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Essential Matrix: Difference between revisions
→Determining rotation \mathbf{R} and translation \mathbf{t}
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==Determining rotation <math>\mathbf{R}</math> and translation <math>\mathbf{t}</math>== | ==Determining rotation <math>\mathbf{R}</math> and translation <math>\mathbf{t}</math>== | ||
Theorem | ;Theorem | ||
A <math>3 \times 3</math> real matrix can be factored into a product of a rotation matrix <math>R</math> and a non-zero skew symmetric matrix <math>S</math> iff <math>Q</math> is two equal non-zero singular values and one zero singular value. | |||
Let the singular value decomposition of our essential matrix <math>Q</math> be <math>U D V^T</math> where <math>D = \operatorname{diag}(k, k, 0)</math>. | Let the singular value decomposition of our essential matrix <math>Q</math> be <math>U D V^T</math> where <math>D = \operatorname{diag}(k, k, 0)</math>. | ||