基于分形的从明暗恢复形状算法研究

从明暗恢复形状是计算机视觉领域中的经典病态问题，传统方法是通过引入光滑约束等条件来获得问题的解，但传统方法存在因过平滑而失真的缺点。针对传统方法恢复结果的局限性，提出了一种基于分形约束的从明暗恢复形状的新算法，该方法首先给出分形约束条件，之后结合反射图线性化与最小能量法来计算出曲面高度。该方法不仅克服了传统算法因基于光滑假设所造成的恢复结果过分平滑而失真的缺点，且不需要可积性的约束条件，也不需要对边界条件的假设，实验结果表明，该方法用于自然景物的三维表面重构，可获得比传统方法更好的恢复效果。

A Method of Shape from Shading Based on Fractal Constraint

SFS(Shape from Shading) is one of the class ill posed problems of Computer Vision. General SFS algorithm often involved some additional constraints, such as smoothness constraint, to find a unique solution. However, this is based on the assumption that the reconstructed surface is continuous. Concerning the disadvantage of tradition shape from shading algorithm, a new algorithm of shape from shading based on fractal constraint is proposed in this paper. The method first introduces a novel fractal constraint, then through formulating the SFS problem using techniques of linearization of the reflectance map and minimizaiton of an energy function calculates the surface height. The proposed method overcome the disadvantage of tradition shape from shading algorithm, that is, distortion of recovered result of the 3D surface causing from assumed smoothness constraint, and does not require any integrability constraint or artificial assumption on boundary conditions. Experimental results show that new method is better than tradition method in aspect of 3D surface reconstruction for natural scenery.