the accuracy of image segmentation improved. However, there are still some problems to be improved. In this(paper,)on the basis of the investigation and summary of traditional image segmentation algorithmss based on partial differential equation and clustering algorithm for image segmentation,we improve some classic image segmentation algorithms, and the contents are as follows:(1)To enlarge capture range of external force field in parameteive contour model and eliminate effect of noise and weak edge on segmentation, this paper combines advantages of parameter active contour model and vector field convolution, and a novel parameter active contour model is proposed. This model gets an edge image according to Harris matrix, then estimates probability of noise using mean and variance in a local region to make sure function weights of parameter active contour model and vector field convolution, and gets a global vector field.(2)Geodesic active region (C-V) model has poor segmentation of images with intensity inhomogeneity. To overcome this problem, we propose an active contour model based on local entropy energy. Firstly, we introduce the concept of local entropy into the C-V model to get inhomogeneity information in local regions according to kernel function, and model local entropy energy function; secondly, we use a variational level set to minimize local entropy function, get gradient descent flow of the level set to drive contour curve, and get segmentation of image; finally, simulation experiments are carried on images with intensity inhomogeneity, and segmentation results show our proposed method is effective.(3)Geodesic active contour (GAC) model has weak edge problem and concavity problem. To solve this problem, this paper improves energy function and curve evolution equation:(a) Improving energy function:We use energy function of the LBF model as a new edge stopping function of the GAC model, normalize it, and get a new energy function, whose gadient descent flow can drive contour curve to move.This method can solve weak edge problem and concavity problem in theory, and simulation experiments show this method is useful.(b) Improving curve evolution equation:The unit inward normal of the GAC model was joined to the gradient vector flow of the GVF model, moving the contour curve towards the boundary of the object.Also, it was joined to the region information of the C-V model,getting the curve not only to move to but also to stay at the boundary of the object, which can deal with drawbacks of GAC model.(4)A visual perception based fuzzy c-means clustering algorithm was proposed to solve the problems that the results of complex structural image segmentation are not satisfactory. Firstly, on the basis of the receptive field properties analysis of neurons in the primary visual cortex, a visual nerve cell response function was proposed to calculate image structural feature. Secondly, a ramp function was used to simulate the visual perception of relative brightness change and calculate the difference between pixels in the image and the cluster centers. By fully considering the relationship in direction, relative position and periodic between neighboring stimuli and the central neuron, the model accurately describes the image structural information and effectively suppresses the noise and the complex texture interferences.