基于视觉心理学的SFS流形算法研究

The manifold algorithm for SFS problems based on visual psychology

通过视觉方法获取形状在科学研究及工程实践中有着重要作用,灰度图像是最容易获取的视觉信息之一。目前由灰度重构的形状(SFS,shape from shading)受到了广泛的关注,但现有的算法稳定性差、效率低,一直阻碍着SFS方法的推广应用。受近期的视觉心理学研究成果的启发,针对SFS问题,从局部分析入手,即:在图像上,在每一灰度极值点附近,根据灰度单调变化的情况,形成一个椭圆形邻域,对应着表面凹凸区;在每一椭圆域上,形状可用抛物面逼近,其参数可由局部辐射度约束求解;整个图像被椭圆形邻域覆盖,这些覆盖可构成一个二维流形;借助于流形上单位分解函数,各局部抛物面粘合在一起,形成光滑的整体形状;总体形状在整幅图像的灰度约束下再进行全局优化,可得到最终的重构结果。给出了初步算例,算法的稳定性和效率均有大幅度提高。

Although shape from shading （SFS） problem has been studied for three decades using mathematical analyses, robust and efficient algorithm is still lacking. Inspired by the recent visual psychological results, a two-stage strategy to solve SFS problem is presented： first reconstruct local shape and then global shape. For each intensity maximum in the image, an ellipse region is generated surround it, in which the shading changes monotonously from center to exterior. These regions can be regarded as corresponds of the concaves and convexes of the 3D shape, which can be approximated by paraboloids and reconstructed from local shading analysis. The adjacent ellipse regions overlap each other and occupy the image in the whole. A 2D manifold can be constructed from these overlapped regions, and the partition of unit functions of the manifold can be used to glue the local surfaces together to represent the whole shape. At last, the whole shape is adjusted to get best result through a global optimization process.