一种由明暗恢复形状的改进变分算法  

Improved Variational Algorithm of Shape-from-Shading

作　　者：杨磊[1] 韩九强[1] 

机构地区：[1]西安交通大学电子与信息工程学院,西安710049

出　　处：《西安交通大学学报》2008年第4期418-422,共5页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(60502021);教育部高等学校博士点专项科研基金资助项目(20050698025)

摘　　要：针对变分算法可能丢失表面细节信息的问题,提出了一种由明暗恢复形状的改进变分算法,使用接近实际的混合反射模型描述的反射图方程和图像梯度方程构造了新的目标泛函,由于图像梯度反映了二维图像的细节信息,新目标泛函比仅使用反射图方程的目标泛函蕴涵了更加丰富的三维形状细节信息.然后,使用变分原理求解该目标泛函,得到由明暗恢复形状的改进变分算法.所提出的算法比基本变分算法三维形状恢复的精度有显著提高.合成半球图像的实验表明,新算法在相同迭代次数时恢复三维形状的平均相对误差比基本变分算法减小了13.45%.实际复杂图像的三维形状恢复结果表明,新算法在恢复表面三维细节时比基本变分算法更加准确.An improved variational approach of shape-from-shading is proposed. A new objective functional is formulated using a reflectance map equation and an image gradient equation. The reflectance map equation is described by a hybrid reflectance model which is prone to reality. Since the gradients of images exhibit the detailed information of two-dimensional image, the new objective functional contains more information of three-dimensional surface than the objective functional formulated by only reflectance map equation. Then, an improved algorithm of shape-fromshading is proposed by using the variational improved evidently compared with the basic principle. The accuracy of the proposed algorithm is variational algorithm, and experiments on synthetic images of hemisphere show that the relative average error of the proposed algorithm is reduced by 13.45% under the same iteration times. Reconstruction results from real complicated images show that the proposed algorithm is more accurate than the basic variational algorithm in dealing with the details of the surface.

关 键 词：变分算法 明暗恢复形状 反射图 图像梯度 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]