Several related inventions for estimating scattered radiation in radiographic projections are disclosed. Several of the inventions use scatter kernels of various forms, including symmetric and asymmetric forms. The inventions may be used alone or in various combinations with one another. The resulting estimates of scattered radiation may be used to correct the projections, which can improve the results of tomographic reconstructions. Still other inventions of the present application generate estimates of scattered radiation from shaded or partially shaded regions of a radiographic projection, which may be used to correct the projections or used to adjust the estimates of scattered radiation generated according to inventions of the present application that employ kernels.