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.