二值化方法：Minimum Error Thresholding

Kittler二值化方法，是一种经典的基于直方图的二值化方法。由Kittler在1986年在论文“Minimum Error Thresholding”提出。

参考了ImageShop提供的C#版本（http://www.cnblogs.com/Imageshop/p/3307308.html），做了简单修改得到了C++版本的，代码如下：

/*灰度图像的二值化方法*/

class CxThreshold
{
public:
    static int CalcKittlerMinError(int* HistGram)
    {
        int X, Y;
        int MinValue, MaxValue;
        int Threshold ;
        long PixelBack, PixelFore;
        double OmegaBack, OmegaFore, MinSigma, Sigma, SigmaBack, SigmaFore;
        for (MinValue = 0; MinValue < 256 && HistGram[MinValue] == 0; MinValue++) ;
        for (MaxValue = 255; MaxValue > MinValue && HistGram[MinValue] == 0; MaxValue--) ;
        if (MaxValue == MinValue) return MaxValue;          // 图像中只有一个颜色
         if (MinValue + 1 == MaxValue) return MinValue;      // 图像中只有二个颜色
         Threshold = -1;
        MinSigma = 1E+20;
        for (Y = MinValue; Y < MaxValue; Y++){
            PixelBack = 0; PixelFore = 0;
            OmegaBack = 0; OmegaFore = 0;
            for (X = MinValue; X <= Y; X++){
                PixelBack += HistGram[X];
                OmegaBack = OmegaBack + X * HistGram[X];
            }
            for (X = Y + 1; X <= MaxValue; X++){
                PixelFore += HistGram[X];
                OmegaFore = OmegaFore + X * HistGram[X];
            }
            OmegaBack = OmegaBack / PixelBack;
            OmegaFore = OmegaFore / PixelFore;
            SigmaBack = 0; SigmaFore = 0;
            for (X = MinValue; X <= Y; X++) SigmaBack = SigmaBack + (X - OmegaBack) * (X - OmegaBack) * HistGram[X];
            for (X = Y + 1; X <= MaxValue; X++) SigmaFore = SigmaFore + (X - OmegaFore) * (X - OmegaFore) * HistGram[X];
            if (SigmaBack == 0 || SigmaFore == 0){
                if (Threshold == -1)Threshold = Y;
            }
            else{
                SigmaBack = sqrt(SigmaBack / PixelBack);
                SigmaFore = sqrt(SigmaFore / PixelFore);
                Sigma = 1 + 2 * (PixelBack * log(SigmaBack / PixelBack) + PixelFore * log(SigmaFore / PixelFore));
                if (Sigma < MinSigma){
                    MinSigma = Sigma;
                    Threshold = Y;
                }
            }
        }
        return Threshold;
    }
};