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Extra resources for Annals of Pure and Applied Logic, Volume 152, Issues 1-3, Pages 1-180 (March 2008)
Object depth or velocity, is used to generate mosaics. This generalizes GV by using this extra 3-D information for mosaic generation. , structure from motion. © 2005 by CRC Press LLC a. b. 13 The background mosaic at the 5th (a) and 11th (b) frames of the “Samir” sequence. S. F. ) The standard structure from motion methods are designed to extract the 3-D object shape (via its depth) and velocity information. This requires the selection of points on these objects, which are tracked in time via their 2-D associated image velocities, that introduces an ad hoc factor: the (3-D) object shape is computed by using the a priori knowledge of its associated (2-D) shape.
This approach requires an impractically small time step to achieve a stable evolution. 2. As the curve evolves, the control points tend to “clump” together near high curvature regions, causing numerical instability. Methods for control points reparameterization are then needed, but they are often less than perfect and hence can give rise to errors. 3. Besides numerical instability, there are also problems associated with the way the Lagrangian approach handles topological changes. As the curve splits or merges, topological problems occur, requiring ad hoc techniques [50, 56] to continue to make this approach work.
62) 2. For r v 1 +rF = Or [A1,r (+rF 1 )] + MrF (Br I r ). 63) These expressions are structurally similar to the ones used for background mosaic generation. 63) is that the latter expressions include a new set of cut-and-paste operators. 57) contain the background B S1 and ﬁgure S1F selection operators. S1F selects from inside image I1 the ﬁgure region, and S1B selects the complement region corresponding to the unoccluded image background. S1B and S1F are instances, for r = 1, of the rth step background and ﬁgure selection operators SrB and SrF , respectively.