190 
  
  
  
  
  
£ Z 
X, À À 
7 e E i 
14 
| À 
R(-90?) 
Mi 5 V, 
Image frame i 
at 90° view Ë Image frame for 
: the frontal view 
X | 
$ V, 
  
Fig. 4: Perspective projection of an object rotated by a = 90° (left). Planar sector defined by Vi' after inverse 
rotation (a = -90?) and the projected vertices v;' (right). 
line segments of the silhouette. Note that the depth values have to pass a z-buffer before entering the depth map to 
prevent points on the 'back' of the object from overlying the points on the 'front' side. Only the latter ones can be seen in 
a frontal view. 
So far, we only have taken advantage of the contours of one image frame recorded under the angle a, and therefore, the 
resulting depth map does not yet give a realistic impression of the object. However, if we repeat the above algorithm for 
all available views, the depth map is gradually refined until finally, when shaded with a proper shading algorithm, it gives 
a good impression of the object seen from a frontal view. 
The resulting depth map can be considered a 2/5 D volume description since it represents only shape information from 
one viewing direction. To receive a complete 3 D representation of the object, we now have to calculate additional depth 
maps from additional viewing directions. To generalize the calculation from a viewing angle B = 0 to an arbitrary viewing 
direction B, we just replace the inverse rotation R(-«) by the inverse rotation R(B-a). The corresponding depth map 
represents the head as seen under the angle p. 
According to the sculptor's principle, the final object volume results from the intersection of all recovered depth maps, i.e. 
the resulting object volume is the maximum volume compatible with all depth maps. The various depth maps from 
different viewing directions are either merged explicitly into a suitable volume description, by following the sculptor's 
principle, or kept as a set for further shape reconstruction modules. 
  
  
  
  
  
Z 
; Ve 
V3 
présent À i i 
ee | 3 i Z(ij) 
\ mg i 
V; | 
UT | 
Viewing ray | 
Vi VW) Depth map Z(i,j) 
errem. + m ... 7 T —— 
8 wt 
(i,j) rf 
Image frame r 
X 
  
Fig. 5: Planar sector projected into the image frame confining pixel (i,j) that correspond to points of the planar 
sector in space (left). Intersecting viewing rays through all pixels (i,j) with the planar sector yields the 
depths values Z(i,j) that represent the depth map (right). 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences”, Zurich, March 22-24 1995