Upper-bound assessment of the spatial accuracy of hierarchical region-based image representations

Hierarchical region-based image representations are versatile tools for segmentation, filtering, object detection, etc. The evaluation of their spatial accuracy has been usually performed assessing the final result of an algorithm based on this representation. Given its wide applicability, however, a direct supervised assessment, independent of any application, would be desirable and fair. A brute-force assessment of all the partitions represented in the hierarchical structure would be a correct approach, but as we prove formally, it is computationally unfeasible. This paper presents an efficient algorithm to find the upper-bound performance of the representation and we show that the previous approximations in the literature can fail at finding this bound.