两种二维交叉熵阈值法等价性证明及快速实现

二维直方图斜分最大类间交叉熵阈值(TOSMICE)法和二维交叉熵直线型阈值(TMCELT)法是两种有效的分割方法，且都是二维交叉熵阈值法，为了考查二者分割结果是否相同，提出对两种二维交叉熵阈值法的等价性探讨。首先分析两种二维交叉熵阈值法：虽然名称不同但经过证明其分割原理相同，然后对两种选取公式进行推导得到一种最简阈值选取公式，从而证明了二者的等价性，随之提出基于最简公式的一般递推算法，最后将二维直方图分布特性与这种算法有机结合得到新型快速的递推算法。实验结果表明，两种方法获取的阈值相等，分割结果相同；并且与当前二维直方图斜分递推算法相比，所提出的新型递推算法速度更快。

Equivalent proof of two 2-D cross entropy thresholding methods and their fast implementation

The method of two-dimensional oblique segmentation maximum inter-class cross entropy (TOSMICE) and the method of two-dimensional maximum cross entropy linear type (TMCELT) are effective cross entropy threshoding methods. To compare their segmentation results, the equivalence about them was discussed in this paper. First the two methods were analyzed: with different names, the cardinal segmentation principles were proved alike; then the formulae were deduced to obtain a simplest formula, the equivalence of two methods was proved, and its recurring algorithm of the formula based on 2-D histogram oblique segmentation was inferred; finally the features of 2-D histogram and the algorithm were combined to get a novel recurring algorithm. The experimental results show that there are equal thresholds in the two methods and that the proposed recurring algorithm's speed is much faster than that of the current method based on 2-D oblique segmentation.