Primate visual cortex contains a set of maps of visual space. These maps are fundamental to early visual processing, yet their form is not fully understood in humans. This is especially true for the central and most important part of the visual field--the fovea. We used functional magnetic resonance imaging (fMRI) to measure the mapping geometry of human V1 and V2 down to 0.5 degrees of eccentricity. By applying automated atlas fitting procedures to parametrize and average retinotopic measurements of eight brains, we provide a reference standard for the two-dimensional geometry of human early visual cortex of unprecedented precision and analyze this high-quality mean dataset with respect to the 2-dimensional cortical magnification morphometry. The analysis indicates that 1) area V1 has meridional isotropy in areal projection: equal areas of visual space are mapped to equal areas of cortex at any given eccentricity. 2) V1 has a systematic pattern of local anisotropies: cortical magnification varies between isopolar and isoeccentricity lines, and 3) the shape of V1 deviates systematically from the complex-log model, the fit of which is particularly poor close to the fovea. We therefore propose that human V1 be fitted by models based on an equal-area principle of its two-dimensional magnification. 4) V2 is elongated by a factor of 2 in eccentricity direction relative to V1 and has significantly more local anisotropy. We propose that V2 has systematic intrinsic curvature, but V1 is intrinsically flat.