基于三维直方图降维和重建的快速最小误差阈值法

3维最小误差阈值分割法(3D-MET)的抗噪性很强，但计算复杂度非常高。其快速递推方法(3D-RMET)通过构建查找表去除了大量冗余操作，但其速度仍然不能满足实际工程要求。该文采用直方图降维和分级策略提出新的快速实现方法。该方法首先将3D-MET的最优阈值判别式进行分解，并给出新的阈值计算公式，将阈值搜索的空间维度从3维降到1维；然后将3维直方图进行分组和重建，进一步提高了算法处理速度。最后给出了3D-MET, 3D-RMET及本文方法的分割结果，并采用量化指标对结果进行对比分析。实验及量化对比结果表明，该文方法保持了原3D-MET法的强抗噪性，且将其时间复杂度降为O(L1/2)。与3D-RMET相比，该文方法快了6个数量级，较有效地解决了原方法时间复杂度高的问题。

Fast Minimum Error Thresholding Based on Dimension Reduction and Rebuilding of the 3-Dimensional Histogram

Three-dimensional Minimum Error Thresholding (3D-MET) is more robust to noise than MET and 2D-MET, but its computational complexity grows exponentially. By constructing look-up tables recursively, its fast algorithm 3D-RMET reduces the complexity from O(L6) to O(L3), but its complexity is still too high to be applied to the project. A novel fast method is proposed based on dimension reduction and grading strategy. Firstly, based on the decomposition of 3D-MET, a new threshold discriminant is proposed to reduce the dimensionality from 3D to 1D. And then, the 3D histogram of test image is grouped and rebuilt to further improve its processing speed. Finally, segmentation results of 3D-MET, 3D-RMET and the proposed method are given and evaluated by performance criteria. Experiments and evaluation results indicate that without losing the robustness to noise, the proposed method reduces the time complexity from O(L6) to O(L1/2). Compared with 3D-RMET, the proposed method is 6 magnitudes faster than the former.