华东师范大学学报(自然科学版) ›› 2007, Vol. 2007 ›› Issue (5): 70-77.

• 数学 统计学 • 上一篇    下一篇

黎曼流形上内蕴方式的图像轮廓提取

范劲松1,2 , 皮　玲, 黎　芳1, 沈超敏4   

  1. 1. 华东师范大学 数学系, 上海 200062; 2. 温州大学 数学与信息科学学院, 浙江 温州 325035; 3. 上海交通大学 数学系, 上海 200030; 4. 华东师范大学 计算机系, 上海 200062
  • 收稿日期:2006-12-29 修回日期:2007-04-23 出版日期:2007-09-25 发布日期:2007-09-25
  • 通讯作者: 沈超敏

Intrinsic Image Segmentation on a Riemannian Manifold(Chinese)

FAN Jin-song1,2, PI Ling3, LI Fang1, SHEN Chao-min4   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200062, China; 2. School of Mathematics and Information Science, Wenzhou University, Wenzhou Zhejiang 325035, China; 3. Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, China; 4. Department of Computer Science, East China Normal University, Shanghai 200062, China
  • Received:2006-12-29 Revised:2007-04-23 Online:2007-09-25 Published:2007-09-25
  • Contact: SHEN Chao-min

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摘要： 提出了一种基于黎曼几何观点的图像轮廓提取模型.
在图像空间上直接赋予一种由图像灰度信息导出的黎曼度量,
使之成为黎曼流形,
然后在此黎曼流形上利用水平集方法对曲线以平均曲率流进行演化.
由于灰度信息已嵌入黎曼流形中, 演化以内蕴方式进行.
计算结果表明该方法是已有模型的推广,
可对曲线演化过程进行更加精细的控制.
数值实验结果证实了该方法的有效性, 并展示了该模型的一些特点.

关键词: 图像处理, 轮廓提取, 黎曼度量, 水平集方法 , 图像处理, 轮廓提取, 黎曼度量, 水平集方法

Abstract: An image segmentation model based on the view of
Riemannian Geometry was proposed. Endowed with a Riemannian metric
derived from the gray scale information of a given image, the image
space became a Riemannian manifold. On this Riemannian manifold, we
evolved a curve by the mean curvature flow using the level set
methods. Because the gray scale information had been embedded into
the Riemannian manifold, the evolution was intrinsic. Calculations
show that the method is an extension of existing models;
furthermore, finer controls for the evolution can be achieved.
Numerical experiments show the effectivity and some good features of
the proposed method.

Key words: segmentation, riemannian metric, level set methods, image processing, segmentation, riemannian metric, level set methods

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