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Best merge region growing normally produces segmentations with closed connected region objects. Recognizing that spectrally similar objects often appear in spatially separate locations, we present an approach for tightly integrating best merge region growing with nonadjacent region object aggregation, which we call hierarchical segmentation or HSeg. However, the original implementation of nonadjacent region object aggregation in HSeg required excessive computing time even for moderately sized images because of the required intercomparison of each region with all other regions. This problem was previously addressed by a recursive approximation of HSeg, called RHSeg. In this paper, we introduce a refined implementation of nonadjacent region object aggregation in HSeg that reduces the computational requirements of HSeg without resorting to the recursive approximation. In this refinement, HSeg's region intercomparisons among nonadjacent regions are limited to regions of a dynamically determined minimum size. We show that this refined version of HSeg can process moderately sized images in about the same amount of time as RHSeg incorporating the original HSeg. Nonetheless, RHSeg is still required for processing very large images due to its lower computer memory requirements and amenability to parallel processing. We then note a limitation of RHSeg with the original HSeg for high spatial resolution images and show how incorporating the refined HSeg into RHSeg overcomes this limitation. The quality of the image segmentations produced by the refined HSeg is then compared with other available best merge segmentation approaches. Finally, we comment on the unique nature of the hierarchical segmentations produced by HSeg.