Many industrial applications require geometric modeling of manufactured
free-form surfaces or naturally occurring sculpted objects that cannot be
modeled using simple volumetric primitives or easily detectable features such
as edges and vertices. Existing object recognition systems are designed more
for specific applications than for general free-form 3D objects.
The authors wish to design a method of representing and recognizing
arbitrarily curved objects without limiting the domain of interest to a fixed
set of geometric shapes.
This paper presents a new surface representation scheme for 3D free-form
objects. An object is described in terms of maximal surface patches of
constant shape index. Every distinct surface shape has its own shape
index. Shape index is basically a measure of surface shape based on principal
curvatures. The maximal patches are mapped onto the unit sphere using their
orientations and aggregated using shape spectral functions.
Properties such
as surface area, curvedness and connectivity are built into the
representation. The notion of shape spectrum, based on the shape index,
is also introduced. The representation scheme is named COSMOS, an
abbreviation for Curvedness-Orientation-Shape Map On Sphere.
The main strength of COSMOS is the integration of local and global shape
information that is easily computed from sensed data and reflective of the
underlying surface geometry. Also it is a general scheme for representing
arbitrarily curved 3D objects including objects with holes. The
representation is compact for all objects except those for which shape index
changes rapidly over the object surface. Some classes of objects are
recoverable from their COSMOS representations. The shape spectrum of an
object is useful for fast matching of an input object view with other views in
a model database. The representation summarizes the surface area of the
object at each shape index value. The assumption is that all objects are
completely unoccluded, but the representation may still work with small
occlusions where the important features of the object are still visible. A
simple prototype using the COSMOS representation scheme for matching
algorithms and for model database organization has been built with good
results.