- 82 - 
structured light method with a resolution of 256 3 and +0.29% 
error (the other method produced there an errror of -1.42%). 
In the second test we build models with constant octree 
resolution of 256 3 and increasing number of views. The angle 
between two neighboring views is always constant. Voxel size 
is 2 mm for all models. The models computed are shown in 
Figure 14. 
4 views 
10 views 
20 views 
60 views 90 views 180 views 
Shape from Structured Light 
30 views 
360 views 
Figure 14. 3D models of synthetic sphere with increasing 
number of views 
for this is that the cone has a large number of octree nodes 
belonging to the surface, and these nodes are the ones 
contributing mostly to the error. The models of the cone built 
with different number of views showed the same behavior as 
the models of the sphere - starting from 20 input views the 
volume error relative to the volume of the object built with 360 
views falls to 1% or less . 
If an object only needs to be visualized, without calculating its 
olume, a model built with the octree resolution 32 3 and 10 input 
views can give a satisfactory result. However, it should be 
noted that the sufficient octree resolution as well as the 
sufficient number of view depend on the properties of the 
camera, the geometry of the acquisition system and the 
properties of the object observed. In the tests with synthetic data 
we dealt with rotational symmetric objects only. For more 
realistic cases with more complex data sets tests with real 
objects are necessary. 
5.2 Real objects 
For tests with real objects we use 7 objects shown in Figure 15: 
a metal cuboid, a wooden cone, a coffee mug, two archaeo 
logical vessels and two archaeological sherds. 
Melai cuboid Wooden cone Coffee mug Vessel#! 
Vessel #2 Sherd #1 Sherd #2 
In the tests with synthetic sphere we compared Shape from 
Silhouette and Shape from Structured Light against one another. 
With respect to octree resolution there was no significant 
difference in the behavior of the two methods — the accuracy of 
the models built was approximately the same, with exception of 
octrees 256 3 and 512 3 , where the volume and size of the Shape 
from Silhouette model started being smaller than the analytical 
values, while the Shape from Structured Light model truly 
converged to the analytical one. This can be explained through 
the complexity of building a Shape from Silhouette based octree 
— each node is projected into all 360 input images by projecting 
its 8 vertices, which means 2880 world-to-image projections of 
points per node. In the Shape from Structured Light method, a 
node is projected into two nearest images only, i.e. there are 16 
world-to-image projections per octree node. Therefore, when 
dealing with octree nodes of finer resolution (when the 
projection of the node has approximately the size of a pixel), 
errors due to numerical instabilities are more likely to happen in 
Shape from Silhouette, especially when using a large number of 
views. 
Regarding number of views, there was also no significant 
difference between the two methods. Using 20 instead of 360 
input views was sufficient for both methods to create models 
less than 1% different from the models built using 360 views. 
Figure 15. Real objects used for tests 
The cuboid and the cone have known dimensions so we can 
calculate their volumes analytically and compare them with the 
volumes of their reconstructed models. Using these two objects 
we can also measure the impact of ignoring camera lens distor 
tion on the accuracy of the models. The other objects have 
unknown volume, so we will just show the models constructed. 
All models shown in this section are built using 360 views, with 
constant angle of 1 0 between two neighboring views. 
Object 
Voxel size 
Measured dimensions (mm) 
Vessel #1 
0.74 mm 
141.2 x 84.8 x 93.7 
Vessel #2 
0.53 mm 
114.2 x 114.6x87.4 
Sherd #1 
0.84 mm 
51.8x 67.0x82.2 
Sherd #2 
0.76 mm 
76.0 x 107.3 x 88.5 
Cup 
0.66 mm 
113.3 x 80.0x98.9 
Object 
Volume (mm 3 ) 
Calculated dimensions (mm) 
Vessel #1 
336131 
139.2 x 83.2x91.4 
Vessel #2 
263696 
113.0x111.9x86.4 
Sherd #1 
35911 
51.0 x 66.0 x 79.4 
Sherd #2 
38586 
74.9 x 103.9 x 86.2 
Cup 
276440 
111.6 x 79.0 x 98.3 
As second test object we used a synthetic cone where the 
relative error of the computed volume of models built with 
increasing octree resolution was much larger than the error of 
the models of the sphere built with same parameters. The reason 
Table 1. Reconstruction of two vessels, two sherds and a cup 
The exact volumes of these objects are unknown and therefore 
the accuracy of the volume calculated through reconstruction