Image Processing Reference
(a) (b) (c)
Figure 6.14: Modeling the surface as a consistent collection of planar patches Va ro l et al. [ 2009 ]. (a)
Image patches are reconstructed individually up to a scale ambiguity which causes their reconstructions
not to be aligned. (b) Using shared correspondences between these patches (blue points), consistent
scales for all patches are recovered and the whole surface is reconstructed up to a single global scale. (c)
Optionally, a triangulated mesh is fitted to the resulting 3D point cloud to account for holes and outliers.
It can be used to provide a common surface representation across the frames and to enforce temporal
consistency. © 2009 IEEE.
While geometric constraints have proved effective at disambiguating reconstruction, all the
methods described above still treat the object of interest as a whole. As a consequence, similarly as
the global models of Chapter 4 , they often are limited to relatively simple deformations. In the next
section, we present approaches that address this shortcoming by separating the object of interest
into local regions.
SPLITTINGAGLOBAL SURFACE INTOLOCALONES
As discussed in Section 22.214.171.124 , even when the global deformations are large, purely local ones tend
to be smaller and easier to recover. Therefore, it has recently been proposed to also perform NRSFM
locally, so that more complex deformations can be handled. As we will see, local deformations can
often be modeled as planar Va ro l et al. [ 2009 ], quadratic Fayad et al. [ 2010 ], or isometric Taylor et al.
[ 2010 ]. In essence, these approaches therefore perform NRSFM to recover local surface patches and
then enforce consistency between these patches to build a global surface. These methods have
significanlty departed from the formulation presented in Chapter 5 .
The method introduced in Va ro l et al. [ 2009 ] and depicted by Fig. 6.14 relies on the fact
that, when the global deformations are not too severe, local surface patches remain approximately
planar. It takes advantage of the fact that the motion of a plane from one image to the next can
be represented as a homography Hartley and Zisserman [ 2000 ]. Given corresponding points in an
image pair, the first image is subdivided into overlapping patches such as those of Fig. 6.14 (a), which
are assumed to remain roughly planar. Within each individual patch, the correspondences are used to
compute a homography that relates its appearance in the first image to that in the second one. From