Detecting Terrain Stoniness From Airborne Laser Scanning Data † †
"> Figure 1
<p>The process flow, methods covered in this paper are highlighted. Data formats: (1) 2 m raster; (2) point cloud; (3) task-specific TIN model; (4) curvature value sets; (5) sample vectors. LLC can optionally use either original point cloud (2) or vertex points (3) produced by SAF TIN model. Wall-to-wall classification is a possibility provided by the resulting binary classifier.</p> "> Figure 2
<p><b>Upper left</b>: The site near Kemijärvi Finland. The research area covered by 120 open data <span class="html-italic">.las</span> files covering 1080 km<math display="inline"> <semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics> </math>. <b>Upper right</b>: the relative location of sample polygons. Amount of sample sets in parenthesis. <b>Lower left</b>: A view of a sample site in boreal forest. <b>Lower right</b>: approximately the same view as at lower left after solid angle filtering (see <a href="#sec2dot4-remotesensing-08-00720" class="html-sec">Section 2.4</a>) of the point cloud. The stone formation has been circled. Location is at UTM map T5212C3, polygon 11240.</p> "> Figure 3
<p>A stony (upper row) and a non-stony (lower row) sample polygon. Original polygons are approximated by <math display="inline"> <semantics> <mrow> <mn>10</mn> <mspace width="0.166667em"/> <mtext>m</mtext> <mo>×</mo> <mn>10</mn> <mspace width="0.166667em"/> <mtext>m</mtext> </mrow> </semantics> </math> batches. The ground height (DEM 2 m) and its Laplace discrete operator signals with 2 m and 4 m radius are depicted. The border noise has been removed from actual analysis. The 100 m scale is aligned to North.</p> "> Figure 4
<p>The solid angle distribution of positive and negative samples among the <span class="html-italic">data2015</span> data set. Averages can be distinguished well but variation among samples is high.</p> "> Figure 5
<p>Approximative properties of <span class="html-italic">data2015</span> data set. Similar qualities of <span class="html-italic">data2014</span> are not available. <b>Left</b>: The number of stones at a spatial partition when the partitioning range (the grid size <span class="html-italic">δ</span>) changes. A sensible approximation of e.g., local ground inclination is possible only when there are at least 3 points per grid square. <b>Right</b>: The difference between positive and negative samples is mainly in stone size distribution. The practical detection limit in size is approx. 1.0 m.</p> "> Figure 6
<p><b>Left</b>: The Laplace difference operator returns the height difference between the center point (1) and the average of points A. The modified Laplace difference operator does the same but using points B. These two kernels define each an average circumferential height difference <math display="inline"> <semantics> <mover accent="true"> <mi>Z</mi> <mo>¯</mo> </mover> </semantics> </math>. <b>Right</b>: The geometric relation between <math display="inline"> <semantics> <mover accent="true"> <mi>Z</mi> <mo>¯</mo> </mover> </semantics> </math> and approximate mean curvature <math display="inline"> <semantics> <msub> <mi>κ</mi> <mi>H</mi> </msub> </semantics> </math>. Horizontal line represents average ground level at the circumference.</p> "> Figure 7
<p>Curvature distributions produced by each method. <b>Upper left</b>: LLC and grid size 2m. <b>Upper right</b>: LLC and grid size 4 m. Larger grid size results in narrow band around <math display="inline"> <semantics> <mrow> <mi>κ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics> </math>. <b>Lower left</b>: DEM curvatures are characterized by kurtosis. <b>Lower right</b>: the LTC distribution.</p> "> Figure 8
<p><b>Left</b>: The local height from DEM files, <math display="inline"> <semantics> <mrow> <mn>30</mn> <mspace width="0.166667em"/> <mtext>km</mtext> <mo>×</mo> <mn>36</mn> <mspace width="0.166667em"/> <mtext>km</mtext> </mrow> </semantics> </math> area depicted. The scale is oriented northwards. The general location of the rectangle can be seen in upper left part of the <a href="#remotesensing-08-00720-f002" class="html-fig">Figure 2</a>. <b>Right</b>: Stoniness probability by DEC method. The scale is probabilty of having stones on a particular pixel. Roads and waterways are classified as stony areas. LLC and LTC methods are much less sensitive to roads and constructed details.</p> "> Figure 9
<p>Solid angle filtering. (<b>A</b>) The set of adjoining triangles <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>k</mi> </msub> </semantics> </math> of a point <math display="inline"> <semantics> <msub> <mi>p</mi> <mi>k</mi> </msub> </semantics> </math> seen from above; (<b>B</b>) A compartment <math display="inline"> <semantics> <mrow> <mi>i</mi> <mi>j</mi> <mi>l</mi> </mrow> </semantics> </math> of the vertex point <math display="inline"> <semantics> <msub> <mi>p</mi> <mi>k</mi> </msub> </semantics> </math> presented in detail. A solid angle <math display="inline"> <semantics> <msub> <mo>Ω</mo> <mi>k</mi> </msub> </semantics> </math> is a sum of compartment angles <math display="inline"> <semantics> <msub> <mi>ω</mi> <mrow> <mi>i</mi> <mi>l</mi> <mi>j</mi> </mrow> </msub> </semantics> </math> of Equation (A2). Point <math display="inline"> <semantics> <msub> <mi>p</mi> <mi>l</mi> </msub> </semantics> </math> is an arbitrary point directly below the vertex point <math display="inline"> <semantics> <msub> <mi>p</mi> <mi>k</mi> </msub> </semantics> </math>.</p> "> Figure 10
<p><b>Left</b>: An individual local plane <math display="inline"> <semantics> <mrow> <mi mathvariant="script">P</mi> <mo>(</mo> <msub> <mi>p</mi> <mi>k</mi> </msub> <mo>,</mo> <msub> <mi mathvariant="bold">n</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> </semantics> </math> at grid point <math display="inline"> <semantics> <msub> <mi>c</mi> <mi>k</mi> </msub> </semantics> </math> and its parameters (local plane center point <math display="inline"> <semantics> <msub> <mi>p</mi> <mi>k</mi> </msub> </semantics> </math> and normal <math display="inline"> <semantics> <msub> <mi mathvariant="bold">n</mi> <mi>k</mi> </msub> </semantics> </math>). A triangulation <span class="html-italic">T</span> of the grid avoids squares with incomplete data. A local cloud point set <math display="inline"> <semantics> <msub> <mi>Q</mi> <msub> <mi>c</mi> <mi>k</mi> </msub> </msub> </semantics> </math> and neighboring triangles <math display="inline"> <semantics> <mrow> <msub> <mi>T</mi> <mi>k</mi> </msub> <mo>⊂</mo> <mi>T</mi> </mrow> </semantics> </math> of a grid slot <math display="inline"> <semantics> <msub> <mi>c</mi> <mi>k</mi> </msub> </semantics> </math> are also depicted. <b>Center</b>: a stone revealed by two adjacent tilted planes. This stone provides a signal with the grid size <math display="inline"> <semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics> </math> m. Note the amount of missing planes due to a lack of cloud points. <b>Right</b>: The grid of size <math display="inline"> <semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics> </math> m at the same spot. The stone does not appear, local variation has disappeared but the grid is almost full approximating the sample polygon shape.</p> ">
Abstract
:1. Introduction
Current Research
- local height difference, see Laplace filtering Section 2.7. This feature was chosen as the baseline method since it is a typical and straightforward GIS technique for a problem like stoniness detection.
- various roughness measures, e.g., rugosity (related trigonometrically to the average slope), local curvature, standard deviation of slope, standard deviation of curvature, mount leveling metric (opposite to a pit fill metric mentioned in [19]).
- multiscale curvature presented in [28]. It is used for dividing the point cloud to ground and non-ground returns, but could be modified to bring both texture information and curvature distribution information. The latter could then be used for the stoninesss prediction like in this study. The methods, possibly excluding interpolation based on TIN, seem to be numerically more costly than our approach.
- surface fitting methods: a parametric surface is fitted to data. Our local linear fit LLC falls on this category, yet does not necessarily require triangularization as a preliminary step.
- total curvature methods: curvature approximant is derived as a function of location. Our local triangular curvature LTC is of this category of methods.
- curve fitting methods.
2. Materials and Methods
2.1. Study Area
2.2. Materials
- All hummocky landforms (i.e., hills) with a convex topographic form were delineated from the ALS derived digital elevation model and its tilt derivative with an Object-Based Image Analysis algorithm developed in eCognition software, see [1]. This step produced data2014 and data2015 polygon sets ( see Table 1 and Figure 2).
- A space partitioning grid was used to cut both the point cloud (ALS) and DEM to polygon samples.
- Point cloud was cut to 2 m height from initial approximate ground level. The mode of heights in partitions was used as the ground level.
2.3. Materials online
2.4. Solid Angle Filtering (SAF)
2.5. Curvature Estimation Based on Local Linear Fit (LLC)
- a space partitioning approach is used instead of a radial kernel function to select the participant points. This is because ground surface can be conveniently space partitioned horizontally unlike in [39], where the point cloud can have all kinds of surface orientations.
- the point set is not from constructed environment. Canopy returns create a 3D point cloud, thus the loss function cannot be symmetrical, but must penalize points below the approximate local ground plane.
2.6. Local Curvature Based on Ground Triangularization (LTC)
2.7. Curvature Based on Filtering DEM by a Modified Discrete Laplace Operator (DEC)
2.8. Vectorization
2.9. Logistic Regression
- to perform a leave-pair-out (L2O) test over all possible positive-negative label pairs P, and
- to measure L2O area under curve by using the Heaviside function for summation.
2.10. Method Parameters and Design Choices
2.11. General Wall-to-Wall Prediction
3. Results
- Local linear fitting (LLC) divides the polygon into 6 different grids. Each grid square is fit by a plane approximating the local ground height of the center of the plane and the plane orientation. Curvatures are computed from these center points and their orientation normals.
- Curvature from DEM (DEC) uses traditional DEM data. Curvatures are approximated by the observed local height difference delivered by a modified discrete Laplace operator.
- Curvature by local triangulation (LTC) has a TIN computed by SAF method of Section 2.4. The curvature is then computed triangle by triangle as in LLC.
4. Discussion
5. Conclusions and Future Research
- Extending the analysis to more dense forests, where stoniness detection occurs only at benevolent cicumstances (forest openings, sparse canopy, hilltops). In this environment the acquired stoniness signal has to be combined to a wide array of open data features to extend prediction to unobservable areas. The corresponding field campaigns will be more elaborate.
- Taking into account the stone coverage and size distribution. It is likely that a multi-grid method like LLC might perform well in this prediction task (given suitable teaching data), whereas DEC may be restricted by the general purpose nature of DEM and its modest grid size.
- Topography and vegetation classification of marshlands. Marshlands have similar high ground return ratio as the current case site. SAF can be tuned by cross-validation to produce a tailored TIN and an improved LTC method with added curvature properties (mean curvature, curvature eigenvectors) could detect various micro-topographic marshland features. It is our assumption that the histogram approach would work also with marshland classification, given a suitable teaching polygon quality produced in field campaigns.
- Using min-cut based segmentation of k-NNG graph of ALS data as described in [15] instead of simple Delaunay triangulation. One has to modify the algorithm to include neighborhood voting to reduce noise. This could be a fruitful approach, since it could suit to 3D analysis of forest tree species, providing more motivation for the implementation.
- Utilizing all relevant LiDAR attribute fields, like return intensity, return number, the scan angle etc. (see [21]).
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
ALS | Aerial laser scan |
AUC | area under curve |
DDG | Discrete differential geometry |
DEC | Curvature based on DEM |
DEM | Digital elevation model |
DTM | Digital terrain model |
GIS | Geographic information system |
k-NNG | k-nearest neihgbors graph |
K-S | Kolmorogov-Smirnov test |
L2O | Leave-pair-out |
LiDAR | Light detection and ranging |
LLC | curvature based on local linear fit |
LTC | local curvature based on ground triangulation |
MDL | Minimum description length principle |
MTLS | Moving total least squares |
NLS | National Land Survey of Finland |
PCA | principal components analysis |
SAF | Solid angle filtering |
TIN | triangulated irregular network |
UAV | Ultra-light vehicle |
Appendix A
Appendix B
- (a)
- raw 3D ALS data
- (b)
- same as (a) with tree and foliage returns cut from approx. 2 m height from approximative ground level
- (c)
- TIN model produced e.g., by solid angle filtering of Section 2.4
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Data Set | Stony Samples | Area km | Non-Stony Samples | Area km | Acquisition |
---|---|---|---|---|---|
data2014 | 56 | 1.7 | 49 | 1.7 | cumulated observations |
data2015 | 471 | 4.7 | 204 | 6.0 | field campaign |
Grid Version | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
Grid constant | 1.25 | 2.0 | 3.0 | 4.0 | 5.0 | 6.0 |
Method | Positive Half of the Bin Values |
---|---|
LLC and DEM | 0.010, 0.030, 0.060, 0.13, 0.25, 0.50, 1.0, 2.0 |
LTC | 0.031, 0.12, 0.25, 0.44 ,0.71, 1.13, 1.8 |
Method | Parameters | Binary Choices |
---|---|---|
SAF | 2 | 0 |
LLC | 3–15 | 63 |
LTC | 0 | 1 |
DEC | 2 | 1 |
Data Set | DEC | LLC | LTC |
---|---|---|---|
data2014 | 0.85 | 0.82 | 0.79 |
data2015 | 0.68 | 0.77 | 0.66 |
Analysis Speed | DEC | LLC | LTC |
---|---|---|---|
200 | 0.5 | 4.0 |
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Nevalainen, P.; Middleton, M.; Sutinen, R.; Heikkonen, J.; Pahikkala, T. Detecting Terrain Stoniness From Airborne Laser Scanning Data †. Remote Sens. 2016, 8, 720. https://doi.org/10.3390/rs8090720
Nevalainen P, Middleton M, Sutinen R, Heikkonen J, Pahikkala T. Detecting Terrain Stoniness From Airborne Laser Scanning Data †. Remote Sensing. 2016; 8(9):720. https://doi.org/10.3390/rs8090720
Chicago/Turabian StyleNevalainen, Paavo, Maarit Middleton, Raimo Sutinen, Jukka Heikkonen, and Tapio Pahikkala. 2016. "Detecting Terrain Stoniness From Airborne Laser Scanning Data †" Remote Sensing 8, no. 9: 720. https://doi.org/10.3390/rs8090720