In this paper, new methods to improve the encoding of connectivity and geom
etry of the topological surgery scheme are proposed. In connectivity compre
ssion, after obtaining the vertex and triangle spanning trees by decomposin
g a three-dimensional object, bits are adaptively allocated to each run of
two spanning trees on a threshold basis. The threshold is the length of a b
inary number of the maximum run length. if a run length exceeds the thresho
ld, it is represented by a binary number of the run length. Otherwise, it i
s represented by a bit sequence. Therefore, compression efficiency is enhan
ced through an adaptive bit allocation to each run of two spanning trees.
In geometry compression, since vertices represented by three-dimensional ve
ctors are stored according to the order of the travelling along vertex span
ning tree by depth-first searching, they have geometrical closeness. The ge
ometry compression efficiency can be improved if the local characteristics
of vectors are considered. Therefore, dynamic finite state vector quantizat
ion, which has subcodebooks depending on a local characteristic of vectors,
is used to encode the geometry information. As it dynamically constructs a
subcodebook by predicting an input vector's state, it produces less distor
tion and gives better visual quality than conventional methods.