Live imaging of subcellular structures is indispensible to advance our understanding of cellular processes. The blurred digital images acquired in light microscopy are, however, complex to analyze, and identification and reconstruction of subcellular structures from such images remains a major challenge. We present a novel, model-based image analysis algorithm to reconstruct outlines of subcellular structures using a sub-pixel representation. The algorithm explicitly accounts for the optical properties of the microscope. We validate the reconstruction performance on synthetic data and apply the new method to fluorescence microscopy images of endosomes identified by the GTPase EGFP-Rab5. The benefits of the new algorithm are outlined by comparison to standard techniques. We demonstrate that the new algorithm leads to better discrimination between different endosomal virus entry pathways and to more robust, accurate, and self-consistent quantification of endosome shape features. This allows establishing a set of features that quantify endosome morphology and robustly capture the dynamics of endosome fusion.