曲率估计在深度图像分析中占有重要地位。传统的有限差分或局部拟合方法未考虑到表面上可能出现的不连续性，因而会不可避免地出现错误。为了得到有效可靠的曲率估计，本文提出了基于自适应局部表面拟合和鲁棒最大似然估计的曲率估计算法。首先，提出曲面是分片光滑的假设，表面曲率需从该像素所属的光滑曲面片来估计。其次，定义了一个能量函数来度量拟合窗的平滑度，在局部表面拟合时，依据最小化能量函数的原则来自适应移动拟合窗的中心，以使拟合窗达到最"光滑"。最后，采用鲁棒最大似然估计以消除仍然存在的"局外点"的影响。理论分析和实验结果证明估计算法是稳健、可靠、有效的且计算复杂度小。%Curvature estimation plays an important role in range imageanalysis.Without consideration of discontinuities possible existing in range image, traditional finite difference or local surface fitting method, inevitably produce errors. To overcome those drawbacks and get a reliable estimation, an estimation algorithm based on adaptive surface fitting and robust M-estimation is proposed. Firstly, this paper assumes that the surface of range image is piecewise smooth, and estimates curvature from the smooth piece of surface to which the current point belongs. Secondly, an energy function is defined to measure the smoothness of the fitting window, and then move the center of fitting window adaptively to minimize the energy function to get the best fitting window. Finally, a robust M-estimation on the data set to eliminate the effects of the remaining“outliers”. Theoretical analysis and experimental results prove that the estimation algorithm is robust, reliable, efficient and the computational complexity is limited.
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