Studying steel microstructures yields important insights regarding its mechanical characteristics. Within steel, microstructures transform based on a multitude of factors including chemical composition, transformation temperatures, and cooling rates. Martensite-austenite (MA) islands in bainitic steel appear as blocky structures with abstract shapes that are difficult to identify and differentiate from other types of microstructures. In this regard, material science may benefit from machine learning models that are able to automatically and accurately detect these structures. However, the training process of the state-of-the-art machine learning models requires a large amount of high-quality data. In this dataset, we provide 1.705 scanning electron microscopy images along with a set of 8.909 expert-annotated polygons to describe the geometry of the MA islands that appear on the images. We envision that this dataset will be useful for material scientists to explore the relationship between the morphology of bainitic steel and mechanical characteristics. Moreover, computer vision researchers and practitioners may use this data for training state-of-the-art object segmentation models for abstract geometries such as MA islands.