An image processing technique is developed to automatically determine both average and instantaneous detonation wave properties within a rotating detonation rocket engine (RDRE) using high-speed imaging. This method entails segmenting the imaged RDRE annulus into 200 azimuthal bins and tracking integrated pixel intensity in each bin. By combining individual pixel intensity temporal histories across the azimuthal bins, this provides what is termed a detonation surface that visualizes the propagation of the individual detonation fronts azimuthally around the annulus. Average detonation modal properties including wave speed Ūwv, operational frequency fdet, and the number of waves m are determined automatically through a two-dimensional Fourier analysis of the detonation surface data. Also, instantaneous wave speeds Uwv for each individual detonation are determined by taking the numerical derivative of each waves' angular position temporal history from the detonation surface. This provides useful insight into wave-to-wave variability for an operating condition, as well as denoting modal transitions and mode stability. For the flow conditions investigated, the number of waves ranges from 2 to 14, with Ūwv varying between 900 and 1700 m/s, corresponding to 33%-71% of the ideal Chapman-Jouguet detonation speed; these modes exhibit an operational frequency of 20-45 kHz, with an average of 40 kHz. Overall, these measurements advance the understanding of RDRE's and may lead to performance gains above those achievable from constant pressure engines.