Grain Size from Digital Images of Sediment
Chezar, H., and Rubin, D., 2004, Underwater microscope system: U.S. Patent and Trademark Office, patent number 6,680,795, January 20, 2004, 9 pages. [Download PDF (507 K)]
Rubin, D.M., 2004, A simple autocorrelation algorithm for determining grain size from digital images of sediment: Journal of Sedimentary Research, v. 74, p. 160-165. doi:10.1306/052203740160
Proposed use of spatial autocorrelation to measure mean grain size; tested with sieved beach and dune sands; provided sample computer code. Included theoretical approach for solving complete grain-size distribution; results for mean size were found to be reliable, but some results for complete grain-size distribution had considerable error.
Rubin, D.M., Chezar, H., Harney, J.N., Topping, D.J., Melis, T.S., and Sherwood, C.R., 2007, Underwater microscope for measuring spatial and temporal changes in bed-sediment grain size: in Hartmann, D., and Flemming, B.W. (eds), From Particle Size to Sediment Dynamics, Sedimentary Geology, v. 202, p. 402-408, doi:10.1016/j.sedgeo.2007.03.020.
Provided descriptions of hardware and guidelines for use.
Barnard, P.L., Rubin, D.M., Harney, J., and, Mustain, N., 2007, Field test comparison of an autocorrelation technique for determining grain size using a digital 'beachball' camera versus traditional methods: Sedimentary Geology, v. 201, p. 180-195. [Download PDF (2242 K)]
Tested accuracy of digital grain-size results compared with mechanical sieving, settling tube analysis, and manual points counts. Explained that results from digital image analysis must be evaluated using point counts—to compare results for exactly the same population of grains.
Mustain, N., Griggs, G. and Barnard, P.L., 2007, A rapid compatibility analysis of potential offshore sand sources for beaches of the Santa Barbara littoral cell. In: Kraus, N.C., Rosati, J.D. (Eds.), Coastal Sediments '07, Proceedings of the 6th International Symposium on Coastal Engineering and Science of Coastal Sediment Processes, American Society of Civil Engineers, New Orleans, LA, Volume 3, p. 2501-2514.
Thousands of digital images were taken of the sediment on the beaches and nearshore in the Santa Barbara littoral cell to identify sources of sediment in the nearshore that could be compatible with adjacent beaches for beach nourishment projects.
Buscombe, D., 2008, Estimation of grain size distributions and associated parameters from digital images of sediment: Sedimentary Geology, v. 210, i. 1-2, p. 1-10, doi:10.1016/j.sedgeo.2008.06.007
Outlines an alternative approach to Rubin (2004) to estimate the distribution of grain sizes within an image of sediment. The method uses non-parametric kernel density functions on the vector of grain sizes per lag found through the least-squares solution of a sample image correlogram compared with a bank of calibration correlograms. Although not a direct solution to the distribution, the advantages of the approach include easily ascribing weightings to the vector of grain sizes, since the information within the correlogram may be a nonlinear function of lag size. Also the form of the distribution (e.g. normal, log-normal), if known for the sediment population under scrutiny, can be specified. Validation with beach gravel in the size range 1.4 and 32mm shows that mean and sorting are well approximated, but higher moments are poorly estimated. Finally, it is suggested that the correlogram should be estimated using a 2D fast Fourier transform approach, rather than the spatial approach of Rubin (2004), because it simultaneously maps energy at all wavelengths and directions. Due to likely anisotropy in images of sediment, a method is presented for estimation of upper and lower bounds on mean grain size using ellipse-fitting on the 2D correlogram.
Buscombe, D., Masselink, G., and Rubin, D.M., 2008, Granular properties from digital images of sediment: implications for coastal sediment transport modelling: Proceedings of International Conference on Coastal Engineering (ICCE), Hamburg, 2008.
Mini-review of digital grain size techniques for a coastal engineering audience. Discusses the importance of the construction of the calibration to avoid making the least-squares problem ill-posed. Evaluation of this may be made through the use of matrix condition numbers. Shows that expressing the calibration catalogue as lags per value of autocorrelation coefficient (rather than the other way round, which is more traditional), can lead to numerically more stable solutions.
Buscombe, D., and Masselink, G., 2009, Grain size information from the statistical properties of digital images of sediment: Sedimentology, v. 56, i. 2, p. 421-438, doi:10.1111/j.1365-3091.2008.00977.x
The problem of estimating grain size from images is assessed using a number of different statistical methods, including autocorrelation, autoregressive spectral density estimation, variograms, and fractal dimensions. It is shown that all of these methods give reasonable estimates of mean grain size for 181 beach gravel samples in the size range 1.4 and 32mm. Due to varying computationally complexity, it is suggested that the autocorrelation approach of Rubin (2004) is the easiest method to use, but the other methods might be useful for different sediment populations. Using a spectral approach to estimate fractal dimensions of images of sediment, it is shown that both the slope and the intercept of the power spectrum is sensitive to mean grain size. The slope quantifies the rate of decay in spatial dependence, so is positively correlated with mean grain size. The intercept tells us the variance, or contrast, in the image, which increases with grain size because the image becomes more varied in a global sense (i.e. more features) so is inversely related to grain size.
Warrick, J.A., Rubin, D.M., Ruggiero, P., Harney, J., Draut, A.E., and Buscombe, D., 2009, Cobble cam: grain-size measurements of sand to boulder from digital photographs and autocorrelation analyses: Earth Surface Processes and Landforms 34, 1811-1821, doi:10.1002/esp.1877. [Download PDF (834 K)]
Extended autocorrelation size analysis to gravel, cobbles, and boulders; presented detailed error analysis; showed that this technique has lower error for a wider range of sizes than edge-detection approaches; presents approach for correcting bias by using point counts.
Buscombe, D., Rubin, D.M., and Warrick, J.A., 2010, A universal approximation to grain size from images of noncohesive sediment: Journal of Geophysical Research, v.115, F02015, doi:10.1029/2009JF001477. [Download PDF (840 K)]
A new method is proposed for estimating mean grain size from an image of sediment without the need for calibration, i.e. read directly from the image. This advance has the potential to make digital grain size considerably easier from a user perspective, and it opens up the possibility of grain size estimation in environments where the calibration procedure is difficult or impossible. The new method is found to give estimates to within 20% without calibration for sediment sizes over 3 orders of magnitude (from fine sands to cobbles). This error can be reduced to approximately 10% by correcting for population-specific bias, which is achieved in practice by carrying out point-counts of end-members of a sediment population. Numerical explanations are offered for the validity of the method. Finally, the new method is explored and tested using physical experiments and computer simulations of synthetic sediment beds.
Rubin, D.M, Topping, D.J., Chezar, H., Hazel, J.E., Schmidt, J.C., Breedlove, M., Melis, T., and Grams, P.E., 2010, 20,000 grain-size observations from the bed of the Colorado River, and implications for sediment transport through Grand Canyon: 2nd Joint Federal Interagency Conference, Las Vegas, NV, June 27 - July 1, 2010, 12 p. [Download PDF (1537 K)]
Shows the examples of sediment-transport interpretations that are possible with large sets of grain-size data.