论文标题
n维凸形和应用的水平集表示方法
A level set representation method for N-dimensional convex shape and applications
论文作者
论文摘要
在这项工作中，我们提出了一种新的有效方法，用于凸形表示，无论相关对象的维度如何，都使用级别集合方法。凸面先验对于计算机视觉中的对象完成非常有用。为高维凸对象表示有效的方法是一项非常具有挑战性的任务。在本文中，我们证明所考虑的对象的凸度等于相关的签名距离函数的凸度。然后，使用凸功能的二阶条件来等效地表征形状凸度。我们将此新方法应用于两个应用程序：具有凸面之前的对象分割和凸出的船体问题（尤其是在离群值的情况下）。对于这两种应用，涉及的问题都可以写为具有三个约束的一般优化问题。为优化问题提供了基于乘数交替方向方法的有效算法。进行数值实验以验证所提出的表示方法和算法的有效性和效率。
In this work, we present a new efficient method for convex shape representation, which is regardless of the dimension of the concerned objects, using level-set approaches. Convexity prior is very useful for object completion in computer vision. It is a very challenging task to design an efficient method for high dimensional convex objects representation. In this paper, we prove that the convexity of the considered object is equivalent to the convexity of the associated signed distance function. Then, the second order condition of convex functions is used to characterize the shape convexity equivalently. We apply this new method to two applications: object segmentation with convexity prior and convex hull problem (especially with outliers). For both applications, the involved problems can be written as a general optimization problem with three constraints. Efficient algorithm based on alternating direction method of multipliers is presented for the optimization problem. Numerical experiments are conducted to verify the effectiveness and efficiency of the proposed representation method and algorithm.
