Position-invariant hierarchical image analysis

Spatial hierarchy is an appealing strategy for image analysis, but standard hierarchical methods give increasingly sparse, position dependent results with increasing level. This paper endows simple hierarchical techniqueswith positioninvariance by an architectural extension, broadening their scope with no increase in algorithmic complexity. The tree structure is extended intoan exhaustive hierarchy containinga node at every image location at every level. This maps straightforwardly to existing parallel computers; one pass takes time on a hypercube and time on a mesh, for an image. We present novel algorithms for labeling connected components; detecting line features robustly; and computing distance transforms. The algorithms are exceedingly simple, usually optimal, and involve a minimum of storage and communication per node.