X-ray and gamma-ray photons are widely used for imaging but require a mathematical reconstruction step, known as tomography, to produce cross-sectional images from the measured data. Theoretically, the back-to-back annihilation photons produced by positron-electron annihilation can be directly localized in three-dimensional space using time-of-flight information without tomographic reconstruction. However, this has not yet been demonstrated due to the insufficient timing performance of available radiation detectors. Here, we develop techniques based on detecting prompt Cerenkov photons, which when combined with a convolutional neural network for timing estimation resulted in an average timing precision of 32 picoseconds, corresponding to a spatial precision of 4.8 mm. We show this is sufficient to produce cross-sectional images of a positron-emitting radionuclide directly from the detected coincident annihilation photons, without using any tomographic reconstruction algorithm. The reconstruction-free imaging demonstrated here directly localizes positron emission, and frees the design of an imaging system from the geometric and sampling constraints that normally present for tomographic reconstruction.