The perceptual representation of individual faces is often explained with reference to a norm-based face space. In such spaces, individuals are encoded as vectors where identity is primarily conveyed by direction and distinctiveness by eccentricity. Here we measured human fMRI responses and psychophysical similarity judgments of individual face exemplars, which were generated as realistic 3D animations using a computer-graphics model. We developed and evaluated multiple neurobiologically plausible computational models, each of which predicts a representational distance matrix and a regional-mean activation profile for 24 face stimuli. In the fusiform face area, a face-space coding model with sigmoidal ramp tuning provided a better account of the data than one based on exemplar tuning. However, an image-processing model with weighted banks of Gabor filters performed similarly. Accounting for the data required the inclusion of a measurement-level population averaging mechanism that approximates how fMRI voxels locally average distinct neuronal tunings. Our study demonstrates the importance of comparing multiple models and of modeling the measurement process in computational neuroimaging.