We presented an approach for speeding-up image acquisition when tasked with localizing specific structures in FIB-SEM imagery. It exploits the fact that low-quality images can be acquired faster than higher-quality ones and yet be sufficient for inference purposes. We have demonstrated greater than five-fold speed-ups at very little loss in accuracy in the context of mitochondria and synapse detection. Furthermore, the algorithm we propose is generic and applicable to many imaging modalities that allow trading quality for speed. The disclosed method of data acquisition for an apparatus having a Scanning Electron Microscope (SEM) for microscopic imaging and a Focused Ion Beam (FIB) unit for sample milling comprises the following steps: scanning a sample with the SEM to obtain an image region (I'); analyzing the image region with a classifier function (hi ) that operates on the image region and returns a classification image whose content depends on whether the classifier estimates that a pixel in the image region belongs to a determined target structure or not; searching in the classification image for disjoint regions that indicate potential target locations and adding the regions so found to a list of candidates; iterating the steps of scanning, analyzing and searching on the members of the list of candidates.