Cours de mathematiques. Notions fondamentales d'algebre et by Chambadal L., Ovaert J.-L.

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By Chambadal L., Ovaert J.-L.

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And tz. 13 . If the object is not rotating around the focal point the translation parameters are much smaller if the information from the rotation center is exploited. 35) MULTIPLE VIEWS AND IMAGE SEQUENCES 37 Flexible Body Motion with Arbitrary Shape. The more sophisticated motion characteristic of deformable objects is also visible in the displacement field in the 20 image plane. q1, ... q1, · . QN-1) . 36) The functions f and g depend on the actual 3D motion and deformation model and the projection used to model the image formation process.

A formal description of the epipolar geometry results in the essential matrix which contains the unknown motion parameters for two calibrated camera views. It has been introduced by [711]. Having two cameras with parameters to, R 0 and t 1 , R 1 , constraints can be defined between the projections XQ, x 1 of an unknown scene point p. Given the known projection XQ, the corresponding 3D point p meets the equation P =to+ poRox. 40) Note, that the distance of p is coded in the value p0 . ____,____..

To compute the full flow field, one needs additional constraints such as the heuristic assumption that the flow field is locally smooth. This, in many cases, leads to an estimated optical flow field that is not the same as the true motion field. In most practical situations the motion field is not homogeneous as there may be several objects undergoing different motions. Most of the existing motion analysis methods would fail to perform under these circumstances. Feature-Based Methods. Scanning the extensive Structurejrom-Motion literature unveils the common assumption that in a pre-processing step 2D features in the first camera image are extracted and labeled.

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