Theoretical Basis for Optical Granulometry by Wavelet Transformation

A theoretical framework for optical granulometry of sands by a wavelet transformation method is presented. The Haar wavelet transformation is explained by using simple mathematics with comparisons drawn to the use of wavelet decomposition in image compression and image enhancement. The use of seven wavelet decomposition levels on thousands of 128×128 pixel areas of a much larger image of a soil specimen presorted by size yields the soil’s particle-size distribution. The method employs previously developed calibration curves of a wavelet index (CA) versus the average number of pixels per particle diameter (PPD). The curves are nonlinear in CA versus log10(PPD) space. This paper demonstrates that the nonlinearity stems from having to use a relatively low number of decomposition levels. With future advances in camera technology, a linear CA versus log10(PPD) calibration curve could be developed requiring a single soil texture index (T) parameter.