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While astrocytes have been traditionally described as passive supportive cells, studies during the last decade have shown they are active players in many aspects of CNS physiology and function both in normal and disease states. However, the precise mechanisms regulating astrocytes function and interactions within the CNS are still poorly understood. This knowledge gap is due in large part to the limitations of current image analysis tools that cannot process astrocyte images efficiently and to the lack of methods capable of quantifying their complex morphological characteristics. To provide an unbiased and accurate framework for the quantitative analysis of fluorescent images of astrocytes, we introduce a new automated image processing pipeline whose main novelties include an innovative module for cell detection based on multiscale directional filters and a segmentation routine that leverages deep learning and sparse representations to reduce the need of training data and improve performance. Extensive numerical tests show that our method performs very competitively with respect to state-of-the-art methods also in challenging images where astrocytes are clustered together. Our code is released open source and freely available to the scientific community.