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Exposed natural surfaces such as landslides, stream beds and fault scarps can provide us with valuable insight into
natural processes and their interaction with the Earth’s surface. By studying the texture left behind on geological media,
we can improve our models for natural processes and our estimation of risk. Research on the surface morphology of
natural materials has been substantially aided in the past decade through the application of remote geodetic data
collection methods including Light Detection and Ranging (LiDAR) which provides high resolution surface geometry
information. Terrestrial LiDAR scanning (TLS) instruments are particularly suited to geological targets due to portability
and high measurement rates. It has long been understood that natural surface roughness is a scale variant phenomenon.
Therefore, accurate modeling of the processes responsible for its generation relies upon accurate morphological
information at the scales under study, without contamination of the data by other morphological scales. Empirical
analysis of the application of TLS to the task of natural surface roughness estimation has indicated that the standard
deviation of surface heights orthogonal to a local planar datum, a commonly employed descriptor of roughness, lacks
stationarity across changes in scan parameters and target scene geometry. A scale dependent bias resulting from
underestimation of surface asperity heights has been found to reduce measured roughness by over 20% of its expected
value. In order to minimize biases imposed on estimated roughness values by scale dependent aspects of the TLS data
collection process multiresolution analysis is applied. A two-dimensional discrete wavelet transform extracts surface
height information present at distinct scales within the data. Roughness is estimated from the reconstructed dataset, with
high frequency noise removed and low frequency surface topography preserved. Using this approach, results show that
surfaces may be compared on the basis of smallest acceptable common textural wavelength and roughness at scales
appropriate to the phenomena being modeled can be isolated and estimated with enhanced accuracy.
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