A practical approach for estimating the red edge position...

A practical approach for estimating the red edge position of plant leafreflectance

G. V. G. BARANOSKI*{ and J. G. ROKNE{{School of Computer Science, University of Waterloo, 200 University Avenue West,

Waterloo, ON N2L 3G1, Canada

{Department of Computer Science, The University of Calgary, 2500 University Drive,

N.W., Calgary, AB, Canada T2N 1N4

(Received 20 August 2003; in final form 24 June 2004 )

The point of maximum slope on the reflectance spectrum of a plant leaf between

red and near-infrared wavelengths is known as the red edge position (REP). The

REP is strongly correlated with foliar chlorophyll content, and hence it provides

a very sensitive indicator for a variety of environmental factors affecting leaves

such as stress, drought and senescence. The REP is also present in spectra for

vegetation recorded by remote sensing methods. Due to its importance for the

application of inversion procedures, a number of techniques have been developed

for determining the REP for foliar spectral reflectance. In this paper a new

approach is proposed. It allows an unsupervised estimation of the REP. The

accuracy of the new approach is evaluated by comparing REP estimates with

values derived from measured spectral data for woody and herbaceous species

available in the LOPEX (Leaf Optical Properties Experiment) database.

1. Introduction

The abrupt change in the 680–800 nm region of reflectance spectra of leaves caused

by the combined effects of strong chlorophyll absorption and leaf internal scattering

is called the red edge. The red edge was first described by Collins (1978), and it is

perhaps the most studied feature on the vegetation spectral curve according to

Schlerf and Atzberger (2001). The existence of the red edge provides the basis for

vegetation identification procedures using combinations of red and infrared

radiances since the feature is also present in remotely sensed spectra as noted by

Horler et al. (1983).

The red edge is a feature of the reflectance curve and hence it can only be

quantified by reflectance data in the spectral region where it occurs. Instrumentation

and methods for measuring the reflectance spectra of vegetation are discussed in for

example the works by Kraft (1996) and Zarco-Tejada and Pushnik (2003). It is an

area of current research outside the scope of the present paper.

A typical plant leaf reflectance spectrum is shown in figure 1. The red edge is a

fairly wide feature. Hence it is often characterized by its maximum slope called the

red edge position (REP) in order that it may be easily compared with measurements

under different conditions and for comparison between different species.

*Corresponding author. Email: [email protected]

International Journal of Remote Sensing

Vol. 26, No. 3, 10 February 2005, 503–521

International Journal of Remote SensingISSN 0143-1161 print/ISSN 1366-5901 online # 2005 Taylor & Francis Ltd

http://www.tandf.co.uk/journalsDOI: 10.1080/01431160512331314029

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The transition for the reflectance spectrum of a single leaf specimen to that of a

vegetation canopy has been discussed by a number of authors (Baret et al. 1987,

Zarco-Tejada and Miller 1999). For the purpose of this paper it suffices to note that

a REP is also present in the reflection spectra from canopies.

Chlorophyll concentration is usually an indicator of nutritional stress, photo-

synthetic capacity and senescence. The REP and the chlorophyll concentration are

strongly correlated as first noted by Gates et al. (1965), and more recently by Zarco-

Tejada et al. (2002). Werner and Atzberger (1996) examined the relationship

between chlorosis and necrosis of leaves and the REP, and a general discussion on

the remote sensing of foliar chemistry by spectral measurements was given by

Curran (1991). The REP is also used, for example, to enable on-line control of

nitrogen spreading for site specific top dressing using sophisticated spectrometers

(Heege and Reusch 2003) where it is noted that a difference in REP of one

nanometre may translate to a difference in nitrogen fertilizer requirement of

15 kg ha21 (Heege and Reusch 2003). Hence the determination of the REP might be

directly translated to an economic parameter. Other constituents of plants such as

amaranthin have also been shown to have functional relationships to the red edge as

noted by Curran et al. (1991).

A further interest in the REP is discussed in the work by Danson and Plummer

(1995) who demonstrated a strong nonlinear correlation between leaf area index

(LAI) for a canopy, the one-sided area of leaves per unit of ground area, and the

REP. The LAI is a key spatial variable required to drive models of forest ecosystems

(Nemani et al. 1993), since it provides a quantitative measure of the surface area

available for interception of photosynthetically active radiation (PAR) and

transpiration. Since direct measurement of canopy LAI is labour intensive and

time consuming Pu et al. (2003) extracted the REP from hyperspectral data and used

it to estimate the LAI.

The estimation of the REP, usually applying numerical methods for generating

derivatives for leaf reflectance spectra, is, therefore, a valuable remote sensing tool

to assess the chemical and morphological status of vegetation (Boochs et al. 1990).

The reader interested in a comprehensive review of these applications is referred to

Figure 1. Reflectance spectrum of a fresh soy leaf (Soja hispida) (Hosgood et al. 1995).

504 G.V.G. Baranoski and J.G. Rokne

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the excellent work by van der Meer and de Jong (2001). The use of derivative

spectrophotometry is also commonly employed to resolve or enhance absorption

features that might be masked by interfering background absorption (Demetriades-

Shah et al. 1990, Filella and Penuelas 1994).

A number of methods for determining the REP have, therefore, been proposed in

the remote sensing literature.

1. The simplest method, first developed by Baret et al. (1987), is based on linear

interpolation. It assumes that the reflectance red edge can be simplified to a

straight line centred around a midpoint between the shoulder reflectance

maximum and the reflectance minimum of the chlorophyll reflectance curve,

which is set usually at about 680 nm. The REP is then estimated by a simple

linear equation using the slope of the line. This method is also used by

Guyot et al. (1992), Danson and Plummer (1995), and more recently by

Clevers and Jongschaap (2001) and Heege and Reusch (2003). A variation

used to estimate the REP for winter-rye crop was given in the work by Heege

and Reusch (2003) as

lp~700z40r 670ð Þzr 780ð Þð Þ=2{r 700ð Þ

r 740ð Þ{r 700ð Þ ð1Þ

where lp is the estimate for the REP and r(670), r(700), r(740) and r(780)

are the reflectances at wavelengths 670, 700, 740 and 780 nm.

2. The inverted Gaussian technique used for example by Bonham-Carter

(1988) and Zarco-Tejada and Miller (1999), was first mentioned by Hare

et al. (1986). It assumes that the data can be fitted by a curve of the form

r lð Þ~rs{ rs{r0ð Þel{l0ð Þ2

2s2 ð2Þ

where r(l) is the reflectance as a function of the wavelength l, r0 is the

reflectance where l5l0 (usually around 680 nm), rs is the ‘shoulder

reflectance’ (frequently set to 800 nm) and s is the Gaussian shape

parameter. The REP is then the inflection point of the curve at lp5s+l0.

A nonlinear equation system would have to be solved in order to find a least-

square fit for (2) to the data. In the work by Bonham-Carter (1988)

constants were selected (choosing between (rs, r0, l0), (rs, r0), (l0) and no

fixed constants) so that the resulting equation can be linearized to a linear

least-squares system, which can be solved easily. In order to compare

qualitatively with the method proposed in this paper we plot the result of

one example from Zarco-Tejada and Miller (1999) where figure 2 shows the

shape of the estimated reflectance of the inverted Gaussian with l05673,

r050.03, rs50.21, s5lp2l0539. Hence lp5712. For this case, r0 and rs

were selected, and the other two parameters, namely l0 and s, were

computed by an iterative least squares procedure. The model was extensively

tested and evaluated by Miller et al. (1990), and also used by, for example

Schlerf and Atzberger (2001).

3. A three-point Lagrange interpolation technique of the derivative of the

spectral data was given by Dawson and Curran (1998). A finite difference

approximation is applied to four data points of r(l) to generate derivative

Estimating red edge position 505

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approximations D(li), i51, 2, 3. Then coefficients

A lið Þ~D lið Þ

P3i=j, j~1 li{lj

� � i~1, 2, 3 ð3Þ

are calculated. These coefficients are used to calculate

REP~A l1ð Þ l2{l3ð ÞzA l2ð Þ l1{l3ð ÞzA l3ð Þ l1{l2ð Þ

2P3

i~1 A lið Þð4Þ

It assumes that the derivative curve is a parabola.

4. Another technique locates the REP as the maximum first derivative of the

reflectance spectrum in the region of the red edge using high-order curvefitting techniques such as third-order polynomials to fit the spectrum

(Demetriades-Shah et al. 1990), then computing the maximum of the

derivative in the range of interest (see also Horler et al. 1983, Clevers and

Buker 1991, Railyan and Korobov 1993). Clevers and Jongschaap (2001),

however, noted that such curve fitting techniques are quite complex and

computationally demanding.

Methods 1–3 above were compared by Dawson and Curran (1998) for different

chlorophyll concentrations. It is noted that the red edge position at 50 mg m22

concentration is 705 nm for the Lagrangian, 707 nm for the inverse Gaussian and

715 nm for the linear interpolation. These differences cast some doubt as to where

the actual REP is located. See Broge and Leblanc (2001) for an in-depth discussionof this issue. Furthermore, the REP for the linear method at 50 mg m22 chlorophyll

concentration is exactly the same as the red edge position for both the Lagrangian

and the inverse Gaussian methods at 350 mg m22 chlorophyll concentration. A

previous comparison by Clevers (1994) found good agreement for the same three

methods. This suggests that the choice of wavelength parameters in the methods can

influence the results drastically. The recent paper by Pu et al. (2003) also reviews the

four methods discussed above with the specific aim of using it for forest LAI

estimation. They noted that the correlation with the LAI was high for 4-pointinterpolation and polynomial fitting, medium for Lagrange interpolation and low

for the inverted Gaussian modelling.

Figure 2. Reflectance spectrum for the inverted Gaussian model (redrawn from Zarco-Tejada and Miller (1999)).


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A different issue is highlighted by Pierce (2002) in the description of REDE 1.0

(Red Edge Detection Engine), which is an application designed to detect the spectra

that correspond to vegetation in multi- and hyper-spectral image datasets, and to

compute a red edge location. Pierce distinguishes between supervised and

unsupervised computations. The former is a computation supervised by a human

expert. The latter is a computation done automatically, i.e. it seeks to achieve

reasonably accurate results without the intervention of an expert. Pierce argues thatthe methods in the literature such as the three-point Lagrangian and the inverted

Gaussian methods are satisfactory for supervised, but not for unsupervised

computations for the REP.

These remarks beg the questions of what exactly is the red edge, how can it becomputed, how can the results be reproducible and to what accuracy can the results

be trusted? The aim of this paper is to provide an alternative method for determining

the REP. The proposed method reduces both the unwanted oscillations and the

computational complexity exhibited by fitting higher order polynomials. The

method is also only dependent on a small number of parameters.

The results of a REP should also be reproducible, that is, given the measurements

for the spectrum for the same specimen, the same sensors and the same geometric

arrangement of the sensors the REP should be the same up to the accuracy of

the instrumentation. Also, the computation of the red edge should be

unsupervised without introducing undue complexity. Finally, the evaluation

of the technique used to estimate the REP should be based on comparisons with

values derived from measured data, so that one can assess its usefulness to remotesensing applications.

2. Proposed approach

Railyan and Korobov (1993) acknowledged that the origin and behaviour of the red

edge is not described and explained completely although the main features are

determined by the electron transitions of chlorophyll a and b when exited by

radiation in the appropriate wavelength (Curran 1991). In fact one can find slightly

different ranges for the red edge in the remote sensing literature. Most works in this

area consider the lower bound to be 680 nm, while values for the upper bound vary

from 740 to 800 nm (Horler et al. 1983, Bonham-Carter 1988, Boochs et al. 1990,

Miller et al. 1990, Railyan and Korobov 1993, Filella and Penuelas 1994, Dawsonand Curran 1998).

If we consider the graph in figure 3, we note that there are essentially three regions

of reflectance in the the red edge. Initially, there is a region of low and relatively

constant reflectance rl, followed by a rapidly rising reflectance curve, which

corresponds to the red edge. Finally, we observe a region of high and relativelyconstant reflectance rh. For this paper the location of rl is at a location ll and the

location of rh is at a location lh where ll and lh are fixed parameters for all

specimens.

Our goal here is to abstract these features by a new function:

f lð Þ~ azblzcl2

1zdlzel2ð5Þ

of five parameters a, b, c, d and e that will encompass the features rl, rh, ll and lh


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mentioned above. The choice of this function could be viewed as an improvement on

the higher order polynomial fitting procedure given in (Demetriades-Shah et al.

1990). It is well known that polynomials tend to exhibit unwanted oscillations which

tend to be suppressed in rational forms (Burden and Faires 1993). Furthermore, it is

also known that rational functions tend to spread the approximation error more

evenly over the approximation interval. From an evaluation point of view rational

functions are the only functions that can be evaluated directly in a digital computer

using the four operations +, 2, 6, /. The proposed approach can also be viewed as

an improvement to the inverted Gaussian technique since the functional form

developed from it is a much simpler form with similar shape characteristics. A

similar function was also used by Baranoski and Rokne (2002) as a field function for

plotting implicit surfaces.

The method developed in this manner is new and it provides an additional choice

of method for determining the REP beyond the four methods most recently

discussed in a recent paper by Pu et al. (2003). Four of the conditions determining

the parameters a, b, c, d and e are

f llð Þ~rl ð6Þ

f 0 llð Þ~0 ð7Þ

f lhð Þ~rh ð8Þ

f 0 lhð Þ~0 ð9Þ

which requires a decision on the locations of (ll, rl) and (lh, rh). The remaining

condition is that a point (lc, rc) in the red-edge region be chosen from the data.

The four equations (6)–(9) together with the value at lc form a mildly nonlinear

565 system of equations. Although it is possible to solve this system directly, it is

Figure 3. Red edge of a fresh soy leaf (Soja hispida) (Hosgood et al. 1995).


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simpler to shift the coordinate system with a linear transformation, so that new

coordinates are (L, P)5(l2ll, r2rl). The origin of the new coordinate system is

given by the pair (ll, rl), and the upper point of the curve is given by the pair (W, R),

where W5lh2ll and R5rh2rl. This is illustrated in figure 4.

A function

g Lð Þ~ AzBLzCL2

1zDLzEL2ð10Þ

is then considered and equations (6)–(9) are replaced by

g 0ð Þ~0 ð11Þ

g0 0ð Þ~0 ð12Þ

g Wð Þ~R ð13Þ

g0 Wð Þ~0 ð14Þ

To solve these equations we first consider g(0)50 which results in A50. From

g9(0)50 we get B50.

Now g(W)5R results in

R~CW 2

1zDWzEW 2ð15Þ

and g9(W)50 gives

2CW 1zDWzEW 2� �

~ Dz2EWð ÞCW 2 ð16Þ

These two equations can be simplified to

DRWzERW 2~CW 2{R ð17Þ

DRz2EWR~2CW ð18Þ

Figure 4. Shifting the origin of the reflectance curve.


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Using Cramer’s rule we get

D~{2=W ð19Þ

E~C=Rz1=W 2 ð20Þ

which determines D and E in terms of a parameter C. Equation (10) can now be

written as

g Lð Þ~ CL2

1{2L=Wz CR

z 1W 2

� �L2

ð21Þ

The point (rc, lc) on the ascending part of the curve is also translated to a point (Lc,

Pc) in the shifted coordinate system and used to determine C as

C~1=Lc{1=Wð Þ2

1=Pc{1=Rð22Þ

Let now

g Lð Þ~ CL2

1zDLzEL2ð23Þ

where C, D, E are defined by equations (20), (17), (18), respectively. The first

derivative is given by:

g0 Lð Þ~ CL 2zDLð Þ1zDLzEL2� �2

ð24Þ

and the second derivative is given by:

g00 Lð Þ~{2C {1zEL2 3zDLð Þ

� �

1zDLzEL2� �3

ð25Þ

Finally, we set g0(L)50 and solve for L. This equation has three roots, one of which

is in the interval [0, W] of interest. Using the auxiliary quantity

P~ D2{2E� �

E2z

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiD2E4 D2{4Eð Þ

q� �1=3,

E ð26Þ

we get

Ls~1

D{

1{iffiffiffi3p� �

22=3P{

P 1ziffiffiffi3p� �

24=3{1

!

ð27Þ

and REP5Ls+ll.

In general we can write down an algorithm for the estimation of the REP as

follows:

FindREP

1. Input (ll, rl), (lh, rh), (lc, rc).


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2. Compute

W~lh{ll ,

R~rh{rl ,

Lc~lc{ll ,

Pc~rc{rl :

3. Calculate D using equation (19).

4. Calculate E using equation (20).

5. Calculate C using equation (22).

6. Solve for L in the equation g"(L)50 in [0, W] using equations (26) and (27).

7. REP5Ls+ll.

8. (Optional PlotRED) Plot’ estimated red edge, g(l), using equation (23)

shifted in wavelength axis according to ll.

9. (Optional PlotRED) Plot derivative of the estimated red edge, g9(l), using

equation (24).

The method developed above is well suited to data given at three wavelengths. It is

also possible to develop methods that include further information for example data

for f9(ll) or f9(lh). This is left for further investigation.

In table 1 the previously published methods for the REP are compared qualitatively

to the proposed method. Recently, Pu et al. (2003) have compared the performance of

the previously published methods with respect to the extraction of REP from remote

sensing data collected with a hyperspectral sensor. They rated the linear interpolation

technique as the most attractive from an implementation point of view.

Arguably one of the major factors affecting the accuracy of REP estimates is the

sampling characteristics of the sensor. One could claim that a method A provides

more accurate estimates than a method B when applied to data from a sensor C.

However, the reverse could be true considering data from a sensor D. Moreover, the

proximity between estimates provided by two methods does not necessarily mean

that both are accurate since both can be far from the true value.

For these reasons we choose to evaluate the accuracy of the estimates provided by

the proposed approach by comparing them with REP values obtained directly from

measured data instead of values provided by other methods. The dataset used in our

evaluation has a reasonable fine resolution that allows an accurate determination of

the REP to be used as a reference for comparison. One could argue that having such

dataset one would not need a specific approach to determine REP. However, to the

best of our knowledge, fine resolution spectral data is usually not readily available

for a large number of species and for many practical purposes, for example towards

the estimation of the REP from satellite imaging sensors, such as MERIS/

ENVISAT, only a limited number of discrete bands are available over the red edge

region.

3. Evaluation

In our evaluation of the proposed approach we compare estimated red edge curves

with spectral curves originated from measured data. More specifically, in our


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experiments we consider specimens whose reflectance spectra are available in the

LOPEX (Leaf Optical Properties Experiment) database (Hosgood et al. 1995). This

database consists of leaf spectra representative of more than 50 woody and

herbaceous species that were obtained from trees and crops near the Joint Research

Centre in Ispra, Italy. The reflectance spectra stored in the LOPEX database cover a

400–2500 nm wavelength interval with a 1 nm step. In our comparisons we also

Table 1. Quantitative comparison of the five methods.

Linearinterpolation

InvertedGaussian

Lagrangianinterpolation Curve fitting

Rationalfunction (new)

Complexity ofevaluation

low high low low low

Datarequirement

Four datapoints

variable variable Four data points Three datapoints

Approxima-tion properties

poor good good good excellent

Computing thefunction

simple estimating ornonlinear

system

simple solving linearsystem

solving oneequation in one

variable

Remark computationallyattractive

needsexponential

computationallyattractive



Table 2. Reflectance values for fresh plant leaves of six different species at specifiedwavelengths: ll5680 nm, lc5725 nm and lh5780 nm. Source: LOPEX (Hosgood et al. 1995).

Specimen rl rc rh

Maize 0.0648 0.2839 0.4657Banana 0.0331 0.3749 0.4916Poplar 0.0627 0.3189 0.4691Soy 0.0410 0.3464 0.4655Maple 0.0382 0.2870 0.4126Tomato 0.0452 0.3215 0.4399

Table 3. Comparing methods for estimating red edge positions for fresh chlorophyllous plantleaves of six different species with red edge position derived from measured data (LOPEX).

SpecimenLOPEX

(nm)

Red edge position Relativeerrors

FindREP(%)

FindREP(nm)

Linear inter-polation

Forward differ-entiation

Backwarddifferentiation

Maize 727 722.20 718.68 703.76 738.57 0.66Banana 708 709.67 717.60 702.93 737.62 0.24Poplar 719 717.09 720.46 704.55 739.47 0.29Soy 711 711.42 719.11 703.92 738.75 0.06Maple 710 714.96 716.26 701.81 736.37 0.70Tomato 712 712.68 720.07 704.55 739.48 0.10


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examined the derivatives of these spectral curves which we computed using a three-

point numerical differentiation formula (Burden and Faires 1993). We also applied a

local average smoothing to reduce noise.

The accuracy of REP locating procedures is sensitive to the red edge bounds used

as input parameters. Supervised approaches usually tailor the choice of sample

wavelengths to the specimen at hand. Unsupervised approaches, like the one

Table 4. Summary of the results of the comparisons between measured (LOPEX) andestimated (FindREP) red edge positions considering 80 reflectance spectra of fresh

chlorophyllous plant leaves of different species.

Relative error (%)

Minimum Maximum Average0.007 0.87 0.26

Figure 5. Estimated (PlotRED) and measured (LOPEX) reflectance and first derivativereflectance spectra for a fresh maize leaf (Zea mays L.).


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proposed in this paper, use fixed values for these parameters. As mentioned earlier,

one can find slightly different values for these bounds in the literature. In our

experiments we use ll5680 nm and lh5770 nm, which seem to provide a tighter

encapsulation for the red edge region. An optimal choice for a point in the red edge

would be given by rc5REP. Clearly this is not an option since if we already knew

the REP, we would not need to estimate it! Therefore, we simply use the average

lc5(ll+lh)/25725 nm for the method. The effect of making different choices for lc is

discussed in section 5.

In our comparisons we considered 80 spectra derived from reflectance

measurements on fresh individual chlorophyllous leaves, and stored in the

LOPEX database. We selected six illustrative specimens representing herbaceous

and woody species: maize (Zea mays L.), banana (Museta ensete), poplar (Populus

Figure 6. Estimated (PlotRED) and measured (LOPEX) reflectance and first derivativereflectance spectra for a fresh banana leaf (Musa ensete).


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tremula L.), soy (Soja hispida), maple (Acer pseudoplatanus L.) and tomato

(Lycopersicum esculentum). Table 2 presents the reflectances (rl, rc and rh) for these

specimens which were also sampled from LOPEX measured data. For completeness,

we also included a summary of the results of our comparisons for all 80 spectra.

4. Results

In the following it is assumed that the comparison results obtained using the

LOPEX data forms the baseline for the evaluation of the new method due to the

high granularity of this data. Figures 5–10 present comparisons between red edge

and derivative curves plotted using PlotRED (which corresponds to the routine

FindREP with the two steps 8, 9 added) and curves derived from LOPEX reflectance

data. A visual inspection of these plots suggests a good agreement between thereflectance curves generated by the new method and curves obtained by detailed

measurements.

Figure 7. Estimated (PlotRED) and measured (LOPEX) reflectance and first derivativereflectance spectra for a fresh poplar leaf (Populus tremula L.).


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While the estimated derivative curves present good qualitative agreement with the

derivative curves determined from measured data, quantitative discrepancies are

noticeable, especially for some of the species considered, namely maize (figure 5) and

maple (figure 9). The inflection points of the curves are, however, fairly close,

suggesting that the proposed approach for the estimation of REP presents an

acceptable level of accuracy.

Table 3 presents the REP values derived from the measured reflectance spectrum

of each of the six illustrative specimens, and values estimated using FindREP. For

four of these specimens the relative error is smaller than 0.3%. A comparison was

made with linear interpolation and two variants of the three-point Lagrangian

technique for estimating the REP since these methods use almost the same

information (i.e. data at four wavelengths) as FindREP. The REP values estimated

using these methods are given in table 3, columns 4 to 6. The poor results for the

three-point Lagrangian techniques as these were originally implemented are due to

Figure 8. Estimated (PlotRED) and measured (LOPEX) reflectance and first derivativereflectance spectra for a fresh soy leaf (Soja hispida).


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the numerical differentiation needed to obtain the required derivative data. It should

also be noted that the data for these methods was given at 670 nm, 700 nm, 740 nm

and 780 nm, i.e. one additional data point as compared to FindREP.

For all 80 spectra considered in our comparisons the relative error is smaller than

1% (table 4), meaning that the deviation between measured and estimated REP was

always below 7 nm. These figures confirm the observations derived from the visual

inspection of the derivative curves, i.e. the estimated REP values closely

approximate the actual values for the tested specimens.

5. Discussion

The proposed approach for the estimation of the REP assumes no a priori

knowledge about the reflectance spectrum of a given specimen. As with previous

techniques used to estimate the REP, it may be affected by the choice of input

Figure 9. Estimated (PlotRED) and measured (LOPEX) reflectance and first derivativereflectance spectra for a fresh maple leaf (Acer pseudoplatanus L.).


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parameters, namely the three wavelength sample positions (ll, lc and lh). Instead of

supervising the choice of these values for each specimen, fixed values (680 nm,

725 nm and 770 nm) were used in the evaluation experiments. As a result the relative

errors fluctuate, but their magnitudes remain within reasonable limits, especially

considering that the comparisons are performed with respect to values derived from

actual measured data, instead of values estimated by other techniques.

The sensitivity of the proposed method to the choice of lc was assessed by

repeating the calculations with lc set to 700 nm and 750 nm. The results of these

calculations are given in tables 5 and 6. It is interesting to note that the results are

still quite good, suggesting that the form of the approximation curve is well suited to

the data.

The analytical solution provided by the proposed approach has the property that

the complex parts cancel out if the arithmetic is exact. Floating point arithmetic,

Figure 10. Estimated (PlotRED) and measured (LOPEX) reflectance and first derivativereflectance spectra for a fresh tomato leaf (Lycopersicum esculentum).


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however, is not exact. As a result, an estimation may have tiny complex parts, in the

order of 10214, which should be discarded. Alternatively, instead of using the closed

formulas given by equations (26) and (27), one could apply a numerical root finding

procedure, such as fzero in Matlab (Hanselman and Littlefield 2001), or an

equivalent in any other numerical software package, with equation (25) as the target

function.

Selecting the ‘best’ REP estimation method is delicate, and no single method is

superior in all the cases. The relative accuracy depends on the biological

characteristics of the specimen at hand. Nonetheless, our experiments suggest that

the proposed algorithmic approach provides REP estimates with reasonably high

accuracy, without requiring human intervention. Hence, it may be suitable for the

estimation and analysis of red edge data in field, laboratory, airborne and

spaceborne settings. Our future efforts will focus on the application of the proposed

approach to estimate REP shifts due to natural seasonal cycles affecting the

concentration of chlorophyll.

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Table 5. Comparison between measured (LOPEX) and estimated (FindREP) red edgepositions for fresh chlorophyllous plant leaves of six different species, lc5700.

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Maize 727 716.46 1.45Banana 708 710.99 0.42Poplar 719 720.90 0.26Soy 711 714.63 0.51Maple 710 718.30 1.17Tomato 712 718.57 0.92

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A practical approach for estimating the red edge position...

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