This paper presents a psychophysical analysis of the discrimination thresholds of human faces that are varied along different directions in Face Space. Generated by a 3D Morphable Model, the stimuli are frontal views of original laser scans that are modified in shape, texture or both. Discrimination thresholds are then measured in a four Alternative Forced Choice (4AFC) design and a staircase method. In Experiment 1, texture and shape are varied separately along a set of principal component directions. For different components, the results show a consistent pattern of high and low thresholds across individual participants. We compare Mahalanobis distance, Euclidean distance in face space, and 2D image differences as potential predictors for human discrimination thresholds. The goal of Experiment 2 is to investigate the interaction between shape and texture. The stimuli include combined and separate variations of shape and texture in the 4AFC staircase setup, which are analyzed in a wi...