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POCalculating camera motion out of corresponding 3d point sets
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copied!<p>I am having a little problem. I wrote a program that extracts a set of three-dimensional points in each frame using a camera and depth information. The points are in the <strong>camera coordinate system</strong>, which means the origin is at the camera center, x is horizontal distance, y vertical distance and z the distance from the camera (along the optical axis). Everything is in meters. I.e. point (2,-1,5) would be two meters right, one meter below and five meters along the optical axis of the camera.</p> <p>I calculate these points in each time frame and also know the correspondences, like I know which point in <code>t-1</code> belongs to which 3d point in <code>t</code>.</p> <p>My goal now is to calculate the motion of the camera in each time frame in my world coordinate system (with z pointing up representing the height). I would like to calculate relative motion but also the absolute one starting from some start position to visualize the trajectory of the camera.</p> <hr> <p>This is an example data set of one frame with the current (left) and the previous 3D location (right) of the points in camera coordinates:</p> <pre><code>-0.174004 0.242901 3.672510 | -0.089167 0.246231 3.646694 -0.265066 -0.079420 3.668801 | -0.182261 -0.075341 3.634996 0.092708 0.459499 3.673029 | 0.179553 0.459284 3.636645 0.593070 0.056592 3.542869 | 0.675082 0.051625 3.509424 0.676054 0.517077 3.585216 | 0.763378 0.511976 3.555986 0.555625 -0.350790 3.496224 | 0.633524 -0.354710 3.465260 1.189281 0.953641 3.556284 | 1.274754 0.938846 3.504309 0.489797 -0.933973 3.435228 | 0.561585 -0.935864 3.404614 </code></pre> <hr> <p>Since I would like to work with OpenCV if possible I found the <code>estimateAffine3D()</code> function in OpenCV 2.3, which takes two 3D point input vectors and calculates the affine transformation between them using RANSAC.</p> <p>As output I get a 3x4 transformation matrix.</p> <p>I already tried to make the calculation more accurate by setting the RANSAC parameters but a lot of times the trnasformation matrix shows a translatory movement that is quite big. As you can see in the sample data the movement is usually quite small.</p> <p>So I wanted to ask if anybody has another idea on what I could try? Does OpenCV offer other solutions for this?</p> <p>Also if I have the relative motion of the camera in each timeframe, how would I convert it to world coordinates? Also how would I then get the absolute position starting from a point (0,0,0) so I have the camera position (and direction) for each time frame?</p> <p>Would be great if anybody could give me some advice!</p> <p>Thank you!</p> <p><strong>UPDATE 1:</strong></p> <p>After @Michael Kupchick nice answer I tried to check how well the estimateAffine3D() function in OpenCV works. So I created two little test sets of 6 point-pairs that just have a translation, not a rotation and had a look at the resulting transformation matrix:</p> <p><em><strong>Test set 1:</em></strong></p> <pre><code>1.5 2.1 6.7 | 0.5 1.1 5.7 6.7 4.5 12.4 | 5.7 3.5 11.4 3.5 3.2 1.2 | 2.5 2.2 0.2 -10.2 5.5 5.5 | -11.2 4.5 4.5 -7.2 -2.2 6.5 | -8.2 -3.2 5.5 -2.2 -7.3 19.2 | -3.2 -8.3 18.2 </code></pre> <p>Transformation Matrix:</p> <pre><code>1 -1.0573e-16 -6.4096e-17 1 -1.3633e-16 1 2.59504e-16 1 3.20342e-09 1.14395e-09 1 1 </code></pre> <p><em><strong>Test set 2:</em></strong></p> <pre><code>1.5 2.1 0 | 0.5 1.1 0 6.7 4.5 0 | 5.7 3.5 0 3.5 3.2 0 | 2.5 2.2 0 -10.2 5.5 0 | -11.2 4.5 0 -7.2 -2.2 0 | -8.2 -3.2 0 -2.2 -7.3 0 | -3.2 -8.3 0 </code></pre> <p>Transformation Matrix:</p> <pre><code>1 4.4442e-17 0 1 -2.69695e-17 1 0 1 0 0 0 0 </code></pre> <p>--> This gives me two transformation matrices that look right at first sight...</p> <p>Assuming this is right, how would I recalculate the trajectory of this when I have this transformation matrix in each timestep?</p> <p>Anybody any tips or ideas why it's that bad?</p>

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