This work reports a study of the ignition processes in a Mach-2 cavity combustor using a three-dimensional (3D) diagnostic with 20 kHz temporal resolution. The diagnostic was based on a combination of tomographic chemiluminescence (TC) and fiber-based endoscopes (FBEs). Customized FBEs were employed to capture line-of-sight integrated chemiluminescence images (termed projections) of the combustor from 8 different orientations simultaneously at 20 kHz. The measured projections were then used in a tomographic algorithm to obtain 3D reconstructions of flame structures. Based on the 3D reconstructions, 3D volume of ignition kernels was extracted to further study the ignition processes. The 3D volume measurements clearly distinguished the ignition stage from the stable combustion stage of the combustor and enabled the determination of a transition time to quantify both stages. These results demonstrated the utility of the 3D diagnostics to overcome some of the limitations of established planar diagnostics and to resolve the dynamics of high-speed combustion devices both spatially and temporally.