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We propose a mathematical framework and algorithms both to build accurate models of fluorescence microscope time series, as well as to design intelligent acquisition systems based on these models. Model building allows the information contained in the 2-D and 3-D time series to be presented in a more useful and concise form than the raw image data. This is particularly relevant as the trend in biology tends more and more towards high-throughput applications, and the resulting increase in the amount of acquired image data makes visual inspection impractical. The intelligent acquisition system uses an active learning approach to choose the acquisition regions that let us build our model most efficiently, resulting in a shorter acquisition time, as well as a reduction of the amount of photobleaching and phototoxicity incurred during acquisition. We validate our methodology by modeling object motion within a cell. For intelligent acquisition, we propose a set of algorithms to evaluate the information contained in a given acquisition region, as well as the costs associated with acquiring this region in terms of the resulting photobleaching and phototoxicity and the amount of time taken for acquisition. We use these algorithms to determine an acquisition strategy: where and when to acquire, as well as when to stop acquiring. Results, both on synthetic as well as real data, demonstrate accurate model building and large efficiency gains during acquisition.