IAGES FOR
| Views are then
. in a 3D model
med to register
- we present an
egistration. Our
ween the views
n a comparative
resultant global
que (Benjemma
dences have al-
roximately reg-
matic 3D mod-
vise correspon-
gistration. Our
f an object and
rithm proceeds
's are identified
rithm. Second,
and correspon-
vs based on the
ndences are fed
and Bennamoun,
To estimate the
mparative anal-
pairwise corre-
nt global regis-
ows. Section 2
] automatic cor-
is the details of
'e report our 3D
alysis of the 3D
lly, in Section 6
E
r automatic cor-
e algorithm the
Our correspon-
nsor-based rep-
sroceeds as fol-
| of a cloud of
es and normals
are calculated for each vertex and triangular facet. Next,
all possible pairs of points that are four mesh resolutions
apart are selected from each mesh. Each point pair, along
with its normals, is used to define a 3D basis centered at
the middle of the line joining them. The average of the two
normals defines the z-axis, the cross-product to the nor-
mals define the x-axis and the cross-product of the z-axis
with x-axis defines the y-axis. This coordinate basis is used
to define a 10 x 10 x 10 grid centered at the origin of the
coordinate basis. The bin size of the grid is selected as a
multiple of the mesh resolution (one mesh resolution in our
case). The area of the triangular facets and their average
weighted normals crossing each bin of the grid is calcu-
lated (using Sutherland Hodgman's algorithm) and stored
in a 4th order tensor.
To find correspondence between say view 1 and view 2,
a tensor is selected at random from view 1 and matched
with all the tensors of view 2. For efficiency, two tensors
> Ii :
e is
greater than 0.6, where > I is the amount of intersection
of the occupied bins and >) U12 is the amount of union of
the occupied bins of the two views. Matching proceeds
as follows. The correlation coefficient of the two tensors
is calculated in their region of overlap. If the correlation
coefficient is higher than a threshold t (which is set dy-
namically), one of the two points used to define the view
2 tensor is transformed to the coordinates of view 1 using
the transformation given by Eqn. 1 and Eqn. 2.
are only matched if their overlap ratio Ro =
BIB, (1)
O, — O5R (2)
Here R and t are the rotation matrix and translation vector
respectively. By and Bo are the matrices of the coordinate
basis of view 1 and view 2 tensors respectively. Oy and Oz
are the vectors of origins of the viewl and view 2 tensors
respectively.
If the distance between the transformed point and its cor-
responding point (of the view 1 tensor) is less than d; (set
to one fourth of the mesh resolution), the entire view 2 is
transformed using Eqn. 1 and Eqn. 2. Finally, all sets of
points of view 1 and view 2 that are within a distance dj»
(set equal to the mesh resolution) are converted into corre-
spondences. If this list of correspondences is greater than
half the total number of points of view 1 or view 2, the
transformation is accepted and refined with the ICP (Besl
and McKay, 1992) algorithm.
3 GLOBAL REGISTRATION FOR 3D MODELING
Our3D modeling approach takes an ordered set of views of
an object and finds correspondences between the overlap-
ping views according to the algorithm described in Section
2. The overlap information is either extracted from the or-
der of the views or it is provided explicitly (see Fig. 3).
119
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
Figure 1: First row contains three 2.5D views of the bunny.
The second row contains the complete 3D model viewed
from different angles.
The transformations accompanied with the above corre-
spondences are applied to each view and all the views are
pairwise registered in the coordinate basis of a reference
view (view | in our case). After all the views are pair-
wise registered, correspondences are established between
all sets of overlapping views on the basis of nearest neigh-
bour that are within a distance d;9. Views that have cor-
respondences less than a threshold (one tenth the number
of points of either view) are considered as non overlapping
views and their correspondences are rejected. The remain-
ing set of correspondences is fed to a global registration
algorithm (Williams and Bennamoun, 2001) which regis-
ters all the views globally.
4 RESULTS
We present two results from our experiments in this pa-
per. The first data set is of a bunny and the second data
set is of a robot. Ten views of the bunny and eleven views
of the robot were taken to make their complete 3D mod-
els. Fig. 1 shows three of the ten 2.5D views of the bunny
and its complete 3D model viewed from three different an-
gles. Similarly Fig. 2 shows three out of the eleven 2.5D
views of the robot and its complete 3D model viewed from
three different angles. Once all the views are registered in
a common coordinate basis, it is easy to integrate them and
reconstruct a single smooth and seamless surface. We have
intentionally presented the raw results of our experiments
without performing integration and reconstruction so that
the accuracy of our algorithm can be appreciated. Note
that the extra parts on the surface of the models (e.g. with
