一种适合漫反射表面从明暗恢复形状的快速算法

王国珲; 韩九强; 张新曼

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一种适合漫反射表面从明暗恢复形状的快速算法

更新时间：2025-07-09

- 一种适合漫反射表面从明暗恢复形状的快速算法
- A Fast Shape from Shading Method for Diffuse Surfaces
- 西安交通大学学报 2009年43卷第10期页码：7-10+21
- 作者机构：
  
  西安交通大学电子与信息工程学院,西安,710049
- 作者简介：
- 基金信息：
  
  : 2009-04-17. 作者简介: 王国珲(1980-),男,博士生;韩九强(联系人),男,教授,博士生导师. 基金项目: 国家自然科学基金资助项目(60602025);教育部高等学校博士点专项科研基金资助项目(20050698025)
- DOI：
  中图分类号： TP391
- 网络首发：2009-10-10，
  
  纸质出版：2009
- 稿件说明：
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王国珲, 韩九强, 张新曼. 一种适合漫反射表面从明暗恢复形状的快速算法[J]. 西安交通大学学报, 2009,43(10):7-10+21.

A Fast Shape from Shading Method for Diffuse Surfaces[J]. 2009, 43(10): 7-10+21.
王国珲, 韩九强, 张新曼. 一种适合漫反射表面从明暗恢复形状的快速算法[J]. 西安交通大学学报, 2009,43(10):7-10+21. DOI：

A Fast Shape from Shading Method for Diffuse Surfaces[J]. 2009, 43(10): 7-10+21. DOI：

摘要

针对使用朗伯反射模型描述漫反射表面的形状恢复算法存在较大误差的问题

提出了一种基于Oren-Nayar反射模型的从明暗恢复形状的快速算法(FSFS-ON).首先假定摄像机采用正交投影

其方向与光源方向一致

建立适合漫反射表面的图像辐照度方程

然后将该方程转化为包含物体深度信息的Eikonal偏微分方程

使用单调迎风Godunov Hamiltonian函数和fast marching方法逼近该微分方程的黏性解

进而得到物体表面的三维形状.合成花瓶图像的实验结果表明:与同类算法相比

FSFS-ON算法所需的CPU运行时间有较大幅度的减少; 与基于朗伯反射模型的算法相比

FSFS-ON算法恢复三维形状高度的均方根误差降低了35.04%.

Abstract

Focusing on the high error of shape from shading(SFS)for diffuse surfaces

a fast SFS method based on Oren-Nayar reflection model(FSFS-ON)is proposed. The image irradiance equation for diffuse surfaces is established under assumptions that the camera performs orthographic projection and its direction is the same as the direction of the light source. The equation is then transformed into the Eikonal partial differential equation(PDE)that includes the shape information of the surface. The viscosity solution of the resulting PDE is approximated by using the monotone upwind Godunov Hamiltonian and the fast marching method so that the heights of three-dimensional surface are obtained. Experimental results and comparisons on synthetic vase image show that the CPU time of the FSFS-ON algorithm is greatly reduced

compared with the existing methods of the same kind

and that the root mean square errors of the heights of the FSFS-ON algorithm are decreased by 35.04%

compared with the method based on Lambertian reflection model

关键词

Keywords

references

HORN B K P. Height and gradient from shading [J]. International Journal of Computer Vision, 1990, 5(1): 37-75.

ZHANG Ruo, TSAI P S, CRYER J E, et al. Shape from shading: a survey [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, 21(8): 690-706.

DUROU J D, FALCONE M, SAGONA M. Numerical methods for shape-from-shading: a new survey with benchmarks [J]. Computer Vision and Image Understanding, 2008, 109(1): 22-43.

杨磊,韩九强.一种含有镜面反射由明暗恢复形状的新算法 [J].西安交通大学学报, 2007, 41(4): 435-438.

YANG Lei, HAN Jiuqiang. New algorithm of shape-from-shading with specular reflectance [J]. Journal of Xi'an Jiaotong University, 2007, 41(4): 435-438.

AHMED A H, FARAG A A. Shape from shading under various imaging conditions [C]∥Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. Los Alamitos, CA, USA: IEEE Computer Society, 2007.

KIMMEL R, SETHIAN J A. Optimal algorithm for shape from shading and path planning [J]. Journal of Mathematical Imaging and Vision, 2001, 14(3): 237-244.

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WOLFF L B, NAYAR S K, OREN M. Improved diffuse reflection models for computer vision [J]. International Journal of Computer Vision, 1998, 30(1): 55-71.

RAGHEB H, HANCOCK E R. Surface normals and height from non-Lambertian image data [C]∥Proceedings of the 2nd International Symposium on 3D Data Processing, Visualization, and Transmission. Los Alamitos, CA, USA:IEEE Computer Society, 2004: 18-25.

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SETHIAN J A. Fast marching methods [J]. SIAM Review, 1999, 41(2): 199-235.

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