A Fast Viscosity Solution Algorithm for Shape from Shading

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A Fast Viscosity Solution Algorithm for Shape from Shading

更新时间：2025-05-08

- A Fast Viscosity Solution Algorithm for Shape from Shading
- Vol. 43, Issue 6, Pages: 43-47(2009)
- 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：
- DOI：
  CLC： TP391
- Online First：10 June 2009，
  
  Published：2009
- 稿件说明：
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A Fast Viscosity Solution Algorithm for Shape from Shading[J]. 2009, 43(6): 43-47.
DOI：

A Fast Viscosity Solution Algorithm for Shape from Shading[J]. 2009, 43(6): 43-47. DOI：

摘要

针对传统的从明暗恢复形状(SFS)算法存在误差大、耗时长的问题

提出了一种SFS的快速黏性解算法(PSFS-FVS).首先假定物体表面反射模型为朗伯模型

建立透视投影下的图像辐照度方程

然后将该方程转化为包含物体表面深度信息的静态Hamilton-Jacobi偏微分方程

使用非线性规划原理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Prados-Faugeras算法相比

PSFS-FVS算法在相同迭代次数时

恢复三维形状高度的平均相对误差降低了8.7%; 在相同的误差条件下

所需的CPU运行时间减少了23.5%.实际人脸图像的三维形状恢复结果表明

PSFS-FVS算法在恢复局部细节信息时更加准确有效.

Abstract

Focusing on the high error and time consuming of the algorithms for shape from shading(SFS)

a fast viscosity solution algorithm of perspective SFS(PSFS-FVS)is proposed. The image irradiance equation is established on the basis of Lambertian reflectance model and perspective camera projection. Then the equation is transformed into a static Hamilton-Jacobi partial differential equation(PDE)that contains the shape information of a surface. The viscosity solution of the resulting PDE is approximated by using a nonlinear programming method

and then the surface shape is generated. Experimental results and comparisons with the Prados-Faugeras algorithm on synthetic vase image show that the mean relative error of the height of the PSFS-FVS algorithm is reduced by 8.7% with the same iterations

and the CPU time of the PSFS-FVS algorithm is decreased by 23.5% at the same error

respectively. Reconstruction results from real face image show that the PSFS-FVS algorithm is more accurate and effective than the Prados-Faugeras algorithm in dealing with the local of the surface.

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references

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

ZHANG R, 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.一种由明暗恢复形状的改进变分算法[J].西安交通大学学报,2008,42(4):418-422.

YANG Lei, HAN Jiuqiang. Improved variational algorithm of shape-from-shading [J]. Journal of Xi'an Jiaotong University, 2008, 42(4): 418-422.

ROUY E, TOURIN A. A viscosity solutions approach to shape-from-shading [J]. SIAM Journal on Numerical Analysis, 1992, 29(3): 867-884.

PRADOS E, FAUGERAS O. Shape from shading: a well-posed problem? [C]∥Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. Los Alamitos, CA, USA: IEEE Computer Society, 2005: 870-877.

PRADOS E, FAUGERAS O, CAMILLI F. Shape from shading: a well-posed problem, RR-5297 [R]. Paris, France: INRIA, 2004.

JIA Honghai, WANG Ying, HAN Jiuqiang, et al. Research on a new sfs shape recovery method based on perceptive model [C]∥Proceedings of the 10th Meeting on Image Recognition and Understanding. Tokyo, Japan: IEICE Information and System Society, 2007: 649-653.

PRADOS E, FAUGERAS O. A rigorous and realistic shape from shading method and some of its applications, RR-5133 [R]. Paris, France: INRIA, 2004.

PRADOS E, CAMILLI F, FAUGERAS O. A unifying and rigorous shape from shading method adapted to realistic data and applications [J]. Journal of Mathematical Imaging and Vision, 2006, 25(3): 307-328.

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