On approaches to polygonal decomposition for hierarchical image representation

Approaches to polygonal decomposition for hierarchical image representation are described. For planar decomposition, quad trees using square and triangular neighborhoods are found to be the only feasible methods, having the same computational complexity. For grid images the choice of the appropriate tree type is determined by the grid topology. Triangular and square quad trees are appropriate for the triangular and square grids, whereas trees of order 7 are necessary for the hexagonal grid.