Out-of-core Algorithms for Binary Partition Hierarchies

Binary partition hierarchies (BPH) and minimum spanning trees are essential data structures for hierarchical analysis, such as quasi-flat zones and watershed segmentation. Traditional BPH construction algorithms are limited by their requirement to load the data entirely into memory, making them impractical for processing large images whose processing exceeds the capacity of the computer’s main memory. To overcome this limitation, an algebraic framework was introduced, enabling the out-of-core computation of BPH leveraging three key operations: select, join, and insert. In this publication, we present two distinct calculi based on these operations: one designed for general spatial partitions and another optimized for causal partitioning. The second calculus is specifically tailored to meet out-of-core constraints, ensuring efficient processing of large-scale data. We provide detailed algorithms, including pseudo-code and complexity analysis, and conduct experimental comparisons between the two approaches.