LAI

For an introduction on LAI we refer to Weiss et al., 2004[1] and Thimonier et al., 2010[2].

Quick Introduction

Install the package through

Pkg.clone("https://github.com/ETC-UA/LeafAreaIndex.jl")

You construct a PolarImage from a Calibration type and an Image (or in general, a Matrix). The calibration requires the image size, the coordinates of the lens center and the (inverse) projection function. (The projection function maps polar distance ρ [in pixels] on the image to the zenith angle θ [in radians] of the scene and is usually not linear.)

using Images
img = imread("image.dng")
imgblue = blue(img) #take the blue channel
using LeafAreaIndex
mycameralens = calibrate(height, width, ci, cj, fθρ, fρθ)
polarimg = PolarImage(imgblue, mycameralens)

The first step is automatical thresholding with the default method Ridler Calvard:

thresh = threshold(polarimg)

The clumping factor can be estimated with the method of Lang Xiang with 45ᵒ segments between view angles θ1 and θ2 using langxiang45(polarimg, thresh, θ1, θ2). Similarly chencihlar(polarimg, thresh, θ1, θ2) for the Chen Chilar method.

There are two methods to estimate LAI assuming an ellipsoidal leave angle distribution, both also estimating the Average Leaf Inclination Angle (ALIA). The first one uses a Lookup Table (LUT) and the second one an optimization method.

LAI1 = ellips_LUT(polarimg, thresh)
LAI2 = ellips_opt(polarimg, thresh)

further methods

For images taken (vertically upwards) on a domain with slope of eg 10ᵒ and downward to the East, you must include this in your PolarImage.

myslope = Slope(10/180*pi, pi/2)
polarimg = PolarImage(img, mycameralens, myslope)

Two more automatic thresholding methods can be used with edge_threshold and minimum_threshhold for the Edge Detection and Minimum algorithm.

Further LAI estimation methods are available: zenith57(polarimg, thresh) for using a view angle of 57ᵒ where the ALIA influence is minimal; miller(polarimg, thresh for miller integration assuming a constant leaf angle; and lang(polarimg, thresh) that uses a first order regression on the miller method.

To access the pixels in a particular zenith range, pixels(polarimg, pi/6, pi/3) will return a vector with pixels quickly, sorted by increasing ρ (and then by polar angles ϕ for identical ρ). A shortcut pixels(polarimg) is translated to pixels(polarimg, 0, pi/2).

The segments function can further split these ring pixels in n segments (eg. for clumping calculation). It returns a vector with n elements, each a vector with segment pixels.

You can also construct an iterator to access a specific zenith range. It will return the pixels on each ring in the range by increasing integer ρ² in a tuple with a vector of polar angles ϕ and a vector of corresponding pixels.

for (ρ², ϕ, px) in rings(polarimg, pi/6, pi/3)
    # do something with each ρ², ϕ, px variable
end

In case of problems or suggestion, don't hesitate to submit an issue through the issue tracker or code suggestions through a pull request.