VOXEL-BASED VOLUME MODELLING OF INDIVIDUAL TREES USING TERRESTRIAL LASER SCANNERS Hongjoo Park School of Surveying and Spatial Information Systems, University of New South Wales, UNSW Sydney, NSW 2052 Australia Phone: +61 (0)2 9385 4184, Fax: +61(0)2 9313 7493
[email protected], Samsung Lim School of Surveying and Spatial Information Systems, University of New South Wales, UNSW Sydney, NSW 2052 Australia Phone: +61 (0)2 9385 4505, Fax: +61(0)2 9313 7493
[email protected] John Trinder School of Surveying and Spatial Information Systems, University of New South Wales, UNSW Sydney, NSW 2052 Australia Phone: +61 (0)2 9385 4197, Fax: +61(0)2 9313 7493
[email protected] Russell Turner Forests NSW, Department of Primary Industries, NSW, Australia,
[email protected]
Abstract Accurate modelling of individual trees is essential for forestry applications e.g. forestry inventory and biomass estimation. This paper aims to utilise Terrestrial Laser Scanners (TLS) in order to derive a three dimensional (3D) tree structure and compute its volume. A new approach is proposed and tested to estimate the tree structure and leaf area using precise voxel-based tree models. In this study, four different types of trees were chosen from Centennial Park, Sydney, and the corresponding TLS data was obtained and co-registered. The 3D information from the TLS data was reproduced in terms of voxel attributes in the 3D voxel arrays and the K-Dimensional tree (KD-tree) algorithms were applied to the voxelisation of the point cloud data and the 3D visualization of trees. This voxel method has advantages for 3D modelling of trees over a pixel-based method as it can be used to render discontinuous surfaces and allows for the simultaneous representation of the trunk and branches as well as the foliage. The 3D visualisation of individual tree surfaces derived from the TLS testing was compared with 3D point cloud data obtained by Airborne Laser Scanning (ALS). These TLS results were processed with the KD-tree algorithms (raw data, 10 cm, 50 cm and 100 cm) acquired by the voxelisation of the tree trunk, branches and the total leaf volume which were then further compared with the ALS data.
Key word: KD-tree algorithms, Voxelisation, 3D Modelling, forestry inventory, Terrestrial Laser Scanner (TLS), Airborne Laser Scanner (ALS) 1. Introduction Terrestrial Laser Scanners (TLS) provide a three-dimensional representation of the surface of objects resulting in a very large number of measured points on an object (Bae 2008). Many researchers have attempted to compute the volume of forests using computer graphics algorithms. Danson et al. in 2007 used TLS to estimate two-dimensional forest canopy; Lawlor (2002) made use of a voxel based parallel collision detection algorithm; Hosoi (2006) proposed the voxelbased 3D modelling of individual trees for estimating leaf area density using high-resolution portable scanning lidar. Dimitry (2010) has attempted the assessment of light environment variability in broad-leafed forest canopies using TLS. Despite the significant effort put into the 3D modelling of individual tree surfaces, it remains challenging to obtain a precise 3D forestry representation. This paper aims to utilise a computer graphics algorithm which combines the KD-tree algorithm and voxel method, in delivering an objective reproduction of individual tree volume using TLS data. The processed data was then compared with Airborne Laser Scanning (ALS) data derived for the same trees with a sampling interval of about 1m. A voxel representation has two main features that are advantageous when rendering TLS data. One is that a voxel can render a discontinuous surface which reduces the distortion when processing TLS data. The other is that a voxel allows for the simultaneous representation of interior and exterior TLS sensor returns (Stoker 2009). It is believed that the use of this algorithm will also enable us to reduce the processing errors in 3D volumes of individual trees. 2. TLS and ALS Data Acquisition and Data Processing A variety of tree types are found in the study area which was 0.5 km by 0.5 km of Centennial Park in Sydney. The TLS data was collected using a Leica HDS 6000 system in May 2009, while the ALS data was collected by Digital Mapping Australia in July 2007 using an RIEGL LMS-Q560 system. Figure 1 presents the aerial view of the testing area with red circles showing four different trees being tested. The imagery on the right-hand side of Figure 1 provides a quick overview of the TLS and the ALS processing procedure. Re-sampling and interpolation of point clouds were necessary to create a 3D voxel model from both the TLS and ALS data. Leica’s Cyclone 6.0 was used for the post-processing of the TLS 3D point clouds. This software offers registration and geo-referencing of point clouds as well as multiple options for post-processing. The horizontal and vertical Root Mean Squares Errors (RMSE) of the geo-referencing were shown to be less than 0.005m. Riegl’s commercial software was used for the processing of ALS data. The two data sets, the TLS and ALS, were rectified with respect to the
GDA94 coordinate system which is similar to the World Geodetic Systems (WGS84) used for GPS.
Figure.1. Testing Area and Flowchart of TLS and ALS Data Processing
3. Voxel-based 3D Representation of Trees Until recently, GIS researchers have used vector points, lines, or polygons or alternatively raster or pixels to represent the features such as trees (Stoker 2009). A volumetric pixel (commonly referred to voxel) is a volume element that represents a certain value with a quadrilateral or a box structure in 3D space. Voxels are valuable for visualizing and analysis of medical and scientific imaging (Saloner 1991), (Steven 1997), as well as in the description of the resolution for volumetric displays. Figure 2 on the right shows examples of three difference sized voxels covering volumes 1×1×1 (yellow), 2×2×2 (red), and 3×3×3 (blue). The unit of this voxel is 1m. Each input frame is an element of the 3-D array, for example, three dimensional matrices with three columns, with the first element (Easting), the second element (Northing), and the third element (Height). Each element of 3D array includes the value of Red, Green and Blue (RGB) as well as the starting point of each voxel.
Figure. 2. The Examples of Voxel matrix
4. KD-tree Algorithms Acquisition of data using TLS often results in too much data to manage and an exceptionally large sample is not always beneficial. To reduce the size of the data K-Dimensional tree data structure (KD-tree) can be used for the reorganisation of the TLS data, which can reduce the overall processing time. A KD-tree enables storing of a finite set of points from K-dimensional space (Moore 1991), as demonstrated by Bentley (1980), Friedman et al., (1977). It is applicable to many tasks including searches by a multidimensional search key. KD-trees are binary trees designed to handle spatial data more simply (Goodman 2004). The KD-tree data structure is utilised for the registration of point clouds from the TLS in this paper. For implementation, a KD-tree library developed by Arya et al (1998) is used. For n points, O(n) space in E and N, O(log n) tree height, if the KD-tree is balanced, finding the minimum root takes no more than O (√n) time in the worst case. The KD-tree supports range and nearest-neighbour queries of data which are nearest to a given input point data. This paper tested the use of neighbourhood processing for range searches of 10cm, 50cm, and 100cm. The search can be done efficiently using the KD-tree properties to quickly eliminate large portions of the search space. At each step, choose one coordinate as a basis of dividing the rest of the points. The efficiency of the KDtree structure for nearest neighbour search for n data is a function of O (n log n). Analyses of binary search in KD-trees have found that the worst case search time for a K-dimensional KD tree containing N nodes or branches (knots) is given by the following equation (1) (Lee 1977). Figure 3 illustrates an example of the KD-tree Algorithms in 2D and 3D.
t
·
Figure. 3. The example of the KD-tree Algorithms (2D, 3D)
(1)
5. Re-Sampling Data Processing Once the processing of the KD-tree has been completed for the TLS raw data, the re-sampled TLS point clouds for different sampling intervals were compared with the raw point clouds. The number of TLS raw data points and the number after processing by KD-tree are illustrated in Table 1 for three different resampling points of 10cm, 50cm and 100cm. For example, Tree No1, following KD-tree processing into 10cm, 50cm and 100cm voxels, was represented by 103,585, 17,855, 982 and 212 respectively. Table. 1. The Re-Sampling of TLS point clouds using KD-tree algorithms vs. the reference data of ALS points TLS 10 cm TLS 50cm TLS 100cm Reference Sample TLS Raw re-sampling re-sampling re-sampling data (ALS Tree data Point Point Point Point data Point) No 1 103,585 17,855 982 212 78 No 2 93,021 21,282 1,366 287 72 No 3 55,883 14,029 1,107 275 173 No 4 227,413 34,894 1,886 397 153
Figure. 4. The representation of ALS (reference data) Data 3D Point Clouds
Figure 4 illustrates the photo of the tree and the samples obtained from the raw ALS point data. The ALS data were classified and filtered according of the height information as like ground (purple colour) and tree (green colour). Sample No3, which was the smallest in size and height, and hence processing time was least, is shown in Figure 5 for TLS point cloud and the 3D tree models reconstructed using the KD-tree algorithm. The heights are colour coded. A tree was reconstructed in 3D using the KD-tree algorithm based on Matlab software to perform each processing step of the neighbourhood processing by eliminating 10cm, 50cm and 100cm data points.
Figure. 5. The representation of TLS Data Point Clouds using the KD-tree method (Raw data, 10 cm re-sampling, 50 cm re-sampling and 100 cm re-sampling)
6. Voxel-Based 3D Modelling Following the KD-tree processing, we have attempted the voxel based 3D volume modelling for each data point cloud. Figure 6 shows the comparison between the photo and ALS point cloud with the 3D tree volume model which has been reconstructed using the voxel-based method using a voxel size of 50cm. the result of voxel based the 3D tree volume of ALS data processing can be compared with the TLS data processing.
Figure. 6. The 50cm voxel based 3D volume modelling of ALS Data Point Clouds
This KD-tree processing was carried out for three different voxel sizes of 10cm, 50cm, and 100cm. A 10cm of voxel size was shown to provide more details
compared to 50cm or 100cm, however, the data set was too large and took too much processing time. A 100cm of voxel size was effective in reducing the overall processing time, however, the data was very limited in detail, similar to the level of detail obtained in the ALS data. Figure 7 compares the postprocessed of TLS point cloud with the 3D tree volume model reproduced using TLS raw data, 10cm re-sampling, 50cm re-sampling and 100cm re-sampling.
Figure. 7. The 50cm voxel based 3D volume modelling of TLS Data Point Clouds (Raw data, 10 cm resolution, 50 cm resolution and 100cm resolution)
7. Conclusions TLS provides a good description of forest canopy, sub-canopy structure, and ground vegetation, as well as discontinuities and break lines. In this paper, TLS was used to deliver 3D representation of individual trees by voxelisation. The point clouds in this paper were processed using KD-tree algorithms, enabling the users to obtain a more accurate 3D image of trees compared to the conventional methods using pixel as the base unit. Three different re-sampling sizes were taken during KD-tree algorithms processing. However, it should be noted that too many points can be removed while re-organising the point clouds using KD-tree algorithms. When three different voxel sizes (10cm, 50cm, 100cm) were used for re-sampling, the larger the voxel size, the poorer the representation of the real object. For the purpose of 3D modelling of trees, it seems ideal to use 50cm voxel size which gives a good picture of the tree being reproduced and also reasonable data processing time. It would be desirable to
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