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This paper addresses the problem of the supervised assessment of hierarchical region-based image representations. Given the large amount of partitions represented in such structures, the supervised assessment approaches in the literature are based on selecting a reduced set of representative partitions and evaluating their quality. Assessment results, therefore, depend on the partition selection strategy used. Instead, we propose to find the partition in the tree that best matches the ground-truth partition, that is, the upper-bound partition selection. We show that different partition selection algorithms can lead to different conclusions regarding the quality of the assessed trees and that the upper-bound partition selection provides the following advantages: 1) it does not limit the assessment to a reduced set of partitions, and 2) it better discriminates the random trees from actual ones, which reflects a better qualitative behavior. We model the problem as a Linear Fractional Combinatorial Optimization (LFCO) problem, which makes the upper-bound selection feasible and efficient.