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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Light Detection and Ranging (LiDAR) technology can be a valuable tool for describing and quantifying vegetation structure. However, because of their size, extraction of leaf geometries remains complicated. In this study, the intensity data produced by the Terrestrial Laser System (TLS) FARO LS880 is corrected for the distance effect and its relationship with the angle of incidence between the laser beam and the surface of the leaf of a Conference Pear tree (

Generally, the canopy represents the interface where most of the fundamental interactions between vegetation and atmosphere take place [

An important index to describe vegetation structure is the Leaf Area Index (LAI) which is used in any flux transfer study as gases exchange e.g., CO_{2} [

Leaf inclination (elevation, roll and azimuth) affects the photosynthesis process in two ways: (i) it provides a mechanism for the plant to achieve favorable photosynthetic rates at specific times during the day, and (ii) it limits the impact of high incidence photon irradiance unfavorable for photosynthesis [

Several innovative remote sensing methods attempted to describe vegetation structure parameters such as LAI or LAD in a fast, repeatable and accurate way. The use of photographs [

However, to get an accurate and precise description of the geometry of a small object as eg. a leaf, the number and density of the point cloud is determinant. In the case of scanned foliage, the scan quality could decrease because of:

The shadow effect. The leaves on the TLS field of view foreground hide leaves on the background. Those are either partially scanned or not scanned at all [

The wind which may move the branches and the leaves during the scan process and decrease the quality of the scan.

The leaves reflectance, the geometric calibration of the TLS, the foliage distance and the TLS beam angle of incidence with the leave surface [

The fact that lasers are spherical range finders. That means that the distance between two points on a flat surface will increase with the distance to the beam aperture [

The light ambiance for large distance [

The ratios between the TLS beam footprint and the size of the scanned object, e.g., leaves [

In conclusion, the point density for the foliage could be too sparse to provide detailed information to derive leaf inclination and other geometric information such as area, shape or inclination. Traditionally, leaf inclination is directly determined with a protractor [

The TLS FARO LS880 is used in this study. The rotation of a mirror placed at 45° to the laser beam aperture (horizontal rotation) and the rotation of its trunnion (vertical rotation) provide a panoramic view of the scene that is surrounding the TLS as a 3D point cloud in a Cartesian or in a spherical basis. The scans are proceeded with an angular resolution of 0.018° for both azimuthal and elevation rotation. This device uses the AM-CW technology: the amplitude of the laser is modulated and an analysis of the frequencies of the backscattered signal provides the distance. Between the mirror and the photodiode of the scanner, optical elements (e.g., filters) reduce the intensity for small distances to avoid overexposure of the sensor. Therefore, the relationship between the intensity and distance follows neither the inverse square power law nor any linear function. In addition, the electric-converted signal passes through a logarithmic amplifier that provides a logarithmic relationship between different reflectance [

Theoretically, the photometric appearance of an object depends on surface geometry, material properties, illumination and viewing direction of the camera (_{T}) and the received power (P_{R}) is highly dependent on angle of incidence, on distance and on material reflectance properties [_{R} the receiver aperture area, η the receiver’s efficiency, ω the angle of incidence with the material, ρ(ω) the reflectance value in function the angle of incidence between the TLS beam and the material surface (constant in the case of Lambertian material) and d the distance between the TLS beam aperture and the scanned object. As the TLS FARO LS880 has an intensity filter and with the assumption that this filter has only an impact on the intensity variations due to distance, the inverse square law could be replaced by a device specific distance function f. Finally, the intensity is modified by a logarithmic converter. The received power could be expressed as follows:
_{1}), (b_{2}) and (b_{3}) are its variable terms. Expressed through a logarithmic function, the nature of the intensity, distance and angular dependencies changes:

- there is a vertical translation of the graphs representing the received power and distance relationship at a fixed angle of incidence appears and this, for two different material reflectances (b_{1} and b_{3}). This is due to the logarithmic product-to-sum reduction.

- With the same reasoning, the received power and angle of incidence relationship has the same shape through distance (b_{2} and b_{3}).

In [

As the objects of our study are leaves, the diameter of the TLS beam footprint is an important parameter. A flat surface with an angle of incidence of ω, which has its center at a distance d from the TLS beam aperture and with a TLS beam radius of r and a divergence of δ, one gets the footprint major axis:

According to the manufacturer, ambient light (e.g., sun) has little impact on the intensity. It does not fade out the signal and the intensity data are similar for scanned scene with different ambient light. However, there is more noise in the point cloud with increasing distance and sometimes even no data at all, especially for low intensity. The FARO LS880 has been designed to be insensitive to solar irradiance, at least for ranges smaller than 10 m and/or for surfaces with medium to high reflectance.

As discussed in Section 2.1.2., the relationship graph between the intensity as the received power and the distance follows the property of a vertical translation for different material reflectances (

In [

Ten leaves were randomly picked from 30 2-year old Conference pear trees on June 16th 2010. Those trees are planted in two rows of 15 trees in an East-West direction with a distance of 30 cm between the trees and 360 cm between the rows. They are located in Heverlee, Belgium (50°51′33.89″N, 4°40′48.45″E). Since the leaves are curled [

In a second experiment, from each of the 15 pear trees of the first row (

In this case, ghost points as wrinkles and curvatures are also selected. Then, the differences (Δω) between the angle of incidence found by this LSR and the angle of incidence provided by the intensity for each hit of the TLS beam are mapped for each of those seven leaves:
_{I}(x), the angle of incidence computed with the intensity and angle of incidence relationship at a point x on the scanned leaf and ω_{LSR} the angle of incidence provided by the LSR on the entire leaf. The distributions (with normalized quantities) of those Δω values are shown. The difference between the angle of incidence provided by the LSR and the one deduced by the average of the corrected intensity on the leaf is calculated.

First, a manual sub-selection of the point cloud and their corresponding intensity is made. A second sub-selection is made based on an intensity and distance threshold [

A first study is made to establish the relationship between the intensity and the distance with the set up described in Section 2.2.1. In [_{99%}).

Once done, a constant value c for a target material at a given ω is determined by the difference between its intensity value and the intensity value of the 99%-Spectralon® at a fixed reference distance d_{ref}. One has c_{ref} = f_{99%}(d_{ref}) − I (d_{ref}) with I (d_{ref}) the recorded intensity at an arbitrary reference distance. For each intensity I (d) for this same target at a distance d, the calibrated intensity, I_{c} (which is now independent of distance) is calculated as:

To know the quality of the distance correction, a Root Mean Square Error (RMSE) between the value of the piecewise polynomial interpolation f_{99%} and the corrected intensity is calculated for each distance. Finally, as the value f(d_{ref}) is unknown, the distance effect on the intensity is corrected with the following formula [_{99%} (d) − I (d).

Further investigation on the intensity correction, reflectance relationship and radiometric calibration could be done. In [

To obtain the angle of incidence with a surface (flat by assumption) represented by a selection from the point cloud, a Least Square Regression (LSR) is proceed on the sub-selection (_{i} to the fitted plane. Finally, the normal angle to the plane is given by the coefficient of the plane equation. The angle of incidence ω with the surface equals:

The accuracy and precision of this method is tested with the goniometric platform with increments of 10° of its azimuthal and elevation angles. As statistical indicators, the r^{2}, slope and intercept of a linear regression of the angle determined by the LSR and the goniometric platform angle are given. The targeted platform is placed at approximately 2.05 m from the TLS beam aperture. Knowing the angle of incidence provided by the LSR, it can finally be related to the intensity averaged over the cloud of points selected (

As in [

_{ref}) is 3.56 m and f_{99%}(d_{ref}) = 1781.45 intensity units. The LS880 logarithm filter effect is clear as can show relationships between the various reflectances measurements. The distance effect correction with the piecewise polynomial is valuable for a distance larger than 1 m, especially for materials with a reflectance larger than 48%, while the 22%-reflectance Canson^{®} paper yields results of inferior quality. This result is analogous to the FARO LS HE80 used in [^{®} and paint) have the worth quality and the graph shows unexpected differences in terms of reflectance that have not been detected by the spectroradiometer. Similarly, the difference between the 80% and the 83% Canson^{®} papers is not clear. The logarithmic correction suggested in [

The RMSE between the translated 99%-spectralon piecewise polynomial interpolation used as reference at a distance of 3.56 m (

The angle of incidence provided by the LSR provides acceptable results with the goniometric platform. The regression of the correlation graph between the angle of incidence calculated manually and the one given by the LSR provides an r^{2} of 1, a slope of 1 for both horizontal and vertical rotation and an intercept of 1° for vertical and 2.8° for horizontal rotation.

The angles of incidence provided by the LSR approximate the ones given by the protractors of the goniometric platform.

No clear difference appears between the azimuthal rotation of the goniometric platform and the elevation rotation. Given with a resolution of 5°, the curve of relationship between the corrected intensity and angle of incidence for the two different rotations are similar and the maximal absolute difference for the intensity is 20 units (corrected intensity) for an angle of incidence of 10°. This is negligible compared to the intensity variation as a function of angle of incidence. We get similar results in the comparison of the abaxial and adaxial sides of the leaves where the maximal absolute intensity difference 38 units (corrected intensity) for an angle of incidence of 10°, which is also negligible. Because of those two results, both cases are not taken into account in this study (graphs not shown).

Because of the size of the beam diameter and divergence, its footprint diameter could become larger than the leaf itself. It ranges from 0.046 m for an angle of incidence of 85° to 0.004 m for an angle of incidence of 0°.

At this distance, the TLS beam footprint diameter is 20% of the leaf width for an angle of incidence smaller than 20°, it is 45% of the leaf width for an angle of incidence greater than 65° and it exceeds the leaf width for an angle of incidence greater than 80°. Though the type of the laser sensor is unknown, the weight of the goniometric platform intensity could be lower than suggested in

In conclusion, retrieving the angle of incidence with the intensity would have a precision of ±5° and because of the diameter of the TLS beam footprint, it is not possible to measure the angle of incidence with the intensity for angle larger than 55–60°.

At a first sight, a logarithmic or cosine fitting could be made as it is insinuated in _{1} and b_{2}). The intensity and angle of incidence relationship can be expressed as:

As one can see, three functions appear:

- the logarithmic function that has not been corrected,

- a cosine function, and

- the reflectance value as a function of angle of incidence with the leaf surface ρ(ω).

As the optical properties of the leaves are unknown (they are not Lambertian [

The test shows a vertical and positive translation in the intensity values for angles smaller than 60° (

As in the previous experiment, the intensity increases with an angle of incidence decrease, but the measured intensity values are higher. It could be interpreted in two ways: (i) it is higher in terms of intensity and is vertically translated to +50 units (corrected intensity) or (ii) it is larger in terms of angle of incidence and is horizontally translated to +10°.

In addition, the precision to find an angle of incidence from the corrected intensity for angles of incidence smaller than 60° is larger than in the previous experiment: (i) ±10° for angles of incidence smaller than 30° and (ii) ±15° for angles of incidence ranging from 60° to 30°.

Many reasons could occur to explain those two facts:

if a leaf that is perpendicular to the beam is selected and if this selection includes a sub-selection which forms a plane which is almost parallel to the beam, then, the LSR on this selection will provide an angle of incidence larger than expected and with a higher intensity (depending on the quantity of undesired points that are selected). That would be the reason why

With a similar reasoning, the selection of a leaf including a zone which has a large angle of incidence with the TLS beam and a curved zone could present a smaller angle of incidence than expected.

Some of the assumptions of the previous section are confirmed by these measurements:

At the opposite, the average intensity for leaves n° 6 and 7 is translated to respectively −10° and −8°. For leaf n° 6 it could be explained by the case i.a) of the Section 3.3.2. as the side of the leaf forms a large angle of incidence with the beam. This provides a larger angle of incidence [

In this study, Conference pear tree leaves are scanned and the intensity data provided by the TLS is analyzed with a particular focus on its properties for describing geometry of leaves. Prior to that, the intensity is corrected for the distance effect and the angle of incidence provided by the LSR is tested on the goniometric platform. Then the relationship between the corrected intensity and the angle of incidence is determined with flattened leaves placed on a goniometric platform. Next, this relationship is tested on flat part of the leaves that are still attached to the pear trees. Finally, the angle of incidence is determined using a LSR on an entire leaf, and this notwithstanding leaf curvatures and wrinkles. The Δω (see

- for the goniometric platform only,

- for flattened leaves placed on the goniometric platform,

- for some parts of the leaves that are fixed on the tree,

- for entire leaves that are fixed on the tree.

It appears that the flattened leaves on goniometric platform provide a good precision (±5°) but maybe a poor accuracy in terms of finding the angle of incidence with the intensity and because of the incomplete radiometric calibration of the TLS intensity. In the case where this radiometric calibration is sufficient, the test made on the partial selection of leaves on the tree would provide a more accurate result (+50 units of corrected intensity). Still, this last test brings a lower precision in the definition of the relationship (from ±10° to ±15° depending on the angle of incidence). This shift in the accuracy could be explained either by:

- the LSR conditions (a low RMSE with a limited number of points that are away of the LSR plane) and the leaf curvatures and its wrinkles,

- the impact of the footprint diameter of the TLS beam,

- the physiological state of the plant, the radiometric calibration of the TLS or even a multiple scattering occurring in the canopy.

In the last test, it is clear that wrinkles and undulations are playing a large role in the precision. It is also shown that angles of incidence larger than 60° with pear tree leaves will provide bad results in term of accuracy and precision. Even the measurement on the goniometric platform could not provide better information because of the 3%-reflectance painting surrounding the leaves and so in the mixing of their intensity in the point cloud. As previously seen, scanning larger leaves could reduce this angle of incidence limit. In addition, if the second experiment shows a consistency in the distance correction, it appears that distance plays a great role in the capacity to extract a good point cloud and this to make a LSR with enough points. That probably depends on leaf size, and one might expect that the measurements should be extended to a wider range and with larger leaves. In general, distance, angle of incidence and leaves dimensions should be taken into account for the set-ups of scanning that aim at extracting leaf geometry. The measurement set-ups suggested in [

In addition, it would be also recommended to test the relationship between intensity and angle of incidence for trees with flat leaves to study the multi scattering effect and/or to change the conditions of selection for the LSR set in point 2.3.2. In the future, a complete radiometric calibration should be set to guaranty the consistency of accuracy of the relationship.

Notwithstanding the aforementioned issues, different potential uses for the intensity can be envisaged. First, the third experiment emphasized the fact that intensity could help in determining the points having a higher probability to be a ghost point:

- The points with a low intensity have a higher probability to be ghost points because they are on the part of the leaves having a large angle of incidence. Those points could be directly deleted or corrected.

- In the case where points with a low intensity constitute a large zone on the leaf, it is more difficult to determine whether they are ghost points or not. This zone appears larger than in the reality. In conclusion, closer is the point to the leaf border, higher is the probability that this one is a ghost point. In those cases, the points should be only corrected as their deletion would diminish the size of the leaf.

Those two points could be used to eliminate ghost point and view as an improvement of the pre-processing methods for point cloud (as e.g., [

Alternatively, using the difference between the angle of incidence provided by the LSR and comparing it to the incidence angle provided by the intensity for each point of the selected leaves (Δω) would give an estimation of the curving and the wrinkling of the leaves and this thanks to the Δω distribution. This could be used as a wrinkle indicator as the amplitude of those ones might be not large enough compared to the distance precision of the TLS. Finally, a promising future in the use of the intensity is given by its use as representing the normal of the surface of leaves.

Finally, new opportunities exist to use the intensity to detect physiological aspects of the leaf such as the chlorophyll content with a LEICA ScanStation2 (532 nm) [

We have investigated the properties of intensity in relation to distance and angle of incidence with leaf surfaces. The distance effect on intensity has been corrected to set a constituent relationship between the intensity and the angle of incidence. The variation of the intensity through angle of incidence seems to be a good indicator to help in the extraction of leaves geometries from TLS point cloud.

Results show that one can expect a precision of ±5° to derive the angle of incidence from intensity data in the case of flat leaves. The results with curved leaves have clearly shown that the curvatures and the wrinkles are the reason for the degradation of the precision in the relation between the intensity and the angle of incidence. Therefore, we could expect to use the intensity to determine angle of incidence with a precision of ±5°.

Two general applications are emphasized in this study:

- Knowing the size, orientation and distance of the leaves, the scanning set-up can be improved for intensity and point cloud quality.

- Intensity could help eliminating/correcting the ghost points, it may help to derive the surface of the leaves and it could be translate to an indicator (Δω distribution) helping to know the geometry of the leaves (wrinkles, curves).

Finally, the corrected intensity could be used to reduce the impact on the point cloud of the factors (i)–(vi) of the introduction.

We thank FARO, Stuttgart, Germany for their useful technical information on the FARO LS 880. Thanks also to Jo Janssen for his help in developing C #. Funding support for this project has been provided by FWO Flanders (G.0392.09N) and the Hyperforest project (SR/00/134).

The goniometric platform with its (

Part of a hemispherical projection of a TLS scan of 15 two years old pear trees (first row). The corrected intensity and angle of incidence relationship is tested on leaves of those trees. Trees are grouped by their distance to the beam aperture (red frames).

Analysis flowchart: (I) A semi-automatic and manual selection in the point cloud is proceeded. It takes into account a distance and an intensity threshold to limit unwanted point as ghost point or leaf curvature. (II) The average distance and average intensity are calculated from the selected point cloud. Their relationship is used to correct the distance effect by replacing the intensity value by a reference value (correction of the distance effect on the intensity). (III) The angle of incidence with the selected surface is calculated thanks to a LSR. (IV) The corrected intensities values of the selected points are averaged. The angle of incidence is then related to this averaged corrected intensity.

Intensity and distance relationship for the FARO LS880 for different materials placed perpendicularly to the laser beam.

Correction of the distance effect on the intensity. The correction is valuable for distance greater than 1 m. The reference distance is 3.56 m.

Corrected intensity and angle of incidence relationship for pear tree leaves placed on the goniometric platform. (•) is the average intensity of the selected point cloud representing the leaf. A fourth degree polynomial fitting is made to model this relationship (bold line). The angles of incidence is found by the LSR on the selected point cloud.

TLS beam footprint diameter as a function of angle of incidence and distance. This beam footprint diameter is compared to the average leaf widths and lengths.

Test of relationship between intensity and angle of incidence for leaves of

Feature provided by the TLS FARO LS 880 constructor.

Continuous wave phase shift | |

| |

320° × 360° | |

785 nm (Near Infra-Red) | |

3 mm, circular | |

0.014° | |

3 mrad | |

0.018° | |

0.6 m–76 m | |

±3 mm at 25 m | |

| |

| |

0.7/2.6 mm | |

1.3/5.2 mm |

(i) Vertical translation (average on the distance) between the intensity value of the 99%-Spectralon® and the intensity value of other materials, (iii) Raw value at the reference distance (3.56 m), (iv) RMSE between the interpolation function f_{99%} of the 99%-Spectralon® intensity (minus a constant, at the reference distance) and the measured intensity for distance larger than 1 m. Raw values range between 0 and 2047.

| ||||
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30.24 | 3.90 | 1749 | 2.98 | |

27.84 | 4.88 | 1750 | 2.50 | |

79.07 | 5.76 | 1705 | 1.60 | |

169.55 | 5.36 | 1619 | 3.66 | |

399.30 | 29.87 | 1408 | 11.49 | |

884.93 | 49.66 | 839 | 21.52 | |

961.55 | 34.09 | 935 | 11.49 |

Distances of the point cloud sub-selections for each of the 15 trees and their number of sub-selections that have been made for the LSR plane fitting. The increase of the distance increases the difficulty to make a correct LSR (no extraction is possible for tree n°15). Trees are grouped by their distances to the beam aperture (>1 m).

| |||
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1–5 | 2.92 | 4.30 | 26 |

6 | 2.43 | 3.22 | 21 |

7 | 1.83 | 2.52 | 50 |

8 | 1.55 | 1.99 | 100 |

9 | 1.44 | 1.83 | 100 |

10 | 1.32 | 1.94 | 70 |

11 | 1.36 | 1.96 | 70 |

12 | 1.68 | 2.55 | 30 |

13 | 2.15 | 3.06 | 24 |

14 | 3.02 | 3.15 | 4 |

15 | X | X | X |