Stem number estimation by kernel smoothing of aerial photos

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Abstract
A digitized aerial panchromatic photo of a thinning experiment in pure even-aged Norway spruce (Picea abies (L.) Karst.) is smoothed by a two-dimensional isotropic Gaussian kernel. The number of stems per hectare is estimated from the number of maxima above a certain level of the smoothed image. For the crucial kernel bandwidth estimation problem we suggest a two-step procedure where the first step consists of computing (for each homogeneous stand (or subplot)) an ''internal curve'' corresponding to the number of maxima at a series or bandwidths. The estimated stem number and the optimal bandwidth is then obtained as the crossing of the internal curve with an ''external curve,'' here assumed to be of a simple parametric form. If a series of stands (or subplots) with different known stem numbers is available, the external curve can be estimated by use of a nonlinear regression method. An experiment with 48-year-old trees and six subplots with varying thinning treatments is analyzed. The stem number estimation method, checked by cross validation, performs satisfactorily for all thinning grades except the unthinned control.

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