基于变换矩阵的三维重建算法研究

Study of 3D Reconstruction Algorithm Based on Inverting Matrix

先对传统明暗恢复形状(Shape From Shading)算法进行简单分析,然后提出了一种改进的SFS算法。在图像亮度与反射图函数的差值采用雅可比迭代方法的基础上,改进变换矩阵,使其特征值包含三个平方项,减少了矩阵的结果无效的情形,并且提高了迭代的收敛速度。针对光照条件不好的图像,提出了一种先旋转坐标轴,后双向重建的算法。通过旋转坐标轴一定角度,改变光源方向,减少图像失真,然后双向重建的两幅图像通过加权平均法得到物体的三维重建图。最后,用Matlab编制相应程序,在计算机上进行仿真。实验结果表明,改进的SFS算法是有效的,能够克服传统SFS算法精度低的缺陷,提高了三维重建的稳定性和精确度,缩短了三维重建的时间。

First,simply analyses traditional Shape From Shading algorithms,and then propose a modified SFS algorithm.Based on the difference between the image brightness and the reflectance function using jacobi iteration,modify inverting matrix,to make its eigenvalues consist of three squared terms,decrease the case in which the result of matrix is not valid,improve the convergent speed of iteration.For the images of bad light conditions,propose an algorithm which first rotates coordinates and then bi-direction reconstruction.By rotating coordinates a certain angle,change the light direction,decrease the distortion of the images,and then two images of bi-direction reconstruction use the method of weighted average to obtain three-dimensional reconstruction image of the object.Finally,use Matlab compiling corresponding progarms,simulate in the computer.The experiment results show that the modified SFS algorithm is effective,can overcome the disadvantage of low precision in traditional SFS,improve the stability and accuracy of three-dimensional reconstruction,and shortens the time of three-dimensional reconstruction.