[1] The two-dimensional spectral decomposition of an image of sediment provides a direct statistical estimate, grid-by-number style, of the mean of all intermediate axes of all single particles within the image. We develop and test this new method which, unlike existing techniques, requires neither image processing algorithms for detection and measurement of individual grains, nor calibration. The only information required of the operator is the spatial resolution of the image. The method is tested with images of bed sediment from nine different sedimentary environments (five beaches, three rivers, and one continental shelf), across the range 0.1 mm to 150 mm, taken in air and underwater. Each population was photographed using a different camera and lighting conditions. We term it a "universal approximation" because it has produced accurate estimates for all populations we have tested it with, without calibration. We use three approaches (theory, computational experiments, and physical experiments) to both understand and explore the sensitivities and limits of this new method. Based on 443 samples, the root-mean-squared (RMS) error between size estimates from the new method and known mean grain size (obtained from point counts on the image) was found to be ±≈16%, with a 95% probability of estimates within ±31% of the true mean grain size (measured in a linear scale). The RMS error reduces to ≈11%, with a 95% probability of estimates within ±20% of the true mean grain size if point counts from a few images are used to correct bias for a specific population of sediment images. It thus appears it is transferable between sedimentary populations with different grain size, but factors such as particle shape and packing may introduce bias which may need to be calibrated for. For the first time, an attempt has been made to mathematically relate the spatial distribution of pixel intensity within the image of sediment to the grain size.

In images of sedimentary or granular material, or simulations of binary (two-phase) granular media, in which the individual grains are resolved, the complete size distribution of apparent grain axes is well-approximated by the global power spectral density function derived using a Morlet wavelet. This approach overcomes many limitations of previous automated methods for estimating the grain-size distribution from images, all of which rely on either: identification and segmentation of individual grains; calibration and/or relatively large sample sizes. The new method presented here is tested using: (i) various types of simulations of two-phase media with a size distribution, with and without preferred orientation; (ii) 300 sample images drawn from 46 populations of sands and gravels from around the world, displaying a wide variability in origin (biogenic and mineralogical), size, surface texture and shape; (iii) petrographic thin section samples from nine populations of sedimentary rock; (iv) high-resolution scans of marine sediment cores; and (v) nonsedimentary natural granular patterns including sea ice and patterned ground. The grain-size distribution obtained is equivalent to the distribution of apparent intermediate grain diameters, grid by number style. For images containing sufficient well-resolved grains, root mean square errors are within tens of percent for percentiles across the entire grain-size distribution. As such, this method is the first of its type which is completely transferable, unmodified, without calibration, for both consolidated and unconsolidated sediment, isotropic and anisotropic two-phase media, and even non-sedimentary granular patterns. The success of the wavelet approach is due, in part, to it quantifying both spectral and spatial information from the sediment image simultaneously, something which no previously developed technique is able to do.

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A new application of the autocorrelation grain size analysis technique for mixed to coarse sediment settings has been investigated. Photographs of sand-to boulder-sized sediment along the Elwha River delta beach were taken from approximately 1·2 m above the ground surface, and detailed grain size measurements were made from 32 of these sites for calibration and validation. Digital photographs were found to provide accurate estimates of the long and intermediate axes of the surface sediment (r 2 > 0·98), but poor estimates of the short axes (r 2 = 0·68), suggesting that these short axes were naturally oriented in the vertical dimension. The autocorrelation method was successfully applied resulting in total irreducible error of 14% over a range of mean grain sizes of 1 to 200 mm. Compared with reported edge and object-detection results, it is noted that the autocorrelation method presented here has lower error and can be applied to a much broader range of mean grain sizes without altering the physical set-up of the camera (~200-fold versus ~6-fold). The approach is considerably less sensitive to lighting conditions than object-detection methods, although autocorrelation estimates do improve when measures are taken to shade sediments from direct sunlight. The effects of wet and dry conditions are also evaluated and discussed. The technique provides an estimate of grain size sorting from the easily calculated autocorrelation standard error, which is correlated with the graphical standard deviation at an r 2 of 0·69. The technique is transferable to other sites when calibrated with linear corrections based on photo-based measurements, as shown by excellent grain-size analysis results (r 2 = 0·97, irreducible error = 16%) from samples from the mixed grain size beaches of Kachemak Bay, Alaska. Thus, a method has been developed to measure mean grain size and sorting properties of coarse sediments.