Image Segmentation Technology Based On Partial Differential Equation

Image segmentation is a vitial image processing technique in computer vision andimage analysis. So far, there are many ways for image segmentation. Among them theactive contour model based on variational method and level set method is one ofimportant image segmentation methods. It has embodied the superiority of partialdifferential equation in image segmentation. It utilizes the idea of dynamic evolution.Researching active contour model is important for image segmentation. Imagesegmentation technology research based on paritial differential equations can promotemultidisciplinary cross fusion. Moreover, the flexible numerical computational methodhas better stability during the discretization of evolutive partial differential equation,and it can meet the demand in high quality image restoration and accurate imagesegmentation, and so on. In recent years, the active contour model is a research focus,and it is widely applied in edge detection, image segmentation for medical image andtarget tracking, etc.In this paper, some related mathematical theory is stated. Image segmentationmodels based on partial differential equation and some existing deficiencies in activecontour segmenting objects are studied. The main contents are listed as follows:(1) If the blurry edge, the strong noise and the intensity inhomogeneity appear inan image, a traditional active contour model fails to segment contours, especially, for amagnetic resonance image and an ultrasound image in medicine. Because of thesereasons, we propose an active contour based on local linear fitting energies for adifference image. The active contour model is solved by minimizing its energyfunctional. The optimum local linear fitting parameters in the model are obtained.Contours for some images with intensity inhomogeneity are successfully extracted.Experimental results show that the method has the capacity of extracting weak edge andobjects with intensity inhomogeneity.(2) Because only average intensity information is considered in the local binaryfitting model, the model can successfully segment some magnetic resonance images inmedicine. However, the local binary fitting model fails to segment an ultrasound imagewith a lot of noise that affects the distribution of intensity. For extending the applicationfield of the local binary fitting model, we propose an active contour based on localintensities and local gradient fitting energy. By utilizing the level set method to solve, we successfully segment the weak edge in magnetic resonance images and contourswith noise in ultrasound images. Experimental results show that the proposed methodhas the capacity of anti-noise. The segmentation accuracy is higher than that of the localbinary fitting, local and global intensity fitting models.(3) An ultrasound image has serious noise, and its target edge is very weak. Forsolving these problems, we propose an active contour based on local intensity and localBhattacharyya distance energy for image segmentation. Through using the level setmethod, the weak edge successfully extracted. The proposed model weakens theinfluence of noise.(4) A shrinkage velocity term in the geodesic active contour model is introduced.The model can segment deep concave contours. But shrinkage velocity is specifiedbefore segmentation. If it is set differently, the segmented results are different.Additionally, the geodesic active contour model fails to segment contour whose edge isweak and blurry. Because of these problems, we propose a local adaptive parametersetting method for parameters automative setting. We integrate local spatial pointsdistance and local intensity information into the geodesic active contour model, theoriginal geodesic active contour model is improved. Automatic setup parameters in themethod can be achieved. Experimental results show that the model enhances thesegmentation accuracy, and realizes the segmentation for blurry boundaries.(5) Owing to introducing a shrinkage velocity term in the geodesic active contourmodel, the constant velocity is set in advance. If it is chosen too large, theover-segmented result may be obtained. If it is very small, the model fails to segmentcorrectly deep concave boundaries. In addition, while there are multiple objectboundaries, the method still fails to extract all boundaries. Because of these problems,we propose a geodesic active contour model including gradient error control. An errorfunction term about gradient norm is introduced into the geodesic active contour model.The proposed model can segment multiple objects correctly, and weaken thedependence on shrinkage velocity and reduce the operating time.