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2. THE SCULPTOR'S PRINCIPLE 
An important consequence of applying ‘shape from contours’ to unconstrained objects is that the resulting solution is 
ambiguous. Any of the recovered volume elements may or may not belong to the physical object. The recovered object 
can be thought of as being located inside an enclosing volume. This is because general objects have arbitrary recesses 
that do not show up in the contours. This ambiguity, to a certain extend, exists in any shape from X procedure, and can 
only be reduced by adding information from complementary shape cues, for instance, in our example by using the image 
content inside the contours. To allow for such an integration, however, the actual output of the preceding shape recovery 
algorithm must be in a form that represents the whole set of possible solutions rather than one particular 'smoothed 
optimum' solution. 
Such a representation of a whole set of solutions should keep to the following two design rules: 
1. Modularity: Complementary shape reconstruction techniques must be able to use the output of the previous shape 
from X algorithm without knowing the details of its implementation. 
2. Simplicity: The output must consist in constraints that are easily integrated in complementary shape reconstruction 
modules. 
The sculptor's principle is a new shape reconstruction approach that accomplishes both design rules in an elegant way. 
According to this principle, a volume removing module - a sculptor - is assigned to each shape information source. 
Starting with a large volume that encloses the true object volume, each sculptor cuts away those pieces that are not 
consistent with its assigned information source. The contour sculptor, for instance, cuts away all the pieces that do not fit 
into the measured contours. The sculptor modules may work in parallel or sequentially. After each working step, the 
resulting volume is the maximum volume that is consistent with all the information that has been exploited so far. This 
volume encloses the true object surface since all sculptor modules work in a conservative way. 
Instead of representing the 'optimum' solution, the output now represents an infinite set of possible solutions which can 
have arbitrary shape but must completely lie within the output volume. This maximum volume approach has direct 
consequences on the design of further shape from X modules: They must only know that the true volume lies within the 
reconstructed volume and, therefore, can simply cut away from this volume, much like a sculptor does with his sculpture. 
This is independent of the number of available views. Complementary reconstruction modules have to cut away more for 
a low view number but do not need to know the error source that led to the enlarged volume. 
3 LOCAL BRIGHTNESS INFORMATION 
We now want to introduce a new approach to handle the recesses that are not exposed to contours, like, for instance, 
the eye region of a face, and therefore are not detected by any shape from contours algorithm. The result of this 
contours algorithm is a cluster of object voxels enclosing the true object surface as described in the preceding section. 
The object voxels of the maximum object volume naturally divide into interior voxels and surface voxels. Every surface 
voxels, obviously, is only visible under a subset of all possible viewing angles. This set, consequently, shall be called the 
angular subset. The surface voxels further divide into true surface voxels, i.e. voxels that correspond to true surface 
points on the real object, and false surface voxels which arise from the unexposed areas mentioned above (Fig. 1). 
The basic idea of the algorithm is explained in Fig. 1. Assume that the marked surface voxel on the left side of Fig. 1 is 
  
S$ 
High gray value 
  
True surface voxel 
Low gray value E False surface voxel 
Fig. 1: Schematic slice of the voxel cluster at eye height: The right side shows false (dark gray) and true (light 
gray) surface voxels. The left side shows a false surface voxel being projected under 0° and 40° which 
leads to two different gray values. 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences", Zurich, March 22-24 1995