Estimating Leaf-Area Index of a Crown Canopy in a Pecan Orchard
Li Xiaowen Wang Jindi, Zhu Chongguang, Liu Yi
Institute of Remote Sensing Application, Chinese Academy of Sciences
Beijing 100101, P.R. China
Alan H. Strahler
Certer for Remote Sensing, Boston University , Boston, MA 02215, USA
Introduction
The advance of remote sensing science and technology has provided new airborne or satellite sensors able to sense the reflectance of a ground target at different directions, which brings once again the anisotropic reflectance characteristics of earth surface to attention of researchers. Many model have been proposed to relate the geometrical and biological parameters of various ground target to directional reflectance data acquired from a remote sensor, although their application and accuracy need large amounts of accurate measurement for model is an essential part in both geometric-optical models and rediative transfer theory.
Pgap is the probability that a photon incident upon a vegetation canopy will pass directly through the canopy without being intercepted by a leaf, branch, or stem. It is thus a function of these structural parameters as well as the pathelength within the canopy.
A recent field experiment (MAC-VI) presented the opportunity to relate gap probability to detailed between-crown information on the size, shape and spacing of individual tree crowns as well as within-crown information on leaf size pecan trees in an orchard near Phoenix, Arizona. The experiment was jointly sponsored by the Canada Center for Remote Sensing (CCRS), Ottawa, and the USDA Water Conservation Laboratory, Phoenix. The tree measurement was designed and carried out by CCRS personnel, with three of authors providing additional help. Our own data collection was to measure the gap probability by photogrammetric methods [1].
It turned out that measuring leaf area index (LAI), leaf angle distribution (LAD) and crown structure in the field was very difficulty and manual – labor intensive, and the large volume of measured data is not easy to handle, either . At this writing , we have not received all planned field data from the collaborating team at the CCRS.
In such circumstances, we have explored the results for a few photos of one of the pecan trees to extract crown information by combining computed tomography and a crown Pgap model. Though the reconstructed crown
parameters still await confirmation, the initial result are reasonable and encouraging. With further development and validation, this technique may have wide application in the future field experiments of forest remote sensing.
This article summarized our tree tomography method to reconstruct crown shape and further estimate LAI, as well as to demonstrate its practicability and rationale. Though further improvements are still needed, our method provides a sound basis for a new approach to data acquisition in forests.
Computed Tomography and Estimation of LAI
Theoretically [2] , computed tomography (CT) can be applied in any reconstruction problem if the signal received by a single detector can be expressed as linear integral along the ray path penetrating the object F(x,y,z)
Pq = ̣Ray(0) f (x,y,z)dsq (1)
Usually, we obtain an array of Po values and call it a projection Po(u,v). If in such a projection, all rays reaching detectors (u,v) are parallel, it is termed a parallel – beam projection. Frequently, we have a fan – beam projection [3]3, in which the rays reaching different detectors are not parallel, but converge to a certain point given 0 and the optical geometry. Various algorithms can be used to reconstruct f(x,y,z(, given enough number of projections at a sufficiently wide range of directions.
Typical models for gap probability in a volume cell of leaf canopy along the ray paths are of the form.
Pgap (q) = e-LK(q)s, (2)
where L is the total single – sided leaf area within a unit volume cell, k (0) is the fraction of the foliage area projected toward the angle of incidence, s is the pathlength of the ray beam through the uniform canopy, and 0 is the zenith angle of incidence [4].
Taking the logarithm of both sides of (2), and allowing changes in the foliage volume de3nsity L, we have:
in Pgap (q) = - ̣Ray (q) L(x,y,z) k (q) ds (3)
It is obvious that reconstruction of a 3-D LAI distribution L(x, y, x) from Pgap measurements can be posed as a typical CT problem.
Among many CT algorithms, we selected back – projection because of its flexibility and simplicity. A simplified example shows how this algorithm works. Assuming 2-D object f (x, y) contains 2*2 cell as follows:
5 4
3 8
Then by (1) we can obtain a horizontal projection (9,11), a vertical projection (8,12), and two 45 degree projections, (2,13,4) and (5,7,8) respectively. Obviously we can solve for f(x,y) by selecting four independent equations. However, when f(x,y) involves hundreds by hundreds of cells, it will be much easier to equally distribute the sums along back projection paths and average all back projections.
First, we back project the vertical projection, and the horizontal, ... it will result the following:
| 4 |
6 |
805 |
10.5 |
15 |
14.5 |
20 |
18 |
|
| 4 |
6 |
9.5 |
11.5 |
12.5 |
18 |
16 |
26 |
Then averaging by total number of back projection for each cell, we obtain
5 4.5
4 6.5
This is close to the original f(x,y) but there are notable errors. The reason is that there is a “quasi-bone” element ( the value 8 is much larger than surrounding ones ) and the projection is unfiltered. However, the more projections we have, the less sudden the change in f(x,y), and the more accurate the algorithm will be.
