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POCamera motion from corresponding images
 

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  1. POCamera motion from corresponding images
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    <p>I'm trying to calculate a new camera position based on the motion of corresponding images. the images conform to the pinhole camera model.</p> <p>As a matter of fact, I don't get useful results, so I try to describe my procedure and hope that somebody can help me.</p> <p>I match the features of the corresponding images with SIFT, match them with OpenCV's FlannBasedMatcher and calculate the fundamental matrix with OpenCV's findFundamentalMat (method RANSAC).</p> <p>Then I calculate the essential matrix by the camera intrinsic matrix (K):</p> <pre><code>Mat E = K.t() * F * K; </code></pre> <p>I decompose the essential matrix to rotation and translation with singular value decomposition:</p> <pre><code>SVD decomp = SVD(E); Matx33d W(0,-1,0, 1,0,0, 0,0,1); Matx33d Wt(0,1,0, -1,0,0, 0,0,1); R1 = decomp.u * Mat(W) * decomp.vt; R2 = decomp.u * Mat(Wt) * decomp.vt; t1 = decomp.u.col(2); //u3 t2 = -decomp.u.col(2); //u3 </code></pre> <p>Then I try to find the correct solution by triangulation. (this part is from <a href="http://www.morethantechnical.com/2012/01/04/simple-triangulation-with-opencv-from-harley-zisserman-w-code/">http://www.morethantechnical.com/2012/01/04/simple-triangulation-with-opencv-from-harley-zisserman-w-code/</a> so I think that should work correct).</p> <p>The new position is then calculated with:</p> <pre><code>new_pos = old_pos + -R.t()*t; </code></pre> <p>where new_pos &amp; old_pos are vectors (3x1), R the rotation matrix (3x3) and t the translation vector (3x1).</p> <p>Unfortunately I got no useful results, so maybe anyone has an idea what could be wrong.</p> <p>Here are some results (just in case someone can confirm that any of them is definitely wrong):</p> <pre><code>F = [8.093827077399547e-07, 1.102681999632987e-06, -0.0007939604310854831; 1.29246107737264e-06, 1.492629957878578e-06, -0.001211264339006535; -0.001052930954975217, -0.001278667878010564, 1] K = [150, 0, 300; 0, 150, 400; 0, 0, 1] E = [0.01821111092414898, 0.02481034499174221, -0.01651092283654529; 0.02908037424088439, 0.03358417405226801, -0.03397110489649674; -0.04396975675562629, -0.05262169424538553, 0.04904210357279387] t = [0.2970648246214448; 0.7352053067682792; 0.6092828956013705] R = [0.2048034356172475, 0.4709818957303019, -0.858039396912323; -0.8690270040802598, -0.3158728880490416, -0.3808101689488421; -0.4503860776474556, 0.8236506374002566, 0.3446041331317597] </code></pre>
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    1. COThere is one more mistake in your computation. `SVD decomp = SVD(E);` is ok but you have to compute a new `newE = U*diag(1,1,0)*Vt` and then again you have to get `SVD decomp2 = SVD(newE);`.
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    2. COinteresting. I never read about that. So I have do calculate R and t with decomp2? btw: thanks for your detailed answer. I have to check all the things and will respond as soon as possible.
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    3. COYes, you have to compute R and t with decomp2. A detailed description is given here (pp 257-260) http://www.robots.ox.ac.uk/~vgg/hzbook/hzbook2/HZepipolar.pdf
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