Image Processing Reference
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(a) (b) (c) (d)
Figure 1.3: Many sports design tasks could benefit from 3D shape recovery. (a,b) Sailors are interested in
knowing the shape of their own sails and that of their opponents. (c,d) Recovering the true deformations
of skis during a race or of a wing in flight could help improve their design.
(a) (b)
Figure 1.4: Surface reconstruction applied to medical imaging. (a) Schematic representation of non-
invasive surgery. (b) Image acquired during endoscopic coronary artery bypass surgery using the da Vinci
robotic system. Courtesy of Mingxing Hu.
calibrated. The multiple cameras can be replaced by a structured-light projector that can be bundled
together with a single camera Microsoft [ 2010 ]. This can produce very reliable depth-maps in real-
time but has limited range and cannot exploit ordinary video footage. Alternatively, photometric
stereo Hernandez et al. [ 2007 ], Hertzmann and Seitz [ 2003 ], Woodham [ 1980 ] could be employed
to reconstruct deformable surfaces by using several images taken under different lighting conditions.
This technique is very reliable and yields outstanding results, but, as multiview-stereo, it requires
an elaborate setup and is not well adapted to capturing rapidly deforming shapes. From a practical
standpoint, there is therefore a strong incentive for achieving this kind of reconstruction from a
single video stream.
Unfortunately, recovering the 3D shape of surfaces such as those shown in Fig. 1.5 from a single
video-stream is an ill-constrained problem. The high number of parameters and the noisy image
information make it impractical to solve without prior knowledge of the possible deformations that
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