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Essential Matrix: Difference between revisions
→Calculating the Essential Matrix from two images
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The goal is to minimize <math>\Vert A\mathbf{x} \Vert </math> such that <math>\Vert \mathbf{x} \Vert = 1</math> | The goal is to minimize <math>\Vert A\mathbf{x} \Vert </math> such that <math>\Vert \mathbf{x} \Vert = 1</math> | ||
;Solution | |||
* First take the SVD of A: <math>A = UDV^T</math> | |||
* Now <math>x = V_j<math>, the j'th column of <math>V</math>. Reshape this to get <math>Q_{est}</math> | |||
* In practice, this may not be rank 2 so we take the SVD <math>Q_{est}=U diag(r,s,t) V^T</math> and zero out the third singular value to get a final estimate | |||
*: <math>Q' = U diag(r,s,0) V^T</math> | |||
==Determining rotation <math>\mathbf{R}</math> and translation <math>\mathbf{t}</math>== | ==Determining rotation <math>\mathbf{R}</math> and translation <math>\mathbf{t}</math>== | ||