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POcorrecting fisheye distortion programmatically
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copied!<blockquote> <p><strong><em>BOUNTY STATUS UPDATE:</em></strong></p> </blockquote> <p><strong><a href="https://stackoverflow.com/questions/2477774/correcting-fisheye-distortion-programmatically/2502276#2502276">I discovered how to map a linear lens</a></strong>, from <code>destination</code> coordinates to <code>source</code> coordinates.<br></p> <p><strong>How do you calculate the radial distance from the centre to go from fisheye to rectilinear?</strong></p> <ul> <li><p><strong>1).</strong> I actually struggle to reverse it, and to map source coordinates to destination coordinates. What is the inverse, in code in the style of the converting functions I posted? <img src="https://i.stack.imgur.com/SIhfE.jpg" width="500" height="194" /><br></p></li> <li><p><strong>2).</strong> I also see that my undistortion is imperfect on some lenses - presumably those that are not strictly linear. What is the equivalent to-and-from source-and-destination coordinates for those lenses? Again, more code than just mathematical formulae please... <img src="https://i.stack.imgur.com/ickIZ.jpg" width="500" height="194" /></p></li> </ul> <hr> <blockquote> <p><strong><em>Question as originally stated:</em></strong></p> </blockquote> <p>I have some points that describe positions in a picture taken with a fisheye lens.</p> <p>I want to convert these points to rectilinear coordinates. I want to undistort the image.</p> <p>I've found <a href="http://wiki.panotools.org/Fisheye_Projection" rel="nofollow noreferrer">this description</a> of how to generate a fisheye effect, but not how to reverse it.</p> <p>There's also a <a href="http://photo.net/learn/fisheye/" rel="nofollow noreferrer">blog post</a> that describes how to use tools to do it; these pictures are from that:</p> <p><strong>(1)</strong> : <code>SOURCE</code> <a href="http://photo.net/learn/fisheye/fe01.jpg" rel="nofollow noreferrer">Original photo link</a> <br> <img src="https://i.stack.imgur.com/qLNQV.jpg" width="500" height="334" /><br> Input : <em>Original image with fish-eye distortion to fix.</em> <br></p> <p><strong>(2)</strong> : <code>DESTINATION</code> <a href="http://photo.net/learn/fisheye/fe04.jpg" rel="nofollow noreferrer">Original photo link</a> <br> <img src="https://i.stack.imgur.com/ogb9b.jpg" width="500" height="237" /><br> Output : <em>Corrected image (technically also with perspective correction, but that's a separate step).</em></p> <p>How do you calculate the radial distance from the centre to go from fisheye to rectilinear?</p> <p>My function stub looks like this:</p> <pre><code>Point correct_fisheye(const Point& p,const Size& img) { // to polar const Point centre = {img.width/2,img.height/2}; const Point rel = {p.x-centre.x,p.y-centre.y}; const double theta = atan2(rel.y,rel.x); double R = sqrt((rel.x*rel.x)+(rel.y*rel.y)); // fisheye undistortion in here please //... change R ... // back to rectangular const Point ret = Point(centre.x+R*cos(theta),centre.y+R*sin(theta)); fprintf(stderr,"(%d,%d) in (%d,%d) = %f,%f = (%d,%d)\n",p.x,p.y,img.width,img.height,theta,R,ret.x,ret.y); return ret; } </code></pre> <p>Alternatively, I could somehow convert the image from fisheye to rectilinear before finding the points, but I'm completely befuddled by the <a href="http://opencv.willowgarage.com/documentation/camera_calibration_and_3d_reconstruction.html#initundistortmap" rel="nofollow noreferrer">OpenCV documentation</a>. Is there a straightforward way to do it in OpenCV, and does it perform well enough to do it to a live video feed?</p>

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