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    <p>You could simply use run-of-the-mill 2D cross correlation and detect where the maximum value lies to determine the (x,y) offset. Following the <a href="http://mathworld.wolfram.com/Cross-CorrelationTheorem.html" rel="nofollow">Cross-correlation theorem</a> you can efficiently implement this in the Fourier domain. </p> <p>See this simple example in Matlab on github, <a href="https://github.com/mdiephuis/sandbox/blob/master/so/m_xcorr2.m" rel="nofollow">cross correlation</a> and <a href="https://github.com/mdiephuis/sandbox/blob/master/so/m_translation_offset.m" rel="nofollow">peak finding</a></p> <p>EDIT</p> <p>Here follows the short and mostly incomplete guide to the <em>rigid registration</em> of images. The gist of the cross correlation idea is as follows: Say I have a 1D vector:</p> <p><code>t = [1 2 3 1 2 3 4 ]</code></p> <p>I shift this vector -4 places resulting in a new vector <code>t2</code>:</p> <p><code>t2 = [2 3 4 1 2 3 1]</code></p> <p>Now I have a look at the so called cross correlation <code>c</code> between <code>t</code> and <code>t2</code>:</p> <p><code>c = [1 5 11 15 17 25 38 37 28 24 29 18 8]</code></p> <p>Now, this cross correlation vector has a maximum of <code>38</code> located on position or index <code>7</code>. This we can use to ascertain the shift as follows:</p> <p><code>offset = round((7-(length(c)+1))/2)</code></p> <p><code>offset = -4</code></p> <p>where <code>length()</code> gives the dimensionality or number of elements in this dimension, of the cross correlation result.</p> <p>Now, as should be evident, the cross correlation in the Spacial domain requires a lot of operations. This is where the above mentioned <a href="http://mathworld.wolfram.com/Cross-CorrelationTheorem.html" rel="nofollow">cross-correlation theorem</a> comes in to play which links correlation in the Spacial domain to multiplication in the Fourier domain. The fourier transform is blessed with a number of very fast implementations (FFT) requiring vastly less operations, hence the reason they are used for determining the cross correlation.</p> <p>There are many methods that deal with so-called rigid registration from stitching of satellite and holiday images a like to overlaying images from different sources as often found in medical imaging applications. </p> <p>In your particular case, you might want to have a look at <a href="http://en.wikipedia.org/wiki/Phase_correlation" rel="nofollow">Phase correlation</a>. Also the <a href="http://www.nr.com/oldverswitcher.html" rel="nofollow">Numercial recipes in c book</a> contains a chapter on fourier and correlation. </p>
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    1. POCheck if a picture is shift of another
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    1. COCan't you explain a little more in details, and in pseudo code maybe coz I don't know much of Matlab.
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    2. CO@thecoder see edit.
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    3. COIn some implementations correlation is run on an image pyramid, starting with the smallest images and working up to full resolution. A match at 1/4 scale can identify the likely region(s) of best fit, then at successfully larger scales one finds a more accurate fit.
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