An approach for the selection of Compton camera shapes, configurations, positions, orientations, trajectory paths, and detector element sets is provided for collecting data for analysis using the surface integral and integral-of-line-integral methods of reconstruction Compton data. Methods are introduced for (1) selecting one or more imaging lines through a radioactive distribution for which approximations of integrals of radioactivity are to be derived, (2) selecting and using Compton camera relative positions, relative orientations, and detector element sets that “correspond to” the selected imaging lines to collect the needed data; and (3) deriving approximations of integrals of radioactivity along those imaging lines. This methodological approach is used to reconstruct line integrals, cross-sections, local volumes, parallel projections, and cone-beam projections of radioactive distributions.