Techniques are presented to progressively approximate and compress in a lossless manner two-colored (i.e.binary) 3D objects (as well as objects of arbitrary dimensionality). 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 children 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 discussed 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 approximation. This makes these methods attractive for use on the worldwide web. Progressive transmission has the drawback that here 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 no 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.