In this paper, we propose a novel approach to speed-up the computation of the histograms of multiple overlapping non rotating regions of a single image. The idea is to exploit the overlaps between regions to minimize the number of redundant computations. More precisely, once the histogram of a region has been computed, this one can be used to compute part of the histogram of another overlapping region. For this purpose, an optimal computation order of the regions needs to be determined and we show how this can be obtained as the solution of a minimum spanning tree of a graph modeling the overlaps between regions. This tree is computed using Kruskal's algorithm and parsing it in a depth-first search manner determines precisely how the histogram of a region can be computed efficiently from that of its parent in the tree. We show that, in practical situations, this approach can outperform the well-known integral histogram both in terms of computation times and in terms of memory consumption.