New Local Linear Algorithm of Shape-From-Shading Based on Finite Element method

3-D shape measurement is widely used in industry such as automatic inspection. And 3-D shape reconstruction from 2-D image(s) is a central problem in computer vision. Lots of shape reconstruction methods based on image(s) have been proposed and used in automatic inspection. A four-neighbor local linear algorithm of shape-from-shading based on Unite element method is proposed. A smooth surface, which is approximated by finite little facets, is expressed by a linear combination of a set of basis functions which are central symmetrical. Hybrid reflection models which contain diffuse reflectance and specular reflectance are used to formulate reflectance map equation because they are prone to reality. Based on a set of basis functions using finite element technique, hybrid reflection models are linearized. Thinking of digital image´s characteristic, the gray value of a pixel of image is regard as the mean value of a small facet´s. When the total brightness error of input image and reflection map is considered, a set of linear equations about the height of unknown surface is derived using minimization approach. The height of unknown surface is calculated using these equations by iterative algorithm. Two series experiments on synthetic images and real images are given to illuminate the efficiency of the proposed method.