Data from the PAMELA satellite experiment were used to perform a detailed measurement of under-cutoff protons at low Earth orbits. On the basis of a trajectory tracing approach using a realistic description of the magnetosphere, protons were classified into geomagnetically trapped and re-entrant albedo. The former include stably-trapped protons in the South Atlantic Anomaly, which were analyzed in the framework of the adiabatic theory, investigating energy spectra, spatial and angular distributions; results were compared with the predictions of the AP8 and the PSB97 empirical trapped models. The albedo protons were classified into quasi-trapped, concentrating in the magnetic equatorial region, and un-trapped, spreading over all latitudes and including both short-lived (precipitating) and long-lived (pseudo-trapped) components. Features of the penumbra region around the geomagnetic cutoff were investigated as well. PAMELA observations significantly improve the characterization of the high energy proton populations in near Earth orbits.