1. In this, the second of a pair of papers on the structure of well-sorted natural granular material (sediment), new methods are described for automated measurements from images of sediment, of: 1) particle-size standard deviation (arithmetic sorting) with and without apparent void fraction; and 2) mean particle size in material with void fraction. A variety of simulations of granular material are used for testing purposes, in addition to images of natural sediment. Simulations are also used to establish that the effects on automated particle sizing of grains visible through the interstices of the grains at the very surface of a granular material continue to a depth of approximately 4 grain diameters and that this is independent of mean particle size. Ensemble root-mean squared error between observed and estimated arithmetic sorting coefficients for 262 images of natural silts, sands and gravels (drawn from 8 populations) is 31%, which reduces to 27% if adjusted for bias (slope correction between observed and estimated values). These methods allow non-intrusive and fully automated measurements of surfaces of unconsolidated granular material. With no tunable parameters or empirically derived coefficients, they should be broadly universal in appropriate applications. However, empirical corrections may need to be applied for the most accurate results. Finally, analytical formulas are derived for the one-step pore-particle transition probability matrix, estimated from the image's autocorrelogram, from which void fraction of a section of granular material can be estimated directly. This model gives excellent predictions of bulk void fraction yet imperfect predictions of pore-particle transitions.