| Abstract | Techniques are presented to progressively approximateand compress in a lossless manner two-colored (i.e. bi-
nary) 3D objects (as well as objects of arbitrary dimen-
sionality). The objects are represented by a region octree
implemented using a pointerless representation based on
locational codes. Approximation is achieved through the
use of a forest. This method labels the internal nodes of
the octree as GB or GW, depending on the number of chil-
dren being of type GB or GW. In addition, all BLACK nodes
are labeled GB, while all WHITE nodes are labeled GW. A
number of different image approximation methods are dis-
cussed that make use of a forest. The advantage of these
methods is that they are progressive which means that as
more of the object is transmitted, the better is the approx-
imation. This makes these methods attractive for use on
the worldwide web. Progressive transmission has the draw-
back that there is an overhead in requiring extra storage.
A progressive forest-based approximation and transmission
method is presented where the total amount of data that is
transmitted is not larger than MIN(B,W), where B and W
are the number of BLACK and WHITE blocks, respectively,
in the region octree of the set of objects.
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