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Abstract Lightness constancy, the ability to create perceptual representations that are strongly correlated with surface albedo despite variations in lighting and context, is a challenging computational problem. Indeed, it has proven difficult to develop image-computable models of how human vision achieves a substantial degree of lightness constancy in complex scenes. Recently, convolutional neural networks (CNNs) have been developed that are proficient at estimating albedo, but little is known about how they achieve this, or whether they are good models of human vision. We examined this question by training a CNN to estimate albedo and illumination in a computer-rendered virtual world, and evaluating both the CNN and human observers in a lightness matching task. In several conditions, we eliminated cues potentially supporting lightness constancy: local contrast, shading, shadows, and all contextual cues. We found that the network achieved a high degree of lightness constancy, outperforming three classic models, and substantially outperforming human observers as well. However, we also found that eliminating cues affected the CNN and humans very differently. Humans had much worse constancy when local contrast cues were made uninformative, but were minimally affected by elimination of shading or shadows. The CNN was unaffected by local contrast, but relied on shading and shadows. These results suggest that the CNN followed an effective strategy of integrating global image cues, whereas humans used a more local strategy. In a follow-up experiment, we found that the CNN could learn to exploit noise artifacts that were correlated with illuminance in ray-traced scenes, whereas humans did not. We conclude that CNNs can learn an effective, global strategy of estimating lightness, which is closer to an optimal strategy for the ensemble of scenes we studied than the computation used by human vision.