Accurate quantification of organ radionuclide uptake is important for patient-specific dosimetry. The quantitative accuracy from conventional conjugate view methods is limited by overlap of projections from different organs and background activity, and attenuation and scatter. In this work, we propose and validate a quantitative planar (QPlanar) processing method based on maximum likelihood (ML) estimation of organ activities using 3D organ VOIs and a projector that models the image degrading effects. Both a physical phantom experiment and Monte Carlo simulation (MCS) studies were used to evaluate the new method. In these studies, the accuracies and precisions of organ activity estimates for the QPlanar method were compared with those from conventional planar (CPlanar) processing methods with various corrections for scatter, attenuation and organ overlap, and a quantitative SPECT (QSPECT) processing method. Experimental planar and SPECT projections and registered CT data from an RSD Torso phantom were obtained using a GE Millenium VH/Hawkeye system. The MCS data were obtained from the 3D NCAT phantom with organ activity distributions that modelled the uptake of (111)In ibritumomab tiuxetan. The simulations were performed using parameters appropriate for the same system used in the RSD torso phantom experiment. The organ activity estimates obtained from the CPlanar, QPlanar and QSPECT methods from both experiments were compared. From the results of the MCS experiment, even with ideal organ overlap correction and background subtraction, CPlanar methods provided limited quantitative accuracy. The QPlanar method with accurate modelling of the physical factors increased the quantitative accuracy at the cost of requiring estimates of the organ VOIs in 3D. The accuracy of QPlanar approached that of QSPECT, but required much less acquisition and computation time. Similar results were obtained from the physical phantom experiment. We conclude that the QPlanar method, based on 3D organ VOIs and accurate models of the projection process, provided a substantial increase in accuracy of organ activity estimates from planar images compared to CPlanar processing and had accuracy approaching that of QSPECT.