A Robust GM-Estimator for the Automated Detection of External Defects on Barked Hardwood Logs and Stems

The ability to detect defects on hardwood trees and logs holds great promise for the hardwood forest products industry. At every stage of wood processing, there is a potential for improving value and recovery with knowledge of the location, size, shape, and type of log defects. This paper deals with a new method that processes hardwood laser-scanned surface data for defect detection. The detection method is based on robust circle fitting applied to scanned cross-section data sets recorded along the log length. It can be observed that these data sets have missing data and include large outliers induced by loose bark that dangles from the log trunk. Because of that and because of the nonlinearity of the circle model, which presents both additive and nonadditive errors, we initiated a new robust generalized M-estimator, for which the residuals are standardized via scale estimates calculated by means of projection statistics and incorporated in the Huber objective function, yielding a bounded influence method. Our projection statistics are based on the 2-D radial vectors instead of the row vectors of the Jacobian matrix as advocated in the literature dealing with linear regression. These radial distances allow us to develop algorithms aimed at pinpointing large surface rises and depressions from the contour image levels, and thereby, locating severe external defects having at least a height of 0.5 in and a diameter of 5 in.