Input point distribution for regular stem form spline modeling

Karel Kuželka, Róbert Marušák


Aim of study: To optimize an interpolation method and distribution of measured diameters to represent regular stem form of coniferous trees using a set of discrete points.

Area of study: Central-Bohemian highlands, Czech Republic; a region that represents average stand conditions of production forests of Norway spruce (Picea abies [L.] Karst.) in central Europe.

Material and methods: The accuracy of stem curves modeled using natural cubic splines from a set of measured diameters was evaluated for 85 closely measured stems of Norway spruce  using five statistical indicators and compared to the accuracy of three additional models based on different spline types selected for their ability to represent stem curves. The optimal positions to measure diameters were identified using an aggregate objective function approach.

Main results: The optimal positions of the input points vary depending on the properties of each spline type. If the optimal input points for each spline are used, then all spline types are able to give reasonable results with higher numbers of input points. The commonly used natural cubic spline was outperformed by other spline types. The lowest errors occur by interpolating the points using the Catmull-Rom spline, which gives accurate and unbiased volume estimates, even with only five input points.

Research highlights: The study contributes to more accurate representation of stem form and therefore more accurate estimation of stem volume using data obtained from terrestrial imagery or other close-range remote sensing methods.

Key words: spline; stem curve; taper model; diameter position; Norway spruce.

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DOI: 10.5424/fs/2015241-05815