%0 Journal Article %J Proc. of the 1st Intl. Symp. on 3D Data Processing, Visualization, and Transmission %D 2002 %T Octree approximation and compression methods %A Samet, Hanan %A Kochut, A. %X 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. %B Proc. of the 1st Intl. Symp. on 3D Data Processing, Visualization, and Transmission %8 2002/// %G eng