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Aims. We report the results of a novel determination of the solar oxygen abundance using spatially resolved observations and inversions. We seek to derive the photospheric solar oxygen abundance with a method that is robust against uncertainties in the model atmosphere. Methods. We use observations with spatial resolution obtained at the Vacuum Tower Telescope (VTT) to derive the oxygen abundance at 40 different spatial positions in granules and intergranular lanes. We first obtain a model for each location by inverting the Fe I lines with the NICOLE inversion code. These models are then integrated into a hierarchical Bayesian model that is used to infer the most probable value for the oxygen abundance that is compatible with all the observations. The abundance is derived from the [O I] forbidden line at 6300 Å taking into consideration all possible nuisance parameters that can affect the abundance. Results. Our results show good agreement in the inferred oxygen abundance for all the pixels analyzed, demonstrating the robustness of the analysis against possible systematic errors in the model. We find a slightly higher oxygen abundance in granules than in intergranular lanes when treated separately (log(ε_O) = 8.83 \pm 0.02 vs log(ε_O) = 8.76 \pm 0.02), which is a difference of approximately 2-σ. This tension suggests that some systematic errors in the model or the radiative transfer still exist but are small. When taking all pixels together, we obtain an oxygen abundance of log(ε_O)=8.80 \pm 0.03, which is compatible with both granules and lanes within 1-σ. The spread of results is due to both systematic and random errors.