3D landscape pattern analysis using wavelets based techniques

Authors and Affiliations: 

Mihai-Sorin Stupariu (1,2), Alin-Ionuţ Pleşoianu (2,3), Ileana Pătru-Stupariu (2,3)

1 University of Bucharest, Faculty of Mathematics and Computer Science, Str. Academiei, 14, 010014 Bucharest, Romania.
2 Institute of Research of University of Bucharest, ICUB; Transdisciplinary Research Centre Landscape-Territory-Information Systems, CeLTIS, Splaiul Independenţei nr. 91-95, 050095 Bucharest, Romania
3 Department of Regional Geography and Environment, Faculty of Geography, University of Bucharest, Bd. N. Bălcescu, 1, 010041 Bucharest, Romania

Corresponding author: 
Mihai-Sorin Stupariu

The 3D component of landscapes is inherently related to the vegetation structure. The availability of high resolution data such as LiDAR point clouds opens new possibilities for the quantification of specific vegetation patterns. It is therefore a challenge to define suitable metrics, i.e. indicators measuring a certain feature. Several steps were already made and 3D metrics were computed for characterizing forest structure. For instance, tree height variance combined with statistical indicators made it possible to model vegetation patterns (Blaschke et al., 2004). Another class of metrics included canopy density, roughness and vertical layering of the forest (Maier et al., 2009). Further metrics such as a penetration index or vegetation surface - volume ratio could be also introduced (Mücke et al., 2010).
It is a natural question whether appropriate metrics could capture patterns at a finer scale, such as species related information or individual tree characteristics. We explored this hypothesis by applying wavelets techniques, which are signal filtering methods used in multiresolution analyses (Addison, 2002). Specifically, we considered the so-called ‘Mexican Hat’ wavelet, whose shape resembles to certain trees species (Falkowski et al., 2006). This wavelet depends on a dilation parameter and the main hypothesis tested was whether this parameter could serve as a metric enabling the detection of small scale landscape and vegetation features (trees, bushes). This could be achieved by applying the mathematical convolution operation to a LiDAR derived 2D Canopy Height Model by using a Mexican Hat wavelet as a convolution mask, i.e. as a shape to be ‘recognized’ in the vegetation model. By varying the dilation parameter, the filtering can be done at different spatial scales in order to detect features with different shapes and sizes. The method was applied in the case of a forested pasture in Fundata, Romania, by using a 1m resolution Canopy Height Model derived from high density LiDAR data. The results show proficiency in detecting trees of various shapes from different species (P. abies, F. sylvatica) with a high detection percentage as well as a slightly better detection percentage for the bushes features (J. communis). Overall, the approach takes advantage of the wavelets analysis capacity to control the level of detail in which to search for features in data, while being able to identify the scale and location.


Addison, P.S. (2002). The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance, CRC Press.

Blaschke, T., Tiede, D., & Heurich, M. (2004). 3D landscape metrics to modelling forest structure and diversity based on laser scanning data. International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, 36, 129-132.

Falkowski, M.J., Smith, A.M.S., Hudak, A.T., Gessler, P.E., Vierling, L.A., & Crookston, N.L. (2006). Automated estimation of individual conifer tree height and crown diameter via two-dimensional spatial wavelet analysis of lidar data. Canadian Journal of Remote Sensing, 32, 153-161.

Maier, B., Tiede, D., & Dorren, I. (2008). Characterising mountain forest structure using landscape metrics on LiDAR-based canopy surface models, in: Blaschke, T., Lang, S. & Hay, G.J. (Eds.), Object-Based Image Analysis, Springer, pp. 625-644.

Mücke, W., Hollaus, M., & Prinz, M. (2010). Derivation of 3D landscape metrics from airborne laser scanning data. Silvilaser Freiburg, Germany.

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