Image Segmentations Via Partial Differential Equations

Image segmentation is an essential preliminary step in most automatic pictorial pattern recognition and scene analysis problems, The target is to isolate the interested objects from an image and to get the boundaries. There are a lot of segmentation methods existing. Image segmentation based on Partial Differential Equation(PDE) get quite a lot attention for its novel and efficient segmentation process. It had been proposed to address a wide range of image segmentation problems in image processing and computer vision. But there are still many drawbacks needed to be improved。The CV Model is one of the most famous region-based methods. The LBF (Local Binary Fitting) model is an improvement of it. Not like the CV model, The LBF model introduced a local binary fitting (LBF) energy with the help of a Gaussian kernel function. Because LBF energy can use the local information of the image, so it solves the inhomogeneous problems of the CV model. But at the same time, the Gaussian kernel function also brings many problems. Because its value is determined completely by the distance between two pixels,this neglect the pixels'own properties and cause fitting errors when the near pixels are un-normal points. And this makes the LBF model sensitive and not stable.So in order to solve these problems and also preserve the advantages, an improved method was proposed. The new method used local entropy of the inputting image as fitting weight, this makes the new method more reasonable because the local entropy was determined by the distribution in the neighborhood. This new approach reduces the affection from noise and edges, makes the model more stable than the CV and LBF model. Experiments show the advantages of our method.And we also proposed a method to locate an initial contour. It was based on the boundary blurring phenomenon during image smoothing. With its help, we can easily locate the initial contour close to the boundary, it reduced a big lot of iterations, and the time cost is about 80% off. And it also makes those models whose energy is non-convex become more robust. We combine this method with the LBF model to show how it works.