We show in this paper that the expression space is not Euclidean. In particular, we measure the JND discrimination thresholds in the expression space. In the 3D space of the first three principle components, these JND thresholds are ellipsoids of which the shape, size are varying for different expressions, which are evidence that the expression space are not Euclidean but distorted or a Riemann space. These JND thresholds also define Riemann metric tensor of the expression space, which suggests the possibility of application using Riemann geometry.