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High-redshift 21-cm observations will provide crucial insights into the physical processes of the Epoch of Reionization. Next-generation interferometers such as the Square Kilometer Array will have enough sensitivity to directly image the 21-cm fluctuations and trace the evolution of the ionizing fronts. In this work, we develop an inferential approach to recover the sources and IGM properties of the process of reionization using the number and, in particular, the morphological pattern spectra of the ionized regions extracted from realistic mock observations. To do so, we extend the Markov Chain Monte Carlo analysis tool 21CMMC by including these 21-cm tomographic statistics and compare this method to only using the power spectrum. We demonstrate that the evolution of the number-count and morphology of the ionized regions as a function of redshift provides independent information to disentangle multiple reionization scenarios because it probes the average ionizing budget per baryon. Although less precise, we find that constraints inferred using 21-cm tomographic statistics are more robust to the presence of contaminants such as foreground residuals. This work highlights that combining power spectrum and tomographic analyses more accurately recovers the astrophysics of reionization.