FFT-based image registration in python

Question

I found simple python code to register images here

in the simple case of translation, we have:

def translation(im0, im1):
    """Return translation vector to register images."""
    shape = im0.shape
    f0 = fft2(im0)
    f1 = fft2(im1)
    ir = abs(ifft2((f0 * f1.conjugate()) / (abs(f0) * abs(f1))))
    t0, t1 = numpy.unravel_index(numpy.argmax(ir), shape)
    if t0 > shape[0] // 2:
        t0 -= shape[0]
    if t1 > shape[1] // 2:
        t1 -= shape[1]
    return [t0, t1]

but I do not understand this part:

if t0 > shape[0] // 2:
    t0 -= shape[0]
if t1 > shape[1] // 2:
    t1 -= shape[1]

also sometimes it gives the wrong shift, so it seems that the output t0, t1 depends on some cases? Maybe because I only have a match between the images?

EDIT:

Also here are my tests using other tools:

For lion img from wikipedia (pure shift)

http://dl.dropbox.com/u/8841028/FFT%20template%20matching/test%20images/im1.png http://dl.dropbox.com/u/8841028/FFT%20template%20matching/test%20images /im2.png

ImageJ gives (second stack relative to the first stack) x = -20 y = -23 R = 0.8126828943265368 (good)

phaseCorrelate x = 20,19 y = 22,56 ( - ?)

no hann window x = 20,23 y = 22,43

python x = -22 y = - 14

, (1,1)

http://dl.dropbox.com/u/8841028/FFT%20template%20matching/test%20images/im2.png http://dl.dropbox.com/u/8841028/FFT%20template%20matching/test%20images/temp_1_1.png

ImageJ ( ) x = 0 y = 1 R = 0,7905318337522524 ( 1 pix)

phaseCorrelate x = -0,4 y = -2,45 ( )

no hann window x = -0,88 y = -0,86

, (18,23)

http://dl.dropbox.com/u/8841028/FFT%20template%20matching/test%20images/im2.png http://dl.dropbox.com/u/8841028/FFT%20template%20matching/test%20images/temp_18_23.png

ImageJ ( ) x = 17 y = 23 R = 0,8119669906973865 ( 1 pix)

phaseCorrelate x = -18 y = -23 (, )

no hann window x = -18 y = -22,98

2 % ( , )

http://dl.dropbox.com/u/8841028/FFT%20template%20matching/test%20images/1.png http://dl.dropbox.com/u/8841028/FFT%20template%20matching/test%20images/2.png

( ) x = 744 y = 0 R = 0,9999999999999999

phaseCorrelate x = -743,48 y = 0 ( )

no hann window x = -743,49 y = 0

http://dl.dropbox.com/u/8841028/FFT%20template%20matching/test%20images/1_.PNG http://dl.dropbox.com/u/8841028/FFT%20template%20matching/test%20images/2_.PNG

ImageJ ( ) x = 878 y = -3 R = 0,9667271264277764

phaseCorrelate x = 34,47 y = -35,5 ()

no hann window x = 146,32 y = 3,06 ()

opencv 2.4.3 (prebuild), .

#include "stdafx.h"
#include <opencv.hpp>

using namespace cv;
using namespace std;

int _tmain(int argc, _TCHAR* argv[])
{
    Mat im1= imread("1.PNG",0);
    Mat im2= imread("2.PNG",0);

    Mat r1;
    im1.convertTo(r1,CV_64F);
    Mat r2;
    im2.convertTo(r2,CV_64F);

    Point2d phaseShift;

    if(r1.cols!=r2.cols||r1.rows!=r2.rows)
    {
        int n_cols= max(r1.cols,r2.cols);
        int n_rows= max(r1.rows,r2.rows);

        Mat r1_pad;
        copyMakeBorder(r1,r1_pad,0,n_rows-r1.rows,0,n_cols-r1.cols, BORDER_CONSTANT, Scalar::all(0));
        Mat r2_pad;
        copyMakeBorder(r2,r2_pad,0,n_rows-r2.rows,0,n_cols-r2.cols, BORDER_CONSTANT, Scalar::all(0));

        Mat hann;
        createHanningWindow(hann, r1_pad.size(), CV_64F);
        phaseShift = phaseCorrelate(r1_pad, r2_pad, hann);
    }
    else
    {
        Mat hann;
        createHanningWindow(hann, r1.size(), CV_64F);
        phaseShift = phaseCorrelate(r1, r2, hann);
    }

    return 0;
}