It is still a standard practice for biologists to manually analyze transmission electron microscopy images. This is not only time consuming but also not reproducible and prone to induce subjective bias. For large-scale studies of insulin granules inside beta cells of the islet of Langerhans, an automated method for analysis is essential. Due to the complex structure of the images, standard microscopy segmentation techniques cannot be applied. We present a new approach to segment and measure transmission electron microscopy images of insulin granule cores and membranes from beta cells of rat islets of Langerhans. The algorithm is separated into two broad components, core segmentation and membrane segmentation. Core segmentation proceeds through three steps: pre-segmentation using a novel level-set active contour, morphological cleaning and a refining segmentation on each granule using a novel dual level-set active contour. Membrane segmentation is achieved in four steps: morphological cleaning, membrane sampling and scaling, vector field convolution for gap filling and membrane verification using a novel convergence filter. We show results from our algorithm alongside popular microscopy segmentation methods; the advantages of our method are demonstrated. Our algorithm is validated by comparing automated results to a manually defined ground truth. When the number of granules detected is compared to the number of granules in the ground truth a precision of 91% and recall of 87% is observed. The average granule areas differ by 13.35% and 6.08% for core and membranes respectively, when compared to the average areas of the ground truth. These results compare favorably to previously published data.