在上一篇 图像解析力算法—SFR（Spatial Frequency Response）源码分析(一） 中介绍了SFR的几个重要函数，接下来我们看一下主流程和其他函数。

4、sfrProc作用：计算SFR数值的主流程函数

short sfrProc (double **freq, double **sfr, 
	       int *len,
	       double *farea,
	       unsigned short size_x, int *nrows,
	       double *slope, int *numcycles, int *pcnt2, double *off, double *R2,
	       int version, int iterate, int user_angle)
  unsigned short i, j, col, err = 0;
  long pcnt;
  double dt, dt1, sfrc, tmp, tmp2;
  double *temp=NULL, *shifts=NULL, *edgex=NULL, *Signal=NULL;
  double *AveEdge=NULL, *AveTmp=NULL;
  long *counts=NULL;
  int nzero;
  unsigned short size_y;
  unsigned int bin_len;
  double avar, bvar, offset1, offset2, offset;
  double centroid;
  int start_row, center_row;
  double *farea_old;
  double cyclelimit;
  FILE *fp = NULL;
  size_y = *nrows;
  /* Verify input selection dimensions are EVEN */
  if (size_x%2 != 0) { 
    fprintf(stderr, "ROI width is not even.  Does this really matter???\n");
    return 1;
  /* At least this many cycles required. */
  /* For special iterative versions of the code, it can go lower */
  if (iterate) cyclelimit = 1.0;
  else cyclelimit = 5.0;
  /* Allocate memory */
  shifts = (double *)malloc(size_y*sizeof(double));
  temp = (double *)malloc(size_y*sizeof(double));
  edgex = (double *)malloc(size_y*size_x*sizeof(double));
  Signal = (double *)malloc(size_y*size_x*sizeof(double));
  if( !user_angle ) {
     //定位矩心位置
    err = locate_centroids(farea, temp, shifts, size_x, size_y, &offset1); 
    if (err != 0)     { return 2; }
    /* Calculate the best fit line to the centroids */
    /*计算矩心的拟合曲线*/
    err = fit(size_y, temp, shifts, slope, &offset2, R2, &avar, &bvar);
    if (err != 0)     { return 3; }
    if (version)
      MTFPRINT4("\nLinear Fit:  R2 = %.3f SE_intercept = %.2f  SE_angle = %.3f\n",  
	      *R2, avar, atan(bvar)*(double)(180.0/M_PI))
  /* Check slope is OK, and set size_y to be full multiple of cycles */
  //检查刀口斜率，以确保后面超采样的质量
  err = check_slope(*slope, &size_y, numcycles, cyclelimit, 1);
  /* Start image at new location, so that same row is center */
  //调整ROI的行
  center_row = *nrows/2;
  start_row = center_row - size_y/2;
  farea_old = farea;
  farea = farea + start_row*size_x;
  /* On center row how much shift to get edge centered in row. */
  /* offset = 0.;  Original code effectively used this (no centering)*/
  if(user_angle)
    offset = *off - size_x/2;
    offset = offset1 + 0.5 + offset2  - size_x/2; 
  *off = offset;
  if(version & ROUND || version & DER3)
    offset += 0.125;
  if (err != 0)     {   /* Slopes are bad.  But send back enough
			   data, so a diagnostic image has a chance. */
    *pcnt2 = 2*size_x;  /* Ignore derivative peak */
    return 4; 
  /* reference the temp and shifts values to the new y centre */
  /* Instead of using the values in shifts, synthesize new ones based on 
     the best fit line. */
  // 基于拟合结果更新shifts
  col = size_y/2;
  for (i=0; i < size_y; i++) {
    shifts[i] = (*slope) * (double)(i-col) + offset;
  /* Don't normalize the data.  It gets normalized during dft process */
  //不要对数据进行归一化，数据在DFT处理过程中会被归一化
  /* To normalize here, set dt = min and dt1 = max of farea data      */
  //如果要在这里初始化，将dt设置为最小值，dt1设置为最大值
  dt = 0.0;
  dt1 = 1.0;
  if (version & ESFFILE)
    fp = fopen("esf.txt","w");
  /* Calculate a long paired list of x values and signal values */
  pcnt = 0;
  for (j = 0; j < size_y; j++) {
    for (i = 0; i < size_x; i++) {
      edgex[pcnt] = (double)i - shifts[j];//计算每个点到刀口的距离
      Signal[pcnt] = ((farea[((j*(long)size_x)+i)]) - dt)/(dt1-dt); //归一化每个点的亮度
      if ((version & ESFFILE) && edgex[pcnt] < size_x/2 + 3 &&
	  edgex[pcnt] > size_x/2 - 3)
	fprintf(fp, "%f %f\n", edgex[pcnt], Signal[pcnt]);
      pcnt++;
  if (version & ESFFILE)
    fclose(fp);
  /* Allocate more memory */
  bin_len = (unsigned int)(ALPHA*size_x);
  AveEdge = (double *)malloc(bin_len*sizeof(double));
  AveTmp = (double *)malloc(bin_len*sizeof(double));
  counts = (long *)malloc(bin_len*sizeof(long));
  /* Project ESF data into supersampled bins */
  //进行超采样，生成长度为size_x*ALPHA(4)的当行图像（ESF），保存在AveEdge中
  nzero = bin_to_regular_xgrid((unsigned short)ALPHA, edgex, Signal, 
			       AveEdge, counts, 
			       size_x, size_y); 
  free(counts);
  free(Signal);
  free(edgex);
  /* Compute LSF from ESF.  Not yet centered or windowed. */
  // 将ESF转换为差分图LSF， 并计算LSF的矩心
  if ( (version&DER3) ) 
    calculate_derivative( bin_len, AveTmp, AveEdge, &centroid, 1);
    calculate_derivative( bin_len, AveTmp, AveEdge, &centroid, 0);
  if (iterate == 0) {
    /* Copy ESF to output area */
    for ( i=0; i<bin_len; i++ )
      farea_old[i] = AveTmp[i];
  /* Find the peak/center of LSF */
  //寻找LSF的最大值
  locate_max_PSF( bin_len, AveEdge, &pcnt);//这里获得了最大值的中心
  free(shifts);
  free(temp);
  if(version)
    MTFPRINT3("Off center distance (1/4 pixel units): Peak %ld  Centroid %.2f\n", 
	      pcnt-bin_len/2, centroid-bin_len/2)
  if((version & PEAK) == 0)//忽略差分后的最大值
    pcnt = bin_len/2;  /* Ignore derivative peak */
    MTFPRINT("Shifting peak to center\n")
  /* Here the array length is shortened to ww_in_pixels*ALPHA,
     and the LSF peak is centered and Hamming windowed. */
  //将LSF的最大值移到中心位置，并加上汉明窗
  apply_hamming_window((unsigned short)ALPHA, bin_len,
		       (unsigned short)size_x, 
		       AveEdge, &pcnt);
  /* From now on this is the length used. */
  *len = bin_len/2;
  if (iterate == 0) {
    /* Copy LSF_w to output area */
    for ( i=0; i<bin_len; i++ )
      farea_old[size_x*(int)ALPHA+i] = AveEdge[i];
  tmp = 1.0;
  tmp2 = 1.0/((double)bin_len) ;
  /* Now perform the DFT on AveEdge */
  /* ftwos ( nx, dx, lsf(x), nf, df, sfr(f) ) */
  //ftwos( number, dx, *lsf, ns, ds, *sfr)
  (void) ftwos(bin_len, tmp, AveEdge, (long)(*len), 
	       tmp2, AveTmp); 
  if(*freq==NULL)
    (*freq) = (double *)malloc((*len)*sizeof(double));
  if(*sfr==NULL)
    (*sfr) = (double *)malloc((*len)*sizeof(double));
  for (i=0; i<(*len); i++) {
    sfrc = AveTmp[i];
    (*freq)[i]= ((double)i/(double)size_x);   //每个点对应的频率
    (*sfr)[i] = (double) (sfrc/AveTmp[0]);    //归一化sfr
  /* Free */
  free(AveEdge);
  free(AveTmp);
  *nrows = size_y;
  *pcnt2 = pcnt;
  return(0);
5、apply_hamming_window作用：对lsf应用汉明窗，减少噪声
 
void apply_hamming_window(  unsigned short alpha,
                            unsigned int oldlen,  //size_x*4
                          unsigned short newxwidth, //size_x
			  double *AveEdge, long *pcnt2)
  long i,j,k, begin, end, edge_offset;
  double sfrc;
  /* Shift the AvgEdge[i] vector to centre the lsf in the transform window */
  // 将Avgedge移到中心位置， 两边由于移动造成的空位由0补齐
  edge_offset = (*pcnt2) - (oldlen/2);//不能理解为什么一定要反着计算，pcnt2肯定是小于oldlen/2吧。。
  if (edge_offset != 0) {                                                   //cer=6
    if (edge_offset < 0 ) {  //这里根据分析的话，应该edge_offset只会小于0啊。。     ↓
      for (i=oldlen-1; i > -edge_offset-1; i--)            //   [l l l l l l l max l l l l l]
                  AveEdge[i] = (AveEdge[i+edge_offset]);   //    ↑     ↑        ↑
      for (i=0; i < -edge_offset; i++)                     //   left center=3 right
                  AveEdge[i] = 0.00; /* last operation */    //offset = center-cer=-3
    } else {                                               //            cer=6
                                                           //              ↓
      for (i=0; i < oldlen-edge_offset; i++)               // [0 0 0 l l l l l l l max l l]
                  AveEdge[i] = (AveEdge[i+edge_offset]);   //  ↑           ↑        ↑
      for (i=oldlen-edge_offset; i < oldlen; i++)          //            center=3
		  AveEdge[i] = 0.00;
  /* Multiply the LSF data by a Hamming window of width NEWXWIDTH*alpha */
  //将begin和end两侧的值用0填充,但是感觉没啥用
  begin = (oldlen/2)-(newxwidth*alpha/2);//上下看来，begin只会等于0，因为oldlen=bin_len, bin_len=size_x*alpha == newxwidth*alpha
  if (begin < 0) begin = 0;
  end = (oldlen/2)+(newxwidth*alpha/2);
  if (end > oldlen )  end = oldlen;
  for (i=0; i< begin; i++) 
    AveEdge[i] = 0.0;
  for (i=end; i< oldlen; i++) 
    AveEdge[i] = 0.0;
  // 给begin和end之间的数据加上汉明窗
  // 汉明窗 W(n,α ) = (1 -α ) - α cos(2*PI*n/(N-1)) ，（0≤n≤N-1）
  // 一般情况下，α取0.46
  // 下面计算方法等于窗发生了平移（故符号发生了变化）， 结果是一样的
  for (i=begin,j = -newxwidth*alpha/2; i < end; i++,j++) {
    sfrc = 0.54 + 0.46*cos( (M_PI*(double)j)/(newxwidth*alpha/2) );
    AveEdge[i] = (AveEdge[i])*sfrc; 
  //将lsfbegin的位置左移到index0的位置
  //但在代码中应该是不会起作用的，
  if (begin != 0) /* Shift LSF to begin at index 0 (rather than begin) */
    for (k=0, i=begin; k<newxwidth*alpha; i++,k++) 
      AveEdge[k] = AveEdge[i];
6、ftwos作用：计算DFT，将空域转换到频域范围上。
 
unsigned short ftwos(long number, double dx, double *lsf, 
		     long ns, double ds, double *sfr)
  double a, b, twopi, g;
  long i,j;
    //                n-1              k
    // DFT ==> X[k] = Σ  x[n]e^(-j2π - n)
    //                n=0              N
  twopi = 2.0 * M_PI;
  for (j = 0; j < ns; j++){//ns=1/2*bin_len  前一半
    g = twopi * dx * ds * (double)j;
    for (i = 0, a = 0, b = 0; i < number; i++) { 
      a += lsf[i] * cos(g * (double)(i));
      b += lsf[i] * sin(g * (double)(i)); 
    sfr[j] = sqrt(a * a + b * b); 
  return 0;
好了，整个SFR的重要代码的注释到这里也就结束了，拖了挺久的，主要是前段时间也是有点忙，大家有啥不清楚或者错误指正可以留言一下。大家互相探讨一波吧~
                    在上一篇图像解析力算法—SFR（Spatial Frequency Response）源码分析(一）中介绍了SFR的几个重要函数，接下来我们看一下主流程和其他函数。4、sfrProc作用：计算SFR数值的主流程函数short sfrProc (double **freq, double **sfr, 	       int *len,	       double *farea,	 ...
				
在图像解析力算法—SFR（Spatial Frequency Response）原理分析(一)中，我们已经分析了SFR的前四个步骤，接下来，我们继续讨论以下的五个步骤
4、重新定位ROI，获得ESF
5、对获得的ESF进行四倍超采样
6、通过差分运算获得LSF
7、对LSF应用汉明窗
8、进行DFT运算
4、重新定位ROI，获得ESF
这一步其实比较复杂，我也不确定在我的讲述之...
				
在上一篇图像解析力算法—SFR（Spatial Frequency Response）源码分析(一）中介绍了SFR的几个重要函数，接下来我们看一下主流程和其他函数。
4、sfrProc作用：计...
				
Imatest SFR（Spatial Frequency Response）算法是一种测试图像分辨率的方法。这个算法是由Imatest公司提出和开发的，被广泛应用于图像质量评价领域。
Imatest SFR算法通过分析图像中的特定频率线条的模糊程度来评估图像的分辨率能力。该算法首先通过计算线条的对比度和峰值位置来确定图像的清晰度和锐度，然后根据模糊度函数将图像的分辨率能力进行量化。
Imatest SFR算法的优点是精确度高、稳定性强。它采用了自动化的分析方法，可以快速准确地评估图像的分辨率能力，避免了主观因素的干扰。此外，该算法还可以基于不同的测试标准进行定制化设置，以适应不同的应用需求。
Imatest SFR算法的应用范围非常广泛。它可以用于评估相机、手机、显示器等各类图像采集和显示设备的分辨率能力。在生产线上，可以使用该算法进行质量控制和检测。在研发过程中，可以利用该算法来优化图像处理算法和参数设置，以提升图像的清晰度和细节还原能力。
总之，Imatest SFR算法是一种强大而高效的图像分辨率评估方法。它能够快速准确地量化图像的分辨率能力，为图像质量评价和优化提供了有力的工具和指导。
				error: (-215:Assertion failed) src_depth != CV_16F && src_depth != CV_32S in function 'convertToShow
					22451