透视投影下的镜面反射表面形状恢复新算法

刘瑞玲; 韩九强

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透视投影下的镜面反射表面形状恢复新算法

更新时间：2025-12-08

- 透视投影下的镜面反射表面形状恢复新算法
- Shape from Shading for Specular Surfaces under Perspective Projection
- 西安交通大学学报 2009年43卷第2期页码：6-9+71
- 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：
  
  : 2008-05-20. 作者简介: 刘瑞玲(1977-),女,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(60502021);教育部高等学校博士学科点专项科研基金资助项目(20050698025)
- DOI：
  中图分类号： TP391
- 网络首发：2009-02-10，
  
  纸质出版：2009
- 稿件说明：
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刘瑞玲, 韩九强. 透视投影下的镜面反射表面形状恢复新算法[J]. 西安交通大学学报, 2009,43(2):6-9+71.

刘瑞玲, 韩九强. Shape from Shading for Specular Surfaces under Perspective Projection[J]. 2009, 43(2): 6-9+71.
刘瑞玲, 韩九强. 透视投影下的镜面反射表面形状恢复新算法[J]. 西安交通大学学报, 2009,43(2):6-9+71. DOI：

刘瑞玲, 韩九强. Shape from Shading for Specular Surfaces under Perspective Projection[J]. 2009, 43(2): 6-9+71. DOI：

摘要

针对含有镜面反射的表面形状恢复算法存在较大误差的问题

提出一种透视投影下基于Ward模型的从明暗恢复形状的新算法.首先假设光源处在相机的光心处

并引入光强衰减距离因子

用Ward模型建立含有强镜面反射的表面反射图方程

进而由反射图方程构造透视投影下关于形状深度信息的偏微分方程

并用Lax-Friedrichs Sweeping方法和改进的非线性黏性因子求解该偏微分方程

得到表面三维形状.新算法具有准确可靠的特点

比同类算法更加稳定.对合成花瓶图像的实验表明

与基于正交投影的算法相比

新算法恢复高度的平均误差下降了13.5%.

Abstract

In order to recover the shape of surfaces that have specular reflection

a new shape from shading method is presented based on the Ward reflectance model and the perspective projection. It is assumed that the light source is located at the camera's optical center and that the attenuation of the illumination due to distance is taken into account. The bidirectional reflectance distribution function of the specular surface based on Ward model is designed

and then a partial differential equation(PDE)of the shape under perspective projection is established. The PDE is solved by the Lax-Friedrichs sweeping method and the modified nonlinear artificial viscosity for the surface shape. The proposed method is more accurate and stable than other existing methods of the same kind. Experiments on synthetic specular vase show that the reduction in the average height error of the proposed method is about 13.5% compared with the method under orthographic projection.

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references

HORN B K P. Shape from shading:a method for obtaining the shape of smooth opaque object from one view [D]. Cambridge, MA, USA: Massachusetts Institute of Technology,1970.

ABDELREHIM A, AFY F. Shape from shading for hybrid surfaces [C]∥IEEE International Conference on Image Processing. Los Alamitos, CA, USA: IEEE Computer Society, 2007: 525-528.

HIDEO S, KAZUKO O, SHINJI O. Recovery of shape and surface reflectance of specular object from relative rotation of light source [J]. Image and Vision Computing, 2003, 21(9): 777-787.

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 reflection [J]. Journal of Xi'an Jiaotong University, 2007, 41(4): 435-438.

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KAO C Y,STANLEY O, QIAN Jianliang. Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations[J]. Journal of Computational Physics, 2004, 196(1): 367-391.

ABDELREHIM A, AFY F. A new formulation for shape from shading for non-Lambertian surfaces [C]∥Proceedings of 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Piscataway, NJ, USA: IEEE, 2006: 1817-1824.

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