Image Segmentations Based On Partial Differential Equations

Image segmentation and boundary extraction are very important in the fields of image understanding, pattern recognition, computer vision and so on. They are also the basis of the later image analysis. Up to now, there is still not a common method for any type of images in image segmentation. There are great deal of researches on how to detect the objects in an image quickly and accurately. Recently, image segmentations based on partial differential equation (PDE) has been studied broadly and become a key technique in the field of image processing.After reviewing the literatures involved image segmentation techniques and PDE–based segmentation methods, this dissertation discusses geometric active contour(GAC) models (implemented via level set methods) and obtains the following results:In PDE-based image segmentations, edge-based GAC models rely on the halting speed function (HSF), which is typically the function of image gradient, to stop the active contour (evolving curve) on the edges of the desired objects. However, the GAC models with original HSF are not able to make the active contour quickly move towards the desired object edges because the HSF is not large enough in homogenous region. Therefore, they have the drawbacks of long evolving time. In order to speed up the evolution of the active contour, this dissertation proposes a scheme that the scale transform is applied to the HSF. Experimental results show that the proposed scheme can significantly reduce segmentation time and perform better in the presence of concave and weak edges.Then, level set method without reinitialization proposed by Li etc [Level set evolution without re-initialization: a new variational formulation. IEEE International Conference on Computer Vision and Pattern Recognition, 2005] is discussed. It has also the drawback of long evolving time. In order to make the curve precisely converge to the object boundary and shorten the segmentation time, this dissertation proposes a new model for binary image segmentations. Experimental results on binary images show the proposed model perform well and greatly reduce the segmentation time.