Information Technology Reference
In-Depth Information
of
v
and appear further on in the list are deleted. The output is a list of corner vox-
els for which
λ >
3
τ
and whose neighbourhoods do not overlap.
2.3 Surface Extraction
After edge and corners detection, it is necessary to determine surface of inbound
object. Many 3D objects can be conveniently described in terms of the shape and
position of the surfaces they are made of. Surface-based descriptions are used for
object classification and motion estimation in the compression process [7]. This
section presents a method of finding patches of various shapes which compose the
visible surface of an object adapted to 3D.
For a given range image
G
, the goal is to compute a new image registered with
G
and with the same size in which each voxel is associated with a local shape
class selected from a given kernel shapes. To solve this problem, two tools are
needed: a dictionary of kernel shape classes and an algorithm determining which
shape class gives the best approximation of the surface at each voxel.
2.3.1 Estimating the Local Shape
To estimate surface shape at each voxel, a local definition of shape is needed. The
method called HK segmentation, described in [8], partitions a range image into re-
gions of homogeneous shape, called homogeneous surface patches. The local sur-
face shape can be classified using the sign of the mean curvature
H
and of the
Gaussian curvature
K
.
In the Table 1, concave and convex are defined with respect to the viewing direc-
tion: a hole in the range surface is concave and its principal curvatures negative. At
cylindrical points, one of the two principal curvatures vanishes, as, for instance, at
any point of a simple cylinder or cone. At elliptic points, both principal curvatures
have the same sign, and the surface looks locally like either the inside of a bowl
(if concave) or the tip of a nose (if convex). At hyperbolic points, the principal cur-
vatures are nonzero and have different signs; the surface is identified as a saddle.
This classification is qualitative in the sense that only the sign of the curvatures,
not their magnitude, influences the result. This offers some robustness, as sign can
often be estimated correctly even when magnitude estimates become noisy.
Table 1
Surface patches classification scheme
K
H
Local shape class
0
0
plane
0
+
concave cylindrical
0
-
convex cylindrical
+
+
concave elliptic
+
-
convex elliptic
-
any
hyperbolic
