Evidence accumulation models have been used to describe the cognitive processes underlying performance across a number of domains. Previous applications of these models have typically involved decisions about basic perceptual stimuli (e.g., motion discrimination). Applied perceptual domains, such as fingerprint discrimination, face recognition or medical image interpretation, however, require the processing of more complex visual information. The ability of evidence accumulation models to account for these more complex decisions is unknown. We apply a dynamic decision-making model – the linear ballistic accumulator (LBA) – to fingerprint discrimination decisions in order to gain insight into the cognitive processes underlying these complex perceptual judgments. We will present data from three experiments showing that the LBA provides an accurate description of the fingerprint discrimination decision processes with manipulations in visual noise, speed-accuracy emphasis, and training. We will argue that our results demonstrate that the LBA is a promising model for furthering our understanding of complex perceptual decisions, and close by contrasting the LBA model with the signal detection model.