图像分析：积分图像与代码实现

客官°小女子只卖身不卖艺 2024-04-19 15:37 55阅读 0赞

积分图像（Integral Image）的概念是由Viola和Jones在文献\[1\]中提出的。

积分图像中任意一点(i,j)的值ii(i,j)为原图像左上角到任意点(i,j)相应对角线区域灰度值总和。可以用如下两式迭代计算得到

> > s(i,j)=s(i,j-1)+i(i,j)
> 
> > ii(i,j)=ii(i-1,j)+s(i,j)

求积分图像只需对原图像所有像素进行一遍扫描。

用C++编程实现如下：（pOutImage为输出的积分图，pInImage为输入的灰度图）

pOutImage[0][0]=pInImage[0][0];
    for (int x=1;x<nWidth;x++)
    {
    	pOutImage[x][0]=pInImage[x-1][0]+pInImage[x][0];
    }
    for(int y=1;y<nHeight;y++)
    {
    	int nSum=0；
    	for(int x=0;x<nWidth;x++)
    	{
    		nSum+=pInImage[x][y];
    		pOutImage[x][y]=pInImage[x][y-1]+nSum;
    	}
    }

OpenCV中的编程实现：

/*
     * icvGetAuxImages
     *
     * Get sum, tilted, sqsum images and calculate normalization factor
     * All images must be allocated.
     */
    static
    void icvGetAuxImages( CvMat* img, CvMat* sum, CvMat* tilted,
                          CvMat* sqsum, float* normfactor )
    {
        CvRect normrect;
        int p0, p1, p2, p3;
        sum_type   valsum   = 0;
        sqsum_type valsqsum = 0;
        double area = 0.0;
    
        cvIntegral( img, sum, sqsum, tilted );
        normrect = cvRect( 1, 1, img->cols - 2, img->rows - 2 );
        CV_SUM_OFFSETS( p0, p1, p2, p3, normrect, img->cols + 1 )
    
        area = normrect.width * normrect.height;
        valsum = ((sum_type*) (sum->data.ptr))[p0] - ((sum_type*) (sum->data.ptr))[p1]
               - ((sum_type*) (sum->data.ptr))[p2] + ((sum_type*) (sum->data.ptr))[p3];
        valsqsum = ((sqsum_type*) (sqsum->data.ptr))[p0]
                 - ((sqsum_type*) (sqsum->data.ptr))[p1]
                 - ((sqsum_type*) (sqsum->data.ptr))[p2]
                 + ((sqsum_type*) (sqsum->data.ptr))[p3];
    
        /* sqrt( valsqsum / area - ( valsum / are )^2 ) * area */
        (*normfactor) = (float) sqrt( (double) (area * valsqsum - (double)valsum * valsum) );
    }

Matlab实现代码如下：

clear all;
    close all;
    clc;
    
    img=double(imread('lena.jpg'));
    [m n]=size(img);
    
    %计算积分图
    I=zeros(m,n);
    for i=1:m
        for j=1:n
            if i==1 && j==1             %积分图像左上角
                I(i,j)=img(i,j);
            elseif i==1 && j~=1         %积分图像第一行
                I(i,j)=I(i,j-1)+img(i,j);
            elseif i~=1 && j==1         %积分图像第一列
                I(i,j)=I(i-1,j)+img(i,j);
            else                        %积分图像其它像素
                I(i,j)=img(i,j)+I(i-1,j)+I(i,j-1)-I(i-1,j-1);  
            end
        end
    end

**reference：**

\[1\] Viola P, Jones M. Rapid object detection using a boosted cascade of simple features\[C\]//Computer Vision and Pattern Recognition, 2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference on. IEEE, 2001, 1: I-511-I-518 vol. 1.

\[2\] [http://www.cnblogs.com/tiandsp/archive/2013/04/12/3016402.html][http_www.cnblogs.com_tiandsp_archive_2013_04_12_3016402.html]

[http_www.cnblogs.com_tiandsp_archive_2013_04_12_3016402.html]: http://www.cnblogs.com/tiandsp/archive/2013/04/12/3016402.html