This work reports the measurements of three-dimensional (3D) flame topography and curvature of a premixed turbulent Bunsen flame at a rate of 5 kHz, using a technique combining chemiluminescence and tomography. Line-of-sight images of chemiluminescence (termed projections) of the target flame were recorded by six cameras from different orientations simultaneously at 5 kHz. Based on these projections, a tomography algorithm reconstructed the 3D flame structure, based on which 3D curvature was then calculated. Due to the 3D nature of the data, statistics of flame properties can then be extracted both in temporal and spatial domains. Probability density function (PDF) of flame topography was extracted from a series of 3D measurements, and the PDFs of the flame at different spatial locations were examined. Furthermore, the instantaneously measured 3D flame topography also enabled the calculation of 3D flame curvature (or 2D curvature along an arbitrary orientation). The PDFs of curvature in 2D and 3D were then extracted and compared. These results provide quantification of the flame surface shape in 3D (cylindrical, elliptic, or hyperbolic), illustrating the utility of 3D diagnostics to fully resolve the dynamics of turbulent flames. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.