基于曲面法向量的曲面恢复

从另一个角度研究三维曲面的恢复,即根据曲面法向量,考虑多块曲面的重构.算法输入的数据是估计的曲面法向量,比如输入的数据是根据从阴影恢复形状或从纹理恢复形状等计算机视觉低层次处理中得到.通过球面坐标变换把曲面法向量分解成两个函数;然后再对这两个函数进行滤波处理,通过对这两个分割的叠加将空间曲面分割成几个子曲面;最后利用Green函数分别恢复各个子曲面.

ISSN 1000-9825, CODEN RUXUEW E-mail: jos@iscas.ac.cn

Journal of Software, Vol.17, Supplement, November 2006, pp.1 10 doc.xuehai.net © 2006 by of Journal of Software. All rights reserved. Tel/Fax: +86-10-62562563

基于曲面法向量的曲面恢复

胡茂林1,2+, 谢世朋1,2

1

2 (安徽大学 智能计算与信号处理实验室,安徽 合肥 230039) (安徽大学 数学与计算科学学院,安徽 合肥 230039)

Recovering Surfaces from the Gauss Map

HU Mao-Lin1,2+, XIE Shi-Peng1,2

1

2(The Laboratory of Intelligent Computing and Signal Processing, Anhui University, Hefei 230039, China) (School of Mathematics and Scientific Computing, Anhui University, Hefei 230039, China)

+ Corresponding author: Phn: +86-551-5107894, E-mail: hml@ahu.edu.cn

Hu ML, Xie SP. Recovering surfaces from the Gauss map. Journal of Software, 2006,17(Suppl.):1 10.

doc.xuehai.net

Abstract: This paper studies 3D surface integration from novel angle. The authors consider the construction to the

multiple surface patches, not one surface, from the Gauss map. The algorithm takes as its input a 2D field of surface

normal estimates, delivered, for instance, by a shape-from-shading or shape-from-texture procedure. The authors

disintegrate the Gauss map into two functions by the spherical coordinates, and then borrow the ideas from routine

image processing theory to filter the two functions and to segment the space surface into several subsurface, at last

the authors use the integrability to recover the subsurface individually. The method only exploits the general

techniques in image processing, but can supply better results than the previous researches, which are only based on

one function model, especially in the preservence the edges between different surfaces. The method is evaluated on

synthetic and real data delivered by a shape-from-shading algorithm. The approach provides an actually way to use

the normal maps of the surface.

Key words: Gauss map; surface recovering; Green formula; shape-from-shading

摘 要: 从另一个角度研究三维曲面的恢复,即根据曲面法向量,考虑多块曲面的重构.算法输入的数据是估计

的曲面法向量,比如输入的数据是根据从阴影恢复形状或从纹理恢复形状等计算机视觉低层次处理中得到.通

过球面坐标变换把曲面法向量分解成两个函数;然后再对这两个函数进行滤波处理,通过对这两个分割的叠加

将空间曲面分割成几个子曲面;最后利用Green函数分别恢复各个子曲面.虽然只利用了一般的图像处理技术,

却能得到比传统的基于曲面法向量的方法更好的结果,特别是边界部分的恢复.这是因为传统的方法只是考虑

恢复一个曲面模型,因此在不同曲面的边界上会产生模糊.最后利用模拟数据和由阴影恢复形状算法获取真实

数据来评价提出的算法,并都与传统的方法进行了比较.

关键词: 曲面法向量;曲面恢复;Green函数;从阴影恢复形状

Supported by the Foundation of Intelligence Project of Higher Education of Anhui, China (安徽省高校“十五”优秀人才计划); the

Innovative Research Team of 211 Project in Anhui University of China (安徽大学创新团队项目)

Received 2006-03-15; Accepted 2006-09-11

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