This thesis develops a strategy for polymerized volume data set construction. Given a volume data set defined over a regular three-dimensional grid, a polymerized volume data set (PVDS) can be defined as follows: edges between adjacent vertices of the grid are labeled 1 (active) or 0 (inactive) to indicate the likelihood that an edge is contained in (or spans the boundary of) a common underlying object, adding information not in the original volume data set. This edge labeling “polymerizes” adjacent voxels (those sharing a common active edge) into connected components, facilitating segmentation of embedded objects in the volume data set. Polymerization of the volume data set also aids real-time data compression, geometric modeling of the embedded objects, and their visualization. To construct a polymerized volume data set, an adjacency class within the grid system is selected. Edges belonging to this adjacency class are labeled as interior, exterior, or boundary edges using discriminant functions whose functional forms are derived for three local adjacency classes. The discriminant function parameter values are determined by supervised learning. Training sets are derived from an initial segmentation on a homogeneous sample of the volume data set, using an existing segmentation method. The strategy of constructing polymerized volume data sets is initially tested on synthetic data sets which resemble neuronal volume data obtained by three-dimensional microscopy. The strategy is then illustrated on volume data sets of mouse brain microstructure at a neuronal level of detail. Visualization and validation of the resulting PVDS is shown in both cases. Finally the procedures of polymerized volume data set construction are generalized to apply to any Bravais lattice over the regular 3D orthogonal grid. Further development of this latter topic is left to future work.