title: Correct way to extract Translation from Essential Matrix through SVD
body: <p>I calibrated my camera and found the intrinsic parameters(K). Also I have calculated the Fundamental Matrix (F).</p>
  
  <p>Now E= K_T* F * K . So far so good.</p>
  
  <p>Now we pass the Essential Matrix(E) to the SVD to use the decomposition values (U,W,V) to extract the Rotation and Translation:</p>
  
  <pre><code> essentialMatrix = K.Transpose().Mul(fund).Mul(K);
   CvInvoke.cvSVD(essentialMatrix, wMatrix, uMatrix, vMatrix, Emgu.CV.CvEnum.SVD_TYPE.CV_SVD_DEFAULT);
  </code></pre>
  
  <p>** Question) At this point, two methods have been proposed, and it has confused me which one really give out the right answer- specifically for Translation:</p>
  
  <p>At first method <a href="http://www.eecis.udel.edu/~cer/arv/readings/old_mkss.pdf" rel="noreferrer">enter link description here</a> the author suggests to compute the R,T as following:  </p>
  
  <p><img src="https://i.stack.imgur.com/oaTuk.png" alt="enter image description here"></p>
  
  <p>But in Second method [<a href="http://isit.u-clermont1.fr/~ab/Classes/DIKU-3DCV2/Handouts/Lecture16.pdf]" rel="noreferrer">http://isit.u-clermont1.fr/~ab/Classes/DIKU-3DCV2/Handouts/Lecture16.pdf]</a> the author provides another formula for T which is +U , -U as shown below:  </p>
  
  <p><img src="https://i.stack.imgur.com/crBMt.png" alt="enter image description here"></p>
  
  <p>I am implementing this on C# .Net using openCv libraries. Anybody knows which Translation Formula is the right one?</p>