Early in life and without special training, human beings discern resemblance between abstract visual stimuli, such as drawings, and the real-world objects they represent. We used this capacity for visual abstraction as a tool for evaluating deep neural networks (DNNs) as models of human visual perception. Contrasting five contemporary DNNs, we evaluated how well each explains human similarity judgments among line drawings of recognizable and novel objects. For object sketches, human judgments were dominated by semantic category information; DNN representations contributed little additional information. In contrast, such features explained significant unique variance perceived similarity of abstract drawings. In both cases, a vision transformer trained to blend representations of images and their natural language descriptions showed the greatest ability to explain human perceptual similarity-an observation consistent with contemporary views of semantic representation and processing in the human mind and brain. Together, the results suggest that the building blocks of visual similarity may arise within systems that learn to use visual information, not for specific classification, but in service of generating semantic representations of objects.