Chan-Vese functional 及其應用

Abstract

影像分割為電腦視覺的典型問題之一，而目前最廣泛使用的方法有 thresholding、clustering、graph cuts、以矩陣分解為基礎的方法與以偏微分方程為基礎的方法；Chan-Vese 模型則屬於以偏微分方程為基礎的方法，且已經被廣泛使用在影像分割的問題上。Chan-Vese 方法可以成功地用二相片段常數模型（two-phase piecewise constant model）逼近原始影像，用以辨別該影像的前景與背景，同時該影像分割的邊界由水平集函數所表示。儘管 Chan-Vese 模型能成功將影像分割出兩個區域，但其對應的最佳化問題卻不是凸的（convex）。本論文將描述 Chan-Vese functional 在水平集與凸最佳化上的表述，同時提出 Chan-Vese model 在重疊影像（overlaying image）上做分離的新應用。

Image segmentation is a classical issue in computer vision and the state-of-the-art methods include thresholding, clustering, graph cuts, matrix decomposition based methods and partial differential equation based methods. The Chan-Vese model which belongs to partial differential equation approaches has been widely used in image segmentation tasks. The Chan-Vese method, typically is used to distinguish the object and the background of the image, successfully fits a two-phase piecewise constant model to the given image and the segmentation boundary is represented implicitly with a level set function. Although Chan-Vese model is able to segment an image into two regions and can get not bad results, the corresponding minimization problem is not convex. This thesis describes the level set formulation and convex formulation of the Chan-Vese functional, and presents a new application to separate an overlaying image which is overlaid by two images by using modified Chan-Vese model.