man pages section 3: Multimedia Library Functions

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Updated: July 2014



mlib_ImageNormCrossCorrel - normalized cross correlation


cc [ flag... ] file... –lmlib [ library... ]
#include <mlib.h>

mlib_status mlib_ImageNormCrossCorrel(mlib_d64 *correl,
     const mlib_image *img1, const mlib_image *img2, const mlib_d64 *mean2,
     const mlib_d64 *sdev2);


The mlib_ImageNormCrossCorrel() function computes the normalized cross-correlation coefficients between a pair of images, on a per-channel basis.

It uses the following equations:

               w-1 h-1
               SUM SUM (d1[x][y][i] * d2[x][y][i])
               x=0 y=0
  correl[i] = -------------------------------------
                         s1[i] * s2[i]

d1[x][y][i] = img1[x][y][i] - m1[i]

d2[x][y][i] = img2[x][y][i] - m2[i]

                1     w-1 h-1
      m1[i] = ----- * SUM SUM img1[x][y][i]
               w*h    x=0 y=0

                1     w-1 h-1
      m2[i] = ----- * SUM SUM img2[x][y][i]
               w*h    x=0 y=0

                    w-1 h-1
      s1[i] = sqrt{ SUM SUM (img1[x][y][i] - m1[i])**2 }
                    x=0 y=0
                    w-1 h-1
      s2[i] = sqrt{ SUM SUM (img2[x][y][i] - m2[i])**2 }
                    x=0 y=0

where w and h are the width and height of the images, respectively; m1 and m2 are the mean arrays of the first and second images, respectively; s1 and s2 are the un-normalized standard deviation arrays of the first and second images, respectively.

In usual cases, the normalized cross-correlation coefficient is in the range of [-1.0, 1.0]. In the case of (s1[i] == 0) or (s2[i] == 0), where a constant image channel is involved, the normalized cross-correlation coefficient is defined as follows:

    #define signof(x) ((x > 0) ? 1 : ((x < 0) ? -1 : 0))

    if ((s1[i] == 0.) || (s2[i] == 0.)) {
        if ((s1[i] == 0.) && (s2[i] == 0.)) {
           if (signof(m1[i]) == signof(m2[i]) {
               correl[i] = 1.0;
           } else {
               correl[i] = -1.0;
        } else {
            correl[i] = -1.0;

The two images must have the same type, the same size, and the same number of channels. They can have 1, 2, 3 or 4 channels. They can be of type MLIB_BYTE, MLIB_SHORT, MLIB_USHORT or MLIB_INT.

If (mean2 == NULL) or (sdev2 == NULL), then m2 and s2 are calculated in this function according to the formulas shown above. Otherwise, they are calculated as follows:

    m2[i] = mean2[i];
    s2[i] = sdev2[i] * sqrt(w*h);

where mean2 and sdev2 can be the output of mlib_ImageMean() and mlib_ImageStdDev(), respectively.


The function takes the following arguments:


Pointer to normalized cross correlation array on a channel basis. The array must be the size of channels in the images. correl[i] contains the cross-correlation of channel i.


Pointer to first image.


Pointer to second image.


Pointer to the mean array of the second image.


Pointer to the standard deviation array of the second image.

Return Values

The function returns MLIB_SUCCESS if successful. Otherwise it returns MLIB_FAILURE.


See attributes(5) for descriptions of the following attributes:

Interface Stability

See also

mlib_ImageAutoCorrel(3MLIB), mlib_ImageAutoCorrel_Fp(3MLIB), mlib_ImageCrossCorrel(3MLIB), mlib_ImageCrossCorrel_Fp(3MLIB), mlib_ImageNormCrossCorrel_Fp(3MLIB), attributes(5)