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Butterflies are increasingly becoming model insects where basic questions surrounding the diversity of their color patterns are being investigated. Some of these color patterns consist of simple spots and eyespots. To accelerate the pace of research surrounding these discrete and circular pattern elements we trained distinct convolutional neural networks (CNNs) for detection and measurement of butterfly spots and eyespots on digital images of butterfly wings. We compared the automatically detected and segmented spot/eyespot areas with those manually annotated. These methods were able to identify and distinguish marginal eyespots from spots, as well as distinguish these patterns from less symmetrical patches of color. In addition, the measurements of an eyespot's central area and surrounding rings were comparable with the manual measurements. These CNNs offer improvements of eyespot/spot detection and measurements relative to previous methods because it is not necessary to mathematically define the feature of interest. All that is needed is to point out the images that have those features to train the CNN.