This paper describes the Bayesian Technique for Multi-image Analysis (BaTMAn), a novel image segmentation technique based on Bayesian statistics, whose main purpose is to characterize an astronomical dataset containing spatial information and perform a tessellation based on the measurements and errors provided as input. The algorithm will iteratively merge spatial elements as long as they are statistically consistent with carrying the same information (i.e. signal compatible with being identical within the errors). We illustrate its operation and performance with a set of test cases that comprises both synthetic and real Integral-Field Spectroscopic (IFS) data. Our results show that the segmentations obtained by BaTMAn adapt to the underlying structure of the data, regardless of the precise details of their morphology and the statistical properties of the noise. The quality of the recovered signal represents an improvement with respect to the input, especially in those regions where the signal is actually constant and/or the signal-to-noise ratio of the measurements is low. However, the algorithm may be sensitive to small-scale random fluctuations (depending on the dimensionality of the data and the adopted priors), and its ability to recover the signal in the presence of spatial gradients is limited. Due to these effects, the output errors may be underestimated by as much as a factor of the order of two. Two of the most interesting aspects of the algorithm are that (i) it will prioritise the conservation of all the statistically-significant information over the reduction of the noise, and (ii) the precise choice of the input data does have a crucial impact on the results. Hence, the philosophy of BaTMAn is not to use it as a "black box" that improves the signal-to-noise ratio, but as a new approach for the characterization of spatially-resolved data prior to its scientific analysis.
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