Theories of cross-linguistic phonetic category perception posit that listeners perceive foreign sounds by mapping them onto their native phonetic categories, but, until now, no way to effectively implement this mapping has been proposed. In this paper, Automatic Speech Recognition systems trained on continuous speech corpora are used to provide a fully specified mapping between foreign sounds and native categories. The authors show how the machine ABX evaluation method can be used to compare predictions from the resulting quantitative models with empirically attested effects in human cross-linguistic phonetic category perception.