The Photogrammetric Journal of Finland, Vol. 24, No. 2, 2015 Received 01.10.2015, Accepted 04.12.2015 Doi:10.17690/015242.2

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FILTERING THE OUTLIERS FROM BACKPACK MOBILE LASER SCANNING DATA

Petri Rönnholm1 Antero Kukko1,2 Xinlian Liang2 Juha Hyyppä2

1 Institute of Photogrammetry and Remote Sensing, Aalto University

2 Finnish Geospatial Research Institute, FGI, National land Survey of Finland

petri.ronnholm@aalto.fi, antero.kukko@nls.fi, xinlian.liang@nls.fi, juha.hyyppa@nls.fi

ABSTRACT Backpack mobile laser scanners provide rapid data acquisition and allow access to all walkable areas. We aim to remove outliers from the data of a prototype backpack mobile laser scanning system. After removing dark intensity points, our approach mainly uses voxel grids. Firstly, we remove points that only have a few points in the neighborhood. Secondly, we search for outlier clusters with a 3D convolution of voxel grids. Thirdly, outlier clusters located in the air or below the ground are removed with a single elimination bin. As a result, the majority of outliers are successfully removed from backpack mobile laser scanning data. 1. INTRODUCTION The terrestrial perspective is highly important when building facades and detailed structures are surveyed in urban areas, as well as when tree details and lower vegetation are measured in natural environments. Even if static terrestrial laser scanning measurements have been proven to provide accurate data (Vastaranta et al., 2008; Lichti, 2010; Polo et al., 2012), mobile laser scanning (MLS) is preferred in many cases because of its rapid data acquisition and high productivity (Talaya et al., 2004; Jaakkola et al., 2008). MLS systems have been attached to vehicles such as cars and boats. However, these platforms limit accessibility to those areas that cannot currently be reached by a vehicle. To overcome accessibility limitations, backpack MLS systems have been developed (Chen et al., 2010). Such systems allow personal laser scanning (PLS) and access to walkable areas. The first prototypes were quite large and heavy to carry, but because of sensor development the size of such systems is getting smaller. One of the earliest prototypes of backpack MLS, AkhkaR2, was developed by the researchers of the Finnish Geodetic Institute. The system was operational in 2011 (Kukko et al., 2012). Backpack MLS require navigational devices, such as GNSS and inertial instruments, combined with a 2D laser scanner or a 3D scanner in profiler mode. Some laser scanners, however, suffer from outliers—especially in profiler mode. In Figure 1, raw data from FARO Focus3D attached to an AkhkaR2 backpack system is illustrated, showing outliers both in the air and below the ground. Without removing outliers, the actual objects cannot be clearly detected. Therefore, reducing outliers is an essential part of the pre-processing of MLS data, before applying further operations.

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Figure 1. Raw backpack laser scanning data shows many outliers. Color coding represents the

time of data acquisition. The reasons why outliers appear in raw laser scanning data may vary. There can be sensor noise, multi-path reflections, faulty time measurements, hits from flying objects (like birds), phase-based scanners creating mixed pixels in breakline areas, background noise, etcetera. Usually, end-users do not get raw data because of automatic or manual outlier removal. However, when collecting raw data with the backpack prototype, all outliers are present before post-processing. The removal of outliers can be a time-consuming phase because data sets are usually very large. Isolated outliers can be eliminated by searching if the neighboring area within a given radius includes fewer points than a threshold, as done in some commercial or free software—for example, TerraScan and LasTools. However, with a high point density and large search radius, computing time increases significantly. In addition, in TerraScan potential air points can be filtered by computing median elevation and a standard deviation within a given distance. All points above the standard deviation multiplied by a given factor are considered air points (TerraScan). LasTools classifies outliers by creating 3 × 3 × 3 cells of adjustable size around a point in focus and by searching if neighboring cells have fewer points than a threshold (LasTools). Papadimitriou et al. (2003) give a good presentation about finding outliers from large data sets. They suggest five categories of outlier detection that are distribution-based, depth-based, clustering, distance-based, and density-based methods. Lehtola et al. (2015) removed the

0 s 50.3125 s

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outliers of a rotating mobile mapping system by examining mean and standard deviation around each point separately. In some cases, the scanning area includes clear surfaces in which planes or polynomial surfaces can be fitted or meshes can be created. In such cases, many outlier removal tools are useful, such as a spatial depth-pass filter (Pauly and Gross, 2001), mesh simplifying (Lee et al., 1998), topological noise removal (Guskov and Wood, 2001), and wavelet denoising (Smigiel et al., 2008), just to name few. Such methods are, however, difficult to apply in a natural environment if information from vegetation is also needed. The objective of this article is to remove outliers from AkhkaR2 backpack MLS data in areas that include both buildings and nature. Our approach mainly utilizes voxel-based methods. In addition, we take the time aspect of backpack MLS data into account. 2. MATERIALS The test was carried out in a mature forest plot in an area in Kirkkonummi (60.15°N, 24.53°E), southern Finland. A 2000 m2 (40 m × 50 m) rectangular forest plot was set for this study, and data was collected for full coverage with overlapping paths. The dominant tree species in the test area is Scots pine (Pinus sylvestris L.). Other species growing in the plot include Norway spruce (Picea abies L.), birch (Betula sp. L.), and aspen (Populus tremula L.).

Table 1. AkhkaR2 backpack specifications

FARO Focus3D 120S

122,000–976,000 pts/s, selectable Vertical and horizontal field of view: 305° × 360° Wavelength 905 nm

NovAtel SPAN GNSS-IMU NovAtel Flexpak6 GNSS receiver and GPS-702-GG antenna

L1, L2, L2C GPS L1, L2 GLONASS Litef UIMU-LCI FOG IMU Gyro rate bias <1.0 deg/h Random walk <0.05 deg/√h Data rate 200 Hz

AkhkaR2 is a backpack MLS system that can be operated on rugged terrain and forest floor for capturing precise and dense point clouds for ground elevation modeling, forestry, and urban mapping (Figure 2). The AkhkaR2 system consists of a NovAtel SPAN GNSS-IMU positioning system integrated with a FARO Focus3D laser scanner (see Table 1 for more technical details). The positioning system observes GPS and GLONASS satellites for global positioning and IMU tracks the system movements during the data collections. Trajectory information is post-processed and fused with laser data from the cross-track profiling scanner to capture the mapped scene by a three-dimensional point cloud (Kukko, 2013; Liang et al., 2014). Data for this study was collected on September 4, 2013 with the scan frequency of 95 Hz and the point measurement rate of 488 kHz, yielding 1.2 mrad angular resolution within the profile. The beam divergence of the scanner was 0.16 mrad, giving a circa 11 mm spot size at 50 m range

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from the scanner. The profile spacing of the data collection at about 1 m/s walking speed gives 1 cm profile spacing along the trajectory. In practice, the turning and swinging of the system on the operator’s back results in variation in the spacing.

Figure 2. The backpack MLS system AkhkaR2 (Photo: H. Kaartinen 2013).

3. METHODS Backpack MLS data is time-dependent. Forest areas usually prevent optimal satellite visibility and IMU systems tend to create some time-dependent orientation errors. In addition, data acquisition in a forest usually leads to a serpentine trajectory. Therefore, the same areas are covered with point clouds from different data acquisition times. If the coordinate system has slightly changed, this causes confusing situations wherein one spatial area might have points in different coordinate systems (Figure 3). Because of this, we chose to process data in relatively short time sequences and not to select data by the area. We processed data in 10-second time periods, which usually included circa 2.5 million laser scanning points. Originally data from the laser scanning campaign was stored in several LAS files, which each included circa 14 million points. A batch-based algorithm was created in Matlab for processing all .las files from a selected directory automatically. LAS file input was developed with C++ and compiled into a MEX file, enabling the use of it via Matlab. Even if data was processed in small parts, the results were stored in files corresponding to the original files.

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Some of FARO Focus3D outliers can be eliminated by using an intensity threshold because many of them typically have a relatively low intensity value. Filtering dark intensity points especially helps to get rid of outliers close to the scanner. However this method does not remove all undesired outliers before affecting real objects. Therefore the filtering threshold cannot be set too high.

Figure 3. The cross-section of a tree trunk reveals the change of orientation within data. Blue

points have been taken circa six seconds before red points. For filtering the remaining outliers a voxel-based system was created, in which each voxel had a count of how many laser points were located within. The size of the total voxel array was determined from original data by searching for the maximum and minimum values in all directions of the coordinate axes. For filtering, there were two parameters: a threshold for the number of points required to be in a voxel and the size of the cubic voxels. These threshold parameters were found empirically. Using just a single voxel array does not work reliably. The reason is, if we have a voxel covering only a part of a point cloud that belongs to some object, the voxel might include so few points that they do not exceed the threshold. In such a case, some parts of real objects would be deleted by outlier filtering. This effect can be eliminated by introducing more voxel arrays that are shifted half of the voxel length in the directions of three coordinate axes, diagonally between the XY, YZ, and XZ axes, and diagonally between all three axes X, Y, and Z. It should be ensured that all data is within voxel grids by adding more voxels if necessary. Working with several voxel arrays is illustrated in Figure 4. For making visualization easier to interpret, we represent the idea in 2D. The workflow of 3D outlier reduction is:

• Create the first voxel array and the shifted voxel arrays (in X, Y, Z, XY, YZ, XZ, and XYZ)

• Go through all laser points and select the closest voxel from all eight voxels arrays • If all voxels include less points than the threshold, then reject this point In the 3D case, it is essential to use all eight voxel arrays in order to prevent the data loss of real objects. Figure 5 illustrates how the results differ if only the original and diagonally shifted voxel arrays are used, compared to using all eight voxel arrays. This comparison reveals that using too few voxels grids causes the loss of edge points and creates small holes in data.

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Figure 4. In the left image, an examination area covers a small part of a real object (the red

points) and one outlier point (the green point). If a threshold were less than four points within the examination area, all three points would be deleted as outliers. In the middle image, two adjacent

examination areas are illustrated with a blue outline and the original examination area is now outlined in gray. The leftmost of the presented two new examination areas covers more real object points than the threshold, which prevents point deletion. The right examination area

includes only one outlier point. In the rightmost image, the outlier point (the gray point) is found because it belongs in two examination areas from different arrays that both have fewer points

than the threshold.

Figure 5. In the left image, only two voxel arrays are applied: the original and diagonally shifted

ones. In the right image, all eight voxel arrays are in use. The difference is clearly visible, especially in the corners of this object.

This kind of voxel-based filtering removes the majority of outliers. However, in some cases it is not possible to set a threshold large enough to remove all outliers without deleting actual object points. As a result, outlier segments can remain in the air and under the ground level. The removal of separate voxels that contain outliers can be solved by applying 3D convolution to regular voxel arrays. We already had a 3D voxel representation of data (A) from the previous step. The result (C) reveals the potential locations of voxels that contain outliers and was achieved by convolving A with a 3D mask (B). ∗ (1)

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The size of the mask B array was (3, 3, 3) and it was filled with ones (Figure 6). The result of convolution was forced to be the same size as the original voxel data A. If we examine a filled but isolated voxel that has no values in the neighborhood voxels, 3D convolution gives exactly the same value that the original voxel had. Otherwise the convolution gives a larger value. We subtracted original voxel data A from the convolution result C and saved only those points that belonged in non-zero voxels. Check_matrix = C - A (2) Also this process requires eight shifted voxel arrays to function properly. In this case points within a voxel are deleted if any of the voxel arrays indicates the presence of outliers. The justification is illustrated in Figure 7—again in 2D.

Figure 6. The 3D convolution mask of the size 3 × 3 × 3 was filled with ones.

Figure 7. In the left image, a non-detected outlier cluster is accidently divided among many

examination areas. In the right image, all outliers belong to the one voxel in the shifted system. Both the outlier reduction and the elimination of separate outlier point blocks can be applied with several voxel sizes and thresholds, depending on the data. However, if outlier point clusters are too large, some of them may still remain in the data. Unwanted air points and outliers under the ground can be filtered out if there is a gap between actual data points and outlier point clusters. Removing this kind of outlier cluster can be achieved either by using voxels or bins. If it can be assumed that all outlier clusters are either higher or lower than the real object point clusters, all data can be handled in one bin. In such a bin, all data is distributed in a single column that is vertically divided into several slots. It is relatively easy to find a potential height slot that most probably includes object points by searching for the one with the maximum amount of included points (Figure 8). From the height of that slot it is possible to search for empty height slots between filled slots. Deleting points from all slots after the first zero-slot found will remove outlier clusters. This can be done either upwards, for removing air

1 1 1 1 1 1

1 1 1

1 1 1 1 1 1

1 1 1

1 1 1 1 1 1

1 1 1

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outlier clusters, or downwards, to get rid of underground outlier clusters. If the data covers a large area or if the terrain shape varies a lot, a similar examination can be applied based on voxels, column by column. In our approach, the following algorithms and parameters were applied:

• Voxel filtering with a 0.3 m voxel size and < 9 points per voxel • Voxel filtering with a 1.0 m voxel size and < 26 points per voxel • Removing isolated outlier clusters with a voxel size of 2.0 m • Removing air and underground outlier clusters with the bin slot height of 4 m

Figure 8. An example of a bin that reveals outlier clusters locating under the ground level. The

examination starts from the slot having the maximum amount of points that can thus be assumed to include real object points.

4. RESULTS In the first step, dark intensity points were deleted and voxel-based outlier filtering was applied with a 0.3 m voxel size and with a threshold deleting points from voxels that include less than nine points (Figure 9, left image). The limit was set to this number experimentally. A threshold of less than 10 points in a voxel removed some points from a wall that is highlighted in Figure 9 (right image). The first filtering removed the majority of the outliers, but not all of them. Because the first filtering could not remove all of obvious outliers, the same algorithm was run again with two sets of parameters: a 0.3 m voxel size and < 9 points per voxel, and a 1.0 m voxel size and < 26 points per voxel. The latter filtering parameters were optimized empirically to reduce the majority of remaining outliers. As a result, only the largest outlier clusters remained, as can be seen from Figure 10 (left image). Visual examination reveals that in this case some outlier clusters still remain in the air and some isolated clusters can also be seen elsewhere. Figure 10 (right image) shows the result when isolated point clusters (voxel size: 2.0 m) have also been deleted.

804 60651

1500827 303423 12531 1659

0 0 0 0 0 0 0 0 55 114 258 0

A starting point with the maximum amount of points

Outlier clusters under the ground

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Figure 9. The left image is the result after the outlier filtering with the parameters of a 0.3 m

voxel size and there being less than nine points in a voxel. The right image illustrates how setting the threshold to less than 10 points in a voxel leads to the loss of some wall points (highlighted

with a red circle).

Figure 10. The left image: Outlier filtering with two sets of threshold parameters: 0.3 m / < 9

points and 1.0 m / < 26 points. The right image: Generated using the same filtering parameters as with the left image but isolated outlier clusters have also been removed.

The final result was achieved after adding a bin-based filter of air and underground outlier clusters. In our case, the height of each slot of the bin was 4 m. If the final results (Figure 11) are compared with raw data (Figure 1), the improvement is obvious. In this example, circa 17% of points were removed during the filtering process. Table 2 illustrates the number of removed points after each processing step. In Figure 12 filtered backpack MLS data is compared against Unmanned Aerial Vehicle (UAV) based airborne laser scanning data. The green circle points out a potential outlier cluster that remains after filtering. Closer examination reveals that this outlier block included nine points, whereas the filtering threshold with the 0.3 m voxel case was set to less than nine points. The second filtering round with a larger voxel size had not removed this outlier cluster because it was located too close to the actual object.

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Table 2. The filtering results of each processing step. Processing step Total amount of points Number of deleted points Original data 14,741,628 -

0.3 m voxel size, < 9 points per voxel

12,278,154 2,463,474

1.0 m voxel size, < 26 points per voxel

12,254,802 23,352

Isolated outlier clusters removed

12,251,240 3562

Air and underground outliers removed

12,250,348 892

Some amount of outliers can be seen, for example, close to a tree trunk. However, such small variation could also happen due to orientation changes between data acquisition times. Orientation errors can potentially be corrected with closer analysis and therefore there is no desire to filter too much data. The lowest branches in backpack MLS data are not visible in UAV data. Because these branches include many points, they can be assumed to be real objects. In the final filtering result (Figure 11) there are some isolated point clusters on the side of the data. These points have been the furthest from the scanner and therefore the point density is generally lower. If only backpack MLS data is examined, it is practically impossible to say if these point clusters belong to real objects or if they are just remaining outliers. However, if data is superimposed onto UAV data (Figure 13), it appears that all of these point clusters belong to real objects. This illustrates how combining several data sources is useful in order to understand data, as well as to gain better coverage. Unfortunately, at some point the point density becomes so sparse that distant objects cannot be discriminated from outliers. Such points will be lost during the filtering process. In order to illustrate the performance of the algorithm, two examination areas were selected. The first one included a tree and the other one a built structure. From these areas potential outliers were manually removed. Even if manual interpretation is difficult, the comparison illustrates the differences between the computational method and human interpretation. In the first test area, the result of our algorithm included 325 points that were not left in the manually filtered data set, and there were 1598 points that existed in the manually filtered data and not in the automatically filtered data (Figure 14, left). The total number of points in this sample area was 24,200. Another sample area included 35,783 points. In this case, comparison revealed 67 points from our algorithm that were not found from the manually filtered point cloud and 1201 points that existed in the manually filtered data and not in the automatically filtered data (Figure 14, right). It appears that in the natural environment more true outliers remain than in the built environment. In the case of the tree, the manual filtering was practically not done within the tree structure and therefore the difference to the algorithm-based filtering included many points. In the case of the built-structure, automatic filtering has removed, e.g., large parts of a “ghost” plane (on the top of the structure) having a sparse point density. The reason for such “ghost” plane is that the orientation has slightly changed within backpack data. This structure was not removed in the manual filtering, which explains quite large difference to the algorithm-based filtering.

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Figure 11. The final filtering result visualized from two viewing perspectives. Color coding

represents the time stamp.

Figure 12. A comparison of backpack MLS data against airborne UAV-based data. The blue dots

are from the UAV and the red ones are from the backpack MLS system. The green circle highlights a potential outlier cluster that remains after the outlier filtering.

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Figure 13. Isolated backpack MLS data clusters located at the far side from the trajectory were

plotted against UAV data. UAV data is visualized in blue and backpack data in other colors.

Figure 14. The automatically filtered point cloud is illustrated with blue dots. The red points are included in the automatically filtered data but cannot be found from the manually filtered data.

The orange points, on the other hand, remain in the manually filtered data but not in the automatically filtered data.

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5. DISCUSSION Not all outliers of backpack data can be filtered with one algorithm. In our case, it took four steps to remove obvious outliers and outlier clusters. Voxel-based methods seem to perform well and are highly adjustable to different situations. However, adjusting parameters needs manual work and empirical testing. In the future, one research topic should be how to automatically adjust these parameters according to data. If the adjustment were automatic, our algorithm could be applied as an integrated part of data acquisition. Optimal filtering parameters are dependent on the device and the type of objects. However, according to our experience, the same parameters are usually valid for most cases when data is acquired with the same device and settings. The majority of outliers can be filtered out with our method. Only a small amount of outliers remain and the data is easily interpretable. However, there is a danger in setting parameters too high as then some object points are also filtered. To overcome this problem, the filter should automatically adjust itself according to local conditions. However, this is also left for further research. Our filtering method is not suitable for removing outliers that appear very close to real objects. Taking account of time stamps is essential with backpack MLS data. In that way filtering parameters can be adjusted to concern only a small time period in which orientation errors do not play a significant role. Otherwise it is possible that orientation differences between different data acquisition times are confused with outliers. 6. CONCLUSIONS Our aim was to filter outliers from AkhkaR2 backpack MLS data. We developed a novel method utilizing voxels to complete this task, providing an alternative way to filter outliers using eight voxel elements at each location. Algorithms included the removal of outlier points by the return intensity value, the voxel-based removal of points on sparse data areas, the voxel-based identification of isolated outlier clusters, and the bin-based removal of the air and the underground points. We had to run the voxel-based removal of points twice with the different parameters in order to achieve sufficient results. As a result, we managed to remove the majority of visually identifiable outliers. All obvious air and underground outliers were successfully removed. However, some outliers remained if they were close to real objects. Such outliers may require further processing. Our method can be adjusted to fit various cases depending on the data acquisition parameters used. Unfortunately, setting filtering parameters is not yet an automatic process and it requires some interactive setting. Once the filtering parameters are set, the algorithms can be applied to a large number of files because of the possibility of batch processing. Even if our method was developed for filtering MLS data, it can also be applied to airborne or terrestrial laser scanning data, or even to photogrammetrically derived point clouds. 7. ACKNOWLEDGEMENTS The authors would like to thank Academy of Finland for financial support through projects “Centre of Excellence in Laser Scanning Research (project decision number 272195)”, “Interaction of Lidar/Radar Beams with Forests using Mini-UAV and Mobile Forest

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Tomography” (259348), “Strategic Research Council project COMBAT” (No. 293389), Tekes projects "Healthy Building", and "EUE", European Union, the European Regional Development Fund, "Leverage from the EU 2014-2020" projects "AKAI" (301130) and "Soludus" (301192), and the Aalto Energy Efficiency Research Programme ("Light Energy-Efficient and Safe Traffic Environments"). 8. REFERENCES Chen, G., Kua, J., Shum, S., Naikal, N., Carlberg, M., Zakhor, A., 2010. Indoor Localization Algorithms for a Human-Operated Backpack System. In Proceedings of the 3D Data Processing, Visualization, and Transmission, Paris, France, 17–20 May 2010, 8 pages. Guskov, I., Wood, Z., 2001. Topological noise removal. In Proceedings on Graphics Interface, pp. 19–26. Jaakkola, A., Hyyppä, J., Hyyppä, H., Kukko, A., 2008. Retrieval Algorithms for Road Surface Modelling Using Laser-Based Mobile Mapping. Sensors, 8(9), pp. 5238–5249. doi:10.3390/s8095238 Kukko, A, Kaartinen, H., Hyyppä J., Chen, Y., 2012. Multiplatform Mobile Laser Scanning: Usability and Performance. Sensors, 12 (9), pp. 11712–11733. Kukko, A., 2013. Mobile Laser Scanning – System development, performance and applications. Publications of the Finnish Geodetic Institute 153, 247 pages. LAStools. https://www.cs.unc.edu/~isenburg/lastools/download/lasnoise_README.txt. [Visited on 25 August] Lee, A., Sweldens, W., Schröder, P., Cowsar, L., Dobkin, D., 1998. Maps: Multiresolution adaptive parameterization of surfaces. In Proceedings of SIGGRAPH 98, pp. 95–104. Lehtola, V. V., Virtanen, J.-P., Kukko, A., Kaartinen, H., Hyyppä, H., 2015. Localization of mobile laser scanner using classical mechanics. ISPRS Journal of Photogrammetry and Remote Sensing, 99, pp. 25–29. Liang, X., Kukko, A., Kaartinen, H., Hyyppä, J., Yu, X., Jaakkola, A., Wang, Y., 2014. Possibilities of a personal laser scanning system for forest mapping and ecosystem services, Sensors 14(1), pp. 1228–1248. Lichti, D., 2010. Terrestrial laser scanner self-calibration: Correlation sources and their mitigation. ISPRS Journal of Photogrammetry and Remote Sensing, 65(1), pp. 93–102. Papadimitriou, S., Kitagawa, H., Gibbons, P.B., Faloutsos, C., 2003. Loci: fast outlier detection using the local correlation integral. In Proceedings of 19th International Conference on Data Engineering, pp. 315–326. Pauly, M., Gross, M., 2001. Spectral processing of point-sampled geometry. In Computer Graphics SIGGRAPH 2001 Proceedings, pp. 379–386.

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Polo, M., Felicisimo, A., Villanueva, A., Martinez-del-Pozo, J., 2012. Estimating the uncertainty of Terrestrial Laser Scanner measurements. IEEE Transactions on Geoscience and Remote Sensing, 50, pp. 4804–4808. Smigiel, E., Alby, E., Grussenmeyer, P., 2008. Terrestrial Laser Scanner Data Denoising by Range Image Processing for Small-Sized Objects. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 37(B5), pp. 445–450. Talaya, J., Alamus, R., Bosch, E., Serra, A., Kornus, W., Baron, A., 2004. Integration of a terrestrial laser scanner with GPS/IMU orientation sensors. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 35 (Part B7), pp. 990–995. TerraScan. TerraScan User’s Guide, 566 pages. https://www.terrasolid.com/download/tscan.pdf. [visited on 25 August] Vastaranta, M., Melkas, T., Holopainen, M., Kaartinen, H., Hyyppä, J., Hyyppä, H., 2008. Comparison of different Laser-based methods to measure stem diameter, In Proceedings of SilviLaser 2008, 17–19 September, Edinburgh, UK, 10 pages.