CLAHE的实现和研究

CLAHE算法对于医学图像，特别是医学红外图像的增强效果非常明显。

CLAHE  https://en.wikipedia.org/wiki/Adaptive_histogram_equalization

中文方面非常好的资料 限制对比度自适应直方图均衡化算法原理、实现及效果

在OpenCV中已经实现了CLAHE,但是它在使用过程中，存在参数选择的问题。为了从根本上搞明白，我参考了网络上的一些代码

主要是来源 http://blog.csdn.net/abcd1992719g/article/details/25483395

实现了基于OpenCV的CLAHE实现和研究。从最基本的开始做，分别实现HE算法，AHE算法，CLHE算法和CLAHE算法。素材分别采用了手部和手臂的红外图片，同时调用OpenCV生成代码和自己编写代码进行比对。

调用代码和实现效果:

int _tmain( int argc, _TCHAR * argv[])
{
     //读入灰度的手部图像
    Mat src  = imread( "arm.jpg", 0);
    Mat dst  = src.clone();
    Mat HT_OpenCV;
    Mat HT_GO;
    Mat AHE_GO;
    Mat CLHE_GO;
    Mat CLAHE_Without_Interpolation;
    Mat CLAHE_OpenCV;
    Mat CLAHE_GO;
    Mat matInter;
     OpenCV HT 方法
    cv : :equalizeHist(src,HT_OpenCV);
     GO HT方法
    HT_GO  = eaualizeHist_GO(src);
     GO AHE方法
    AHE_GO  = aheGO(src);
     GO CLHE方法
    CLHE_GO  = clheGO(src);
     clahe不计算差值
    CLAHE_Without_Interpolation  = claheGoWithoutInterpolation(src);
     OpenCV CLAHE 方法
    Ptr <cv : :CLAHE > clahe  = createCLAHE(); //默认参数
    clahe - >apply(src, CLAHE_OpenCV);
     GO CLAHE方法
    CLAHE_GO  = claheGO(src);
 
     结果显示
    imshow( "原始图像",src);
    imshow( "OpencvHT",HT_OpenCV);
    imshow( "GOHT",HT_GO);
    imshow( "GOAHE",AHE_GO);
    imshow( "GOCLHE",CLHE_GO);
    imshow( "GOCLAHE",CLAHE_GO);
    imshow( "CLAHE_Without_Interpolation",CLAHE_Without_Interpolation);
    imshow( "OpencvCLAHE",CLAHE_OpenCV);
    waitKey();
     return  0;
}

原始图像

GOCLAHE效果

OpenCV CLAHE效果

HE算法： Mat eaualizeHist_GO(Mat src)
{
     int width  = src.cols;
     int height = src.rows;
    Mat HT_GO  = src.clone();
     int tmp[ 256]  ={ 0};
     float C[ 256]  = { 0. 0};
     int total  = width *height;  
     for ( int i = 0 ;i <src.rows;i ++)
    {
         for ( int j = 0;j <src.cols;j ++)
        {
             int index  = src.at <uchar >(i,j);
            tmp[index]  ++;
        }
    }
     //计算累积函数  
     for( int i  =  0;i  <  256 ; i ++){  
         if(i  ==  0)  
            C[i]  =  1.0f  * tmp[i]  / total;  
         else  
            C[i]  = C[i - 1]  +  1.0f  * tmp[i]  / total;  
    }  
     //这里的累积函数分配的方法非常直观高效
     for( int i  =  0;i  < src.rows;i ++){  
         for( int j  =  0;j  < src.cols;j ++){      
             int index  = src.at <uchar >(i,j);
            HT_GO.at <uchar >(i,j)  = C[index]  *  255  ;
        }  
    }  
     return HT_GO;
}

 

 

AHE算法:
Mat aheGO(Mat src, int _step  =  8)
{
    Mat AHE_GO  = src.clone();
     int block  = _step;
     int width  = src.cols;
     int height  = src.rows;
     int width_block  = width /block;  //每个小格子的长和宽
     int height_block  = height /block;
     //存储各个直方图  
     int tmp2[ 8 * 8][ 256]  ={ 0};
     float C2[ 8 * 8][ 256]  = { 0. 0};
     //分块
     int total  = width_block  * height_block; 
     for ( int i = 0;i <block;i ++)
    {
         for ( int j = 0;j <block;j ++)
        {
             int start_x  = i *width_block;
             int end_x  = start_x  + width_block;
             int start_y  = j *height_block;
             int end_y  = start_y  + height_block;
             int num  = i +block *j;  
             //遍历小块,计算直方图
             for( int ii  = start_x ; ii  < end_x ; ii ++)  
            {  
                 for( int jj  = start_y ; jj  < end_y ; jj ++)  
                {  
                     int index  =src.at <uchar >(jj,ii);
                    tmp2[num][index] ++;  
                }  
            } 
             //计算累积分布直方图  
             for( int k  =  0 ; k  <  256 ; k ++)  
            {  
                 if( k  ==  0)  
                    C2[num][k]  =  1.0f  * tmp2[num][k]  / total;  
                 else  
                    C2[num][k]  = C2[num][k - 1]  +  1.0f  * tmp2[num][k]  / total;  
            }  
        }
    }
     //将统计结果写入
     for ( int i = 0;i <block;i ++)
    {
         for ( int j = 0;j <block;j ++)
        {
             int start_x  = i *width_block;
             int end_x  = start_x  + width_block;
             int start_y  = j *height_block;
             int end_y  = start_y  + height_block;
             int num  = i +block *j;  
             //遍历小块,计算直方图
             for( int ii  = start_x ; ii  < end_x ; ii ++)  
            {  
                 for( int jj  = start_y ; jj  < end_y ; jj ++)  
                {  
                     int index  =src.at <uchar >(jj,ii);
                     //结果直接写入AHE_GO中去
                    AHE_GO.at <uchar >(jj,ii)  = C2[num][index]  *  255  ;
                }  
            } 
        }
    }
     return AHE_GO;
}

 

CLHE算法：

//这里是在全局直方图加入“限制对比度”方法
Mat clheGO(Mat src, int _step  =  8)
{
     int width  = src.cols;
     int height = src.rows;
    Mat CLHE_GO  = src.clone();
     int tmp[ 256]  ={ 0};
     float C[ 256]  = { 0. 0};
     int total  = width *height;  
     for ( int i = 0 ;i <src.rows;i ++)
    {
         for ( int j = 0;j <src.cols;j ++)
        {
             int index  = src.at <uchar >(i,j);
            tmp[index]  ++;
        }
    }
     /限制对比度计算部分,注意这个地方average的计算不一定科学
     int average  = width  * height  /  255 / 64;  
     int LIMIT  =  4  * average;  
     int steal  =  0;  
     for( int k  =  0 ; k  <  256 ; k ++)  
    {  
         if(tmp[k]  > LIMIT){  
            steal  += tmp[k]  - LIMIT;  
            tmp[k]  = LIMIT;  
        }  
    }  
     int bonus  = steal / 256;  
     //hand out the steals averagely  
     for( int k  =  0 ; k  <  256 ; k ++)  
    {  
        tmp[k]  += bonus;  
    }  
     ///
     //计算累积函数  
     for( int i  =  0;i  <  256 ; i ++){  
         if(i  ==  0)  
            C[i]  =  1.0f  * tmp[i]  / total;  
         else  
            C[i]  = C[i - 1]  +  1.0f  * tmp[i]  / total;  
    }  
     //这里的累积函数分配的方法非常直观高效
     for( int i  =  0;i  < src.rows;i ++){  
         for( int j  =  0;j  < src.cols;j ++){      
             int index  = src.at <uchar >(i,j);
            CLHE_GO.at <uchar >(i,j)  = C[index]  *  255  ;
        }  
    }  
     return CLHE_GO;
}

CLAHE不包括插值算法：
Mat claheGoWithoutInterpolation(Mat src,  int _step  =  8)
{
    Mat CLAHE_GO  = src.clone();
     int block  = _step; //pblock
     int width  = src.cols;
     int height = src.rows;
     int width_block  = width /block;  //每个小格子的长和宽
     int height_block  = height /block;
     //存储各个直方图  
     int tmp2[ 8 * 8][ 256]  ={ 0};
     float C2[ 8 * 8][ 256]  = { 0. 0};
     //分块
     int total  = width_block  * height_block; 
     for ( int i = 0;i <block;i ++)
    {
         for ( int j = 0;j <block;j ++)
        {
             int start_x  = i *width_block;
             int end_x  = start_x  + width_block;
             int start_y  = j *height_block;
             int end_y  = start_y  + height_block;
             int num  = i +block *j;  
             //遍历小块,计算直方图
             for( int ii  = start_x ; ii  < end_x ; ii ++)  
            {  
                 for( int jj  = start_y ; jj  < end_y ; jj ++)  
                {  
                     int index  =src.at <uchar >(jj,ii);
                    tmp2[num][index] ++;  
                }  
            } 
             //裁剪和增加操作，也就是clahe中的cl部分
             //这里的参数 对应《Gem》上面 fCliplimit  = 4  , uiNrBins  = 255
             int average  = width_block  * height_block  /  255;  
             int LIMIT  =  4  * average;  
             int steal  =  0;  
             for( int k  =  0 ; k  <  256 ; k ++)  
            {  
                 if(tmp2[num][k]  > LIMIT){  
                    steal  += tmp2[num][k]  - LIMIT;  
                    tmp2[num][k]  = LIMIT;  
                }  
            }  
             int bonus  = steal / 256;  
             //hand out the steals averagely  
             for( int k  =  0 ; k  <  256 ; k ++)  
            {  
                tmp2[num][k]  += bonus;  
            }  
             //计算累积分布直方图  
             for( int k  =  0 ; k  <  256 ; k ++)  
            {  
                 if( k  ==  0)  
                    C2[num][k]  =  1.0f  * tmp2[num][k]  / total;  
                 else  
                    C2[num][k]  = C2[num][k - 1]  +  1.0f  * tmp2[num][k]  / total;  
            }  
        }
    }
     //计算变换后的像素值  
     //将统计结果写入
     for ( int i = 0;i <block;i ++)
    {
         for ( int j = 0;j <block;j ++)
        {
             int start_x  = i *width_block;
             int end_x  = start_x  + width_block;
             int start_y  = j *height_block;
             int end_y  = start_y  + height_block;
             int num  = i +block *j;  
             //遍历小块,计算直方图
             for( int ii  = start_x ; ii  < end_x ; ii ++)  
            {  
                 for( int jj  = start_y ; jj  < end_y ; jj ++)  
                {  
                     int index  =src.at <uchar >(jj,ii);
                     //结果直接写入AHE_GO中去
                    CLAHE_GO.at <uchar >(jj,ii)  = C2[num][index]  *  255  ;
                }  
            } 
        }
    
     }  
     return CLAHE_GO;
}

 

CLAHE算法：

Mat claheGO(Mat src, int _step  =  8)
{
    Mat CLAHE_GO  = src.clone();
     int block  = _step; //pblock
     int width  = src.cols;
     int height = src.rows;
     int width_block  = width /block;  //每个小格子的长和宽
     int height_block  = height /block;
     //存储各个直方图  
     int tmp2[ 8 * 8][ 256]  ={ 0};
     float C2[ 8 * 8][ 256]  = { 0. 0};
     //分块
     int total  = width_block  * height_block; 
     for ( int i = 0;i <block;i ++)
    {
         for ( int j = 0;j <block;j ++)
        {
             int start_x  = i *width_block;
             int end_x  = start_x  + width_block;
             int start_y  = j *height_block;
             int end_y  = start_y  + height_block;
             int num  = i +block *j;  
             //遍历小块,计算直方图
             for( int ii  = start_x ; ii  < end_x ; ii ++)  
            {  
                 for( int jj  = start_y ; jj  < end_y ; jj ++)  
                {  
                     int index  =src.at <uchar >(jj,ii);
                    tmp2[num][index] ++;  
                }  
            } 
             //裁剪和增加操作，也就是clahe中的cl部分
             //这里的参数 对应《Gem》上面 fCliplimit  = 4  , uiNrBins  = 255
             int average  = width_block  * height_block  /  255;  
             //关于参数如何选择，需要进行讨论。不同的结果进行讨论
             //关于全局的时候，这里的这个cl如何算，需要进行讨论 
             int LIMIT  =  40  * average;  
             int steal  =  0;  
             for( int k  =  0 ; k  <  256 ; k ++)  
            {  
                 if(tmp2[num][k]  > LIMIT){  
                    steal  += tmp2[num][k]  - LIMIT;  
                    tmp2[num][k]  = LIMIT;  
                }  
            }  
             int bonus  = steal / 256;  
             //hand out the steals averagely  
             for( int k  =  0 ; k  <  256 ; k ++)  
            {  
                tmp2[num][k]  += bonus;  
            }  
             //计算累积分布直方图  
             for( int k  =  0 ; k  <  256 ; k ++)  
            {  
                 if( k  ==  0)  
                    C2[num][k]  =  1.0f  * tmp2[num][k]  / total;  
                 else  
                    C2[num][k]  = C2[num][k - 1]  +  1.0f  * tmp2[num][k]  / total;  
            }  
        }
    }
     //计算变换后的像素值  
     //根据像素点的位置，选择不同的计算方法  
     for( int  i  =  0 ; i  < width; i ++)  
    {  
         for( int j  =  0 ; j  < height; j ++)  
        {  
             //four coners  
             if(i  < = width_block / 2  && j  < = height_block / 2)  
            {  
                 int num  =  0;  
                CLAHE_GO.at <uchar >(j,i)  = ( int)(C2[num][CLAHE_GO.at <uchar >(j,i)]  *  255);  
            } else  if(i  < = width_block / 2  && j  > = ((block - 1) *height_block  + height_block / 2)){  
                 int num  = block *(block - 1);  
                CLAHE_GO.at <uchar >(j,i)  = ( int)(C2[num][CLAHE_GO.at <uchar >(j,i)]  *  255);  
            } else  if(i  > = ((block - 1) *width_block +width_block / 2)  && j  < = height_block / 2){  
                 int num  = block - 1;  
                CLAHE_GO.at <uchar >(j,i)  = ( int)(C2[num][CLAHE_GO.at <uchar >(j,i)]  *  255);  
            } else  if(i  > = ((block - 1) *width_block +width_block / 2)  && j  > = ((block - 1) *height_block  + height_block / 2)){  
                 int num  = block *block - 1;  
                CLAHE_GO.at <uchar >(j,i)  = ( int)(C2[num][CLAHE_GO.at <uchar >(j,i)]  *  255);  
            }  
             //four edges except coners  
             else  if( i  < = width_block / 2 )  
            {  
                 //线性插值  
                 int num_i  =  0;  
                 int num_j  = (j  - height_block / 2) /height_block;  
                 int num1  = num_j *block  + num_i;  
                 int num2  = num1  + block;  
                 float p  =  (j  - (num_j *height_block +height_block / 2)) /( 1.0f *height_block);  
                 float q  =  1 -p;  
                CLAHE_GO.at <uchar >(j,i)  = ( int)((q *C2[num1][CLAHE_GO.at <uchar >(j,i)] + p *C2[num2][CLAHE_GO.at <uchar >(j,i)]) *  255);  
            } else  if( i  > = ((block - 1) *width_block +width_block / 2)){  
                 //线性插值  
                 int num_i  = block - 1;  
                 int num_j  = (j  - height_block / 2) /height_block;  
                 int num1  = num_j *block  + num_i;  
                 int num2  = num1  + block;  
                 float p  =  (j  - (num_j *height_block +height_block / 2)) /( 1.0f *height_block);  
                 float q  =  1 -p;  
                CLAHE_GO.at <uchar >(j,i)  = ( int)((q *C2[num1][CLAHE_GO.at <uchar >(j,i)] + p *C2[num2][CLAHE_GO.at <uchar >(j,i)]) *  255);  
            } else  if( j  < = height_block / 2 ){  
                 //线性插值  
                 int num_i  = (i  - width_block / 2) /width_block;  
                 int num_j  =  0;  
                 int num1  = num_j *block  + num_i;  
                 int num2  = num1  +  1;  
                 float p  =  (i  - (num_i *width_block +width_block / 2)) /( 1.0f *width_block);  
                 float q  =  1 -p;  
                CLAHE_GO.at <uchar >(j,i)  = ( int)((q *C2[num1][CLAHE_GO.at <uchar >(j,i)] + p *C2[num2][CLAHE_GO.at <uchar >(j,i)]) *  255);  
            } else  if( j  > = ((block - 1) *height_block  + height_block / 2) ){  
                 //线性插值  
                 int num_i  = (i  - width_block / 2) /width_block;  
                 int num_j  = block - 1;  
                 int num1  = num_j *block  + num_i;  
                 int num2  = num1  +  1;  
                 float p  =  (i  - (num_i *width_block +width_block / 2)) /( 1.0f *width_block);  
                 float q  =  1 -p;  
                CLAHE_GO.at <uchar >(j,i)  = ( int)((q *C2[num1][CLAHE_GO.at <uchar >(j,i)] + p *C2[num2][CLAHE_GO.at <uchar >(j,i)]) *  255);  
            }  
             //双线性插值
             else{  
                 int num_i  = (i  - width_block / 2) /width_block;  
                 int num_j  = (j  - height_block / 2) /height_block;  
                 int num1  = num_j *block  + num_i;  
                 int num2  = num1  +  1;  
                 int num3  = num1  + block;  
                 int num4  = num2  + block;  
                 float u  = (i  - (num_i *width_block +width_block / 2)) /( 1.0f *width_block);  
                 float v  = (j  - (num_j *height_block +height_block / 2)) /( 1.0f *height_block);  
                CLAHE_GO.at <uchar >(j,i)  = ( int)((u *v *C2[num4][CLAHE_GO.at <uchar >(j,i)]  +   
                    ( 1 -v) *( 1 -u) *C2[num1][CLAHE_GO.at <uchar >(j,i)]  +  
                    u *( 1 -v) *C2[num2][CLAHE_GO.at <uchar >(j,i)]  +  
                    v *( 1 -u) *C2[num3][CLAHE_GO.at <uchar >(j,i)])  *  255);  
            }  
             //最后这步，类似高斯平滑
            CLAHE_GO.at <uchar >(j,i)  = CLAHE_GO.at <uchar >(j,i)  + (CLAHE_GO.at <uchar >(j,i)  <<  8)  + (CLAHE_GO.at <uchar >(j,i)  <<  16);         
        }  
    }  
   return CLAHE_GO;
}

原始图像

GOCLAHE效果

OpenCV CLAHE效果

从结果上来看，GOCLAHE方法和OpenCV提供的CLAHE方法是一样的。

再放一组图片

代码实现之后，留下两个问题：

集中在这段代码

             //这里的参数 对应《Gem》上面 fCliplimit  = 4  , uiNrBins  = 255
             int average  = width_block  * height_block  /  255;  
             //关于参数如何选择，需要进行讨论。不同的结果进行讨论
             //关于全局的时候，这里的这个cl如何算，需要进行讨论 
             int LIMIT  =  40  * average;  
             int steal  =  0;  

1、在进行CLAHE中CL的计算，也就是限制对比度的计算的时候，参数的选择缺乏依据。在原始的《GEMS》中提供的参数中，  fCliplimit  = 4  , uiNrBins  = 255. 但是在OpenCV的默认参数中，这里是40.就本例而言，如果从结果上反推，我看10比较好。这里参数的选择缺乏依据；

2、CLHE是可以用来进行全局直方图增强的，那么这个时候，这个 average 如何计算，肯定不是width * height/255,这样就太大了，算出来的LIMIT根本没有办法获得。

但是就实现血管增强的效果而言，这些结果是远远不够的。一般来说，对于CLAHE计算出来的结果，进行Frangi增强或者使用超分辨率增强？结果就是要把血管区域强化出来。

p.s:

arm.jpg 和 hand.jpg