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POCan I convert screen coord to camera coordinate using this procedure?
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copied!<p>I want to find camera coordinate from pixel/screen coordinate using opencv.</p> <p>Suppose my cameras are calibrated and I got intrinsic parameter (matrix with focal length and principal point) and extrinsic parameter (rotation and translation matrix) using opencv. Then <a href="http://opencv.willowgarage.com/documentation/cpp/camera_calibration_and_3d_reconstruction.html" rel="nofollow">this website</a> for 3d reconstruction with opencv says:</p> <pre><code>s * [q 1]^{Transpose} = [K] * [([R] * P) + T] </code></pre> <p>where <code>[q]</code> is 2d pixel coordinate, <code>s = 1</code>, <code>K</code> is a (<code>3x3</code>) intrinsic matrix, <code>R</code> is a (<code>3x3</code>) rotation matrix, <code>P</code> is (<code>3x1</code>) in world coordinate and <code>T</code> is a (<code>3x1</code>) translation matrix.</p> <p>So:</p> <pre><code>[R]^{-1} * ( [ [K]^{-1} * [q 1 ]^{Transpose} ] - [T] ) = [P] </code></pre> <p>And then:</p> <pre><code>[U] = ([R] * [P]) + [T] </code></pre> <p>where <code>[U]</code> is (<code>3x1</code>) in camera coordinate. So now <code>[q]</code> which is in pixel coordinate will be converted to camera coordinate <code>[U]</code>. </p> <p>Am I right to convert pixel coordinate to camera coordinate like this? Is rotation matrix (<code>[R]</code>) or intrinsic matrix (<code>[K]</code>) always invertible? Or are there times when rotation matrix and/or intrinsic matrix can't be inverted?</p> <p>Is it possible to kindly confirm this?</p>

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