mlib_ImageNormCrossCorrel_Fp

- normalized cross correlation

Synopsis

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

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

Description

The mlib_ImageNormCrossCorrel_Fp() function computes the normalized cross-correlation coefficients between a pair of floating-point 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_FLOAT or MLIB_DOUBLE.

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.

In some cases, the resulting coefficients of this function could be NaN, Inf, or -Inf.

Parameters

The function takes the following arguments:

correl

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.

img1

Pointer to first image.

img2

Pointer to second image.

mean2

Pointer to the mean array of the second image.

sdev2

Pointer to the standard deviation array of the second image.

Return Values

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

Attributes

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

See Also

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