Learning extrinsic parameters (exterior orientation problem). Given points ${w}_{i=1} ^{I}$ on a known object (blue lines), their positions $x^{I}_{i=1}$ in the image (circles on image plane), and known intrinsic parameters $\Lambda$.

Find the rotation $\Omega$ and translation $\tau$ relating the camera and the object.

a) When the rotation or translation are wrong, the image points predicted by the model (where the rays strike the image plane) do not agree well with the observed points xi.

b) When the rotation and translation are correct, they agree well and the likelihood $Pr(x_{i}|w,\Lambda, ;\Omega,\tau )$ will be high.

Problem figure


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