Estimating Leaf area index with Polarised Pano imaging

Exploring method to compute the leaf area index with 360 cameras

Published in

Forestree

6 min readSep 15, 2023

In the remote sensing and forestry aspect, leaf area index was an important indicator to determine the tree growth, biomass estimation and vegetation density cover from the forest. Usually, there are serval tools that using fish-eye lens to capture the forest structure, but they will use the gap fraction to estimate the leaf density between the captured sky and leaf ratio. This process would be regards as the ground-based leaf area index computation.

On the other hand, Panoramic images (pano image) has the same properties that captured the sky and vegetation leaf from close-ranging approaches in the forest. Still, the methods to compute the leaf area index with 360 cameras should be explore with different developed formulas in the remote sensing industry.

Sample pano image 1 from Google Street View used to estimated the leaf area index

Framework and workflow

Download the pano image from google street view (recommended that no need to download in a very high resolution)
Reproject the pano image into cubemap
Trim the reprojected cubemap according to the top view
Segment the trimmed image by color (leaf-wood-sky segmentation)
Compute the fraction of foliage and crown cover, crown porosity, clumping index, effective leaf area index and estimated leaf area index
Plot those image and result accordingly

Concept of the leaf area index (simple layer estimation verse multi-parameters computations)

The leaf area index is multi-dimensional tree structural density estimation, not only about the bottom masking and segmentation, but also includes a lot of overlapping areas.

Simple layer estimation would be a binary solution to estimated the gap fraction between the leaf and sky areas, by dividing the segmented leaf area by all the captured area. It would be a fast and easy method, but in low accuracy, because it does not evaluated the complexity of the tree crown, its structural and arrangement. The result from the simple dividing method only screen the last (bottom) leaf layer of the tree, so the estimation index will be within or below 1.

Sample of the computed leaf area index by simple layer estimation, the Estimated LAI was only in single layer, it means the 71.084% of ground was covered by leafs.

In computer science, we can simply do the overlapping area computation by the pixel clustering color, texture, depth, contouring and many computer vision methods as we can. Still, the overlapping results may not be the facts in our forest. Therefore, we should derive more parameters for the leaf area computation other than only evaluated the leaf, sky and overlapping areas.

On the other hand, Multi-parameter computation is a multi-dimentional approches, that involves different computation process to estimate the leaf area index more accuratly, by knowing the ratio of the foliage and crown cover, crown porosity and clumping index for the trimmed images.

Sample pano image 2 from Google Street View used to estimated the leaf area index

Color segmentation for the leaf-sky pixels

The method to segment the leaf, wood body and sky is by three condition, as we know the leaf color area lie in the range of greens, wood body are in the range of browns. Therefore, we segment the (1) leaf first, then segment the (2) brown wood body, then the remaining will be the (3) sky. Since the sky changes with different captured weathers, sometimes it may be blue and in some condition it may be in white color.

Formulas to estimated the leaf area index from the polarised panoramic images

(1) The fractions of foliage cover and crown cover:

ff = 1 — (g/T)
fc = 1 — (g/L)

ff is the fraction of foliage cover,
fc is the fraction of crown cover,
g is the number of big gaps,
T is the total number of pixels and
L is the total number of pixels in the leaf area.

(2) The equation of the crown porosity:

Φ = 1 — ff/fc

Φ is the crown porosity
ff is the fraction of foliage cover and
fc is the fraction of crown cover.

(3) The equation of the clumping index:

Ω0 = (1-Φ) * ln(1-ff) / ln(Φ) * ff

Ω0 is the clumping index,
Φ is the crown porosity
ff is the fraction of foliage cover and
fc is the fraction of crown cover.

(4) The equation of the light extinction coefficient,

k = -fc * Ω0 * ln(Φ) / LAI_T

fc is the fraction of crown cover,
Ω0 is the clumping index,
Φ is the crown porosity and
LAI_T is the true leaf area index measured from the vegetation
The value of k can be set as a default value of 0.70

(5) The equation of the effective leaf area index,

LAI_M = -fc * Ω0 * ln(Φ)/k

fc is the fraction of crown cover,
Ω0 is the clumping index,
Φ is the crown porosity and
k is the light extinction coefficient.

(6) The equation of the estimated leaf area index,

LAI = LAI_M / e^(-k)

LAI_M is the effective leaf area index and
k is the light extinction coefficient.

Results analaysis

Generally, this method is accurate and reliable, from the calculated samples, it shows the estimated leaf area index changes by different sky, leaf conditions. Multi leaf layers can be evaluated under this method and it can be adopted widely with the Google Street View and pano images captured by the users with mobile mapping system (MMS). Giving us an alternative method to understand our forest density, structure, topology better than the ordinary aerial, oblique and vertical photogrammetry. We can simply rectifies, trimming, segments and computed the index by those formula to batch process the 360 degrees imaging automatically with computer vision.

Roadside spread leaf sample from the Hong Kong Trail, Po Fu Lam 1

Denser leaf sample from the Hong Kong Trial, Po Fu Lam 2

Dense leaf sample form Hong Kong Trail, Po Fu Lam 3

Dense and multi-layered leaf sample from Hong Kong Trail, Po Fu Lam 4

Still, the determination of the k (light extinction coefficient) should be calculated by the ground truth rationing with the estimated local parameters.

Reference

Alonso, L., Torres-Sánchez, J., Pérez-Pérez, J. G., & López-Granados, F. (2019). Leaf Area Index Estimation of Pergola-Trained Vineyards in Arid Regions Based on UAV RGB and Multispectral Data Using Machine Learning Methods. Remote Sensing, 11(18), 2146.

Macfarlane, C.; Hoffman, M.; Eamus, D.; Kerp, N.; Higginson, S.; McMurtrie, R.; Adams, M. Estimation of leaf area index in eucalypt forest using digital photography. Agric. For. Meteorol. 2007, 143, 176–188.

Poblete-Echeverria, C.; Fuentes, S.; Ortega-Farias, S.; Gonzalez-Talice, J.; Yuri, J.A. Digital Cover Photography for Estimating Leaf Area Index (LAI) in Apple Trees Using a Variable Light Extinction Coefficient. Sensors 2015, 15, 2860–2872.

Fuentes, S.; Palmer, A.R.; Taylor, D.; Zeppel, M.; Whitley, R.; Eamus, D. An automated procedure for estimating the leaf area index (LAI) of woodland ecosystems using digital imagery, MATLAB programming and its application to an examination of the relationship between remotely sensed and field measurements of LAI. Funct. Plant Biol. 2008, 35, 1070–1079

Leblanc, S.G. Correction to the plant canopy gap-size analysis theory used by the Tracing Radiation and Architecture of Canopies instrument. Appl. Opt. 2002, 41, 7667–7670.

Acknowledgments

This is a volunteering pilot study from the Team of Forestree, Remote Sensing and Forestry, used to study the close-ranging photogrammetry, image processing and computer vision.

All the Pano image was download from the Google Street View and processed image was create by Yu Kai Him Otto developed algorithm.