3D Reconstruction of the Human Rib Cage from 2D Projection ... - ZIB

3.3. Distance Measures
of the 3D model in an ICP-like manner.
Zheng et al. [ZGS + 09] first, establish point correspondences between contours in
the 2D image I and contours from the projection of a 3D surface model A using
a symmetric injective nearest-neighbor (SIN) mapping operator. The SIN mapping
ensures that (1) each point in both contours is only mapped to at most one point
on the other contour, (2) these matched pairs of points are symmetrically closest
points, and (3) no cross-matching occur, as illustrated Fig. 3.6(top). The 2D point
correspondences are then used to build 3D to 3D correspondences between the 3D
model and back-projected 2D contour points of the 2D image (see Fig. 3.5). The
reconstruction is accomplished using the 3D to 3D correspondences.
Delorme et al. [DPdG + 03] establish 3D to 3D point correspondences between
anatomical landmarks. For this, 3D points are reconstructed from landmarks in
the 2D images using DLT. A 3D model, with landmarks that correspond to the
reconstructed 3D point, is deformed using a 3D geometrical free-form deformation
to match the 3D points.
In the work of Lamecker et al. [LWH06], 2D to 2D correspondences from contours
of the projection of an 3D SSM and contours within the 2D image (and vices versa)
are determined via the computation of the two-sided Euclidean distance between
the points of both contour sets. No explicit correspondences between the 3D model
and the 2D image need to be used.
Figure 3.5: Correspondence building according to Zhang et al.:
For points of the image contour I, associated 3D points v are
determined, which are located on the projection line between the
focal point of the projection source and the points in I. The
points in v possess the shortest distance to the apparent contour
Ω of the 3D surface (adopted from [ZGS + 09]).
Figure 3.6: Point correspondences
build using
ICP (top) in comparison
to the SIN
mapping operator of
Zhang et al. (bottom).
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