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We introduce a versatile and spatially resolved morphologicalcharacterisation of binary fields, rooted in the opening transform ofmathematical morphology. We subsequently apply it to the thresholded ionizationfield in simulations of cosmic reionization and study the morphology of ionizedregions. We find that an ionized volume element typically resides in an ionizedregion with radius $\sim8\,h^{-1}\mathrm{cMpc}$ at the midpoint of reionization($z\approx7.5$) and follow the bubble size distribution even beyond the overlapphase. We find that percolation of the fully ionized component sets in when 25%of the universe is ionized and that the resulting infinite cluster incorporatesall ionized regions above $\sim8\,h^{-1}\mathrm{cMpc}$. We also quantify theclustering of ionized regions of varying radius with respect to matter and onsmall scales detect the formation of superbubbles in the overlap phase. Onlarge scales we quantify the bias values of the centres of ionized and neutralregions of different sizes and not only show that the largest ones at thehigh-point of reionization can reach $b\approx 30$, but also that early smallionized regions are positively correlated with matter and large neutral regionsand late small ionized regions are heavily anti-biased with respect to matter,down to $b\lesssim-20$.

Opening Reionization: Quantitative Morphology of the Epoch of Reionization and Its Connection to the Cosmic Density Field