LAL- La In(1- 1). (0) 
In order to retrieve f, @ constrained linear unmixing 
procedure was applied to the image (reflectance) cube to map 
the different field components represented by the endmembers 
of crop, weeds, and soil. These endmembers were selected 
from the cube itself. A principal component (PC) analysis 
was then performed on the cube and scatter plots of a pair of 
PCs were generated. The endmembers were selected from 
averages of those pixels located in the extremities of the 
scatter plot. These pixels are often referred to as the “purest 
pixels” (Boardman, 1993). 
The retrieved endmembers were then used in unmixing, which 
expresses the reflectance spectrum of an image pixel as a 
linear sum of N endmember spectra as follows (Shimabukuru 
and Smith, 1991; Boardman, 1995): 
(xy) (xy) 
ee SU KM (8) 
where P, (x. Y) is the reflectance in band k of the spectrum for 
pixel (x, y), S,, is the reflectance in band k of the eth 
endmember spectrum, f,‘*) is the fraction of endmember e 
contributing to the spectrum of pixel (x, y), and M is the total 
number of bands in the spectrum. In constrained unmixing, 
the fractions are positive and the sum of the fractions for pixel 
(x, y) equals 1. 
An overview of the data processing layout for computing the 
effective LAI is presented in Figure 3. 
5.0 RESULTS 
Validation of the estimated LAI was performed for the three 
crop types of bean, canola, and wheat, each with a distinct 
plant architecture. The estimated LAI values were compared 
against those derived from direct measurements and those 
calculated with a semi-empirical approach using the 
normalized difference vegetation index (NDVI) as a function 
of surface reflectance using casi bands 36 (659 nm) and 63 
(813 nm). 
51 Comparison With Ground-based Measurements 
Due to the uncertainty of locating the biomass sample plots in 
the imagery, a 3 by 3 pixel average of the crop fractions 
corresponding to the sample plot areas was used to compute 
the LAI with equation (7). Subsequently, the results were 
compared to the LAI derived from the biomass samples 
(Figure 4). The root mean square deviation from the x=y line 
is 0.9. These validation results indicate that the LAI based on 
the image fraction provides an absolute measure of the LAI 
accurate to within 0.9, two thirds of the time. Some of the 
deviation can be related to the difficulties of locating the 
sample plots in the imagery. An accurate location of the 
sample plot is important since the fractions can vary up to 
30% within the selected 3 by 3 pixel window. 
Table 2 indicates that the LAI, of beans was smaller than the 
measured LAI on average. This is probably due to the foliage 
clumping as a result of the distinct row structure. For the 
40 
other two crops without open row struture £2 — 1, therefore 
LAI should be approximately equal to LAI. The estimated 
LAI, of canola agrees quite well on average with the 
measured LAI, but the LAI, of wheat was overestimated. It is 
possible that the wheat foliage was more regularly distributed 
than random. 
Table 2. 
Comparison of leaf area index determined from the image 
fraction (LAL) and direct measurements (LAI) for different 
crop types. LAI, and LAI represent the mean of the sample 
plots per field; s is the standard deviation, and n is the number 
of sample plots. 
  
  
  
  
  
  
Field n LAL +s LAI +s 
Bean 10 2.38 + 0.72 2.68 + 1.25 
Canola 5 3.06 + 0.68 3.02 + 0.86 
Wheat 9 1.76 + 0.81 1.38 + 0.60 
  
  
5.2 Comparison with LAI Calculated from NDVI 
Additional validation tests were carried out comparing the 
LAI values calculated from the crop fraction with those 
derived from NDVI. The following relationship was used to 
compute the LAI for the different crop types (Baret and 
Guyot, 1991): 
1 ( NDVI- NDVI,, 
LAI, (NDVI) - - — In 
NDVL-NDVI. l' (9) 
k |NDVI -NDVI, 
where NDVI, is the maximum value of NDVI found in the 
image (asymptotic value of NDVI when LAI, tends towards 
infinity), NDVI is the NDVI of soil retrieved from the site 
under consideration in the imagery, and k is the coefficient 
which controls the slope of the relationship. The parameters 
to calculate LAI, (NDVI) are listed in Table 3. Equation (7) 
was used to calculate the LAI, (f.) from the image fraction. 
The fraction f. includes in this case the crop as well as the 
other vegetative fractions such as weeds since NDVI 
represents a value for the total vegetation cover. k in equation 
(9) was selected such that 
LAI, (NDVI) = LAI, (7. [1: s]. (10) 
where s is the standard deviation of LAI. The results as 
shown in Table 3 for the different crop types indicate that 
values of LAI, (NDVI) and LAI, (f,) are within a standard 
deviation of about 0.3 for beans and wheat and 0.2 for canola. 
Table 3 
Standard deviation (s) of the computed LAI, (f) with respect 
to the LAI(NDVI) estimated from NDVI. Parameters 
required to calculate the NDVI based LAI are also listed. 
(NDVIm = maximum value of NDVI found in the image, 
NDVIg = NDVI value of soil retrieved from the image, k = 
coefficient which controls the relationship as stated in 
equation (9)). 
  
  
  
  
  
  
Field NDVIy | NDVI k S 
Beans 0.97 0.22 0.52 0.29 
Canola 0.97 0.22 0.55 0.21 
Wheat 0.96 0.31 0.83 0.30 
  
  
Intemational Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998