Knyaz, Vladimir 
  
    
(a) (b) (c) 
Figure 2: Structural light for spatial reconstruction. 
The developed techniques for automated multiplied points3D measurements allow to produce 3D-point cloud for 
following surface reconstruction. The metric characteristics of generated VR models are provided by calibration 
procedure with the accuracy being at the level of 1/10 pixel. 
3 SURFACE RECONSTRUCTION 
The spatial coordinates for complex 3D object such as sculpture, tooth, etc. can be obtained by various means and 
usually they are presented as coordinate cloud P = Ÿ X,,V; 7; )f in given Cartesian system of coordinates. To 
determinate the surface of reconstructed object it is necessary to set links between points. It can be done by common 
Delaunay triangulation procedure if points can be single valued projected on the plane. For closed object such a plane 
does not exist. 
For surface generation it is proposed to take special projection. The first approach selects the space figure (like cylinder, 
sphere, etc.) on which object point cloud can be projected single valued. The kind of space figure is selected based on 
object configuration but the approach to uniform surface reconstruction can be illustrated for sphere. 
The points in 3D cloud can be represented as set of clusters each cluster containing union of points for given image 
acquisition condition (for object meridian in our method of 3D cloud generation). Then it is necessary to find the origin 
of spherical coordinate system providing single valued function 7 = f (2,0). This problem is solved by following 
procedure. The first iteration for coordinate system origin is computed as center of weight for 3D-point cloud. Then for 
every point j the condition of single value is checked. For performing this check every point of first cluster (meridian) is 
connected with the set of points of the next meridian resulting in the set of 3D faces which represent the local surface 
between sequential meridians. If vector rj intersect this surface the new origin is selected providing the condition of 
not intersecting considered local surface. If not then the next meridian is processed. 
Then the procedure repeated until the optimal origin is found or another space figure is tested. If procedure is failed the 
uniform surface can be generated only by object fragmentation. 
In selected coordinate system spherical coordinates (r, „A p; )for every point are found. Then À, coordinates 
with distance metric Ir rA) -(ro) | are used for Delaunay triangulation procedure performing which result in the 
list of 3D point’s links in triangles form. The typical sample (tooth model) of triangulation mesh in À, (p coordinates is 
shown in Fig. 3 (a). 
Then the obtained list of triangles is used for surface presentation in Cartesian coordinate system. The result of surface 
reconstruction in Cartesian coordinates is presented in Fig. 3 (b). 
  
430 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000.