基于Phong模型的明暗恢复形状的新算法

计算机工程与科学

基于Phong模型的明暗恢复形状的新算法

赵中滨，张志毅，邢彩燕

(西北农林科技大学信息工程学院，陕西西安 712100)

收稿日期:2016-08-16 修回日期:2016-12-07 出版日期:2018-03-25 发布日期:2018-03-25
基金资助:
国家863计划(2013AA10230402)；国家自然科学基金(61303124)

A new shape-from-shading algorithm

based on Phong model

ZHAO Zhongbin,ZHANG Zhiyi,XING Caiyan

（College of Information Engineering,Northwest A & F University,Xi’an 712100,China）

Received:2016-08-16 Revised:2016-12-07 Online:2018-03-25 Published:2018-03-25

摘要/Abstract

摘要：

针对传统的混合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从单幅图像混合表面明暗信息恢复形状的新算法。采用Phong反射模型来描述物体表面反射特性，假设光源处于相机的光心处，建立透视投影下的图像辐照度方程。然后由辐照度方程构造包含物体深度信息的HamiltonJacobi偏微分方程，引入局部高阶LLF通量分裂格式和五阶WENO格式逼近微分方程的粘性解，最终得到物体表面三维形状。实验结果表明，与传统算法相比，新算法的恢复高度的最大误差和平均误差均显著降低。

关键词: 明暗恢复形状, Phong反射模型, 透视投影, 粘性解

Abstract:

Focusing on the big error in traditional ShapeFromShading (SFS) algorithms for hybrid surfaces, a new SFS algorithm for a single image under hybrid surfaces based on perspective projection is proposed. In this paper, the Phong reflection model is used to describe the reflectance property of the surfaces. Assuming that the light source is located at the camera’s optical center, the image irradiance equation is established for this model. Then, the image irradiance equation is transformed into the HamiltonJacobi Partial Differential Equation (PDE) including the shape information of the surfaces. Using the highorder LaxFriedrichs (LLF) flux splitting scheme and fiveorder Weighted Essentially NonOscillatory (WENO) scheme approximates the viscosity solution of the PDE. Finally, the heights of threedimensional surface are obtained. Experimental results show that themaximum error and the mean error of 3D surface recovery of the new algorithm are significantly reduced, compared with the traditional algorithm.

Key words: shape from shading, Phong reflection model, perspective projection, viscosity solution

赵中滨，张志毅，邢彩燕. 基于Phong模型的明暗恢复形状的新算法[J]. 计算机工程与科学.

ZHAO Zhongbin,ZHANG Zhiyi,XING Caiyan.

A new shape-from-shading algorithm

based on Phong model

[J]. Computer Engineering & Science.