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Radiometric corrections of topographically induced effects on Landsat TM data in an alpine environment
Volume 48, number 4, 1993
17
P e t e r M e y e r 1,., K l a u s I. I t t e n 1, Tobias K e l l e n b e r g e r 1, S t e f a n S a n d m e i e r 1 and Ruth Sandmeier 1
Radiometric corrections of topographically induced effects on Landsat TM data in an alpine environment Four radiometric correction methods for the reduction of slope-aspect effects in a Landsat TM data set are tested in a mountainous test site with regard to their physical soundness and their influence on forest classification, as well as on the visual appearance of the scene. Excellent ground reference information and a fine-resolution DEM allowed precise assessment of the applicability of the methods under investigation. The results of the study presented here demonstrate the weakness of the classical cosine correction method for radiometric correction in rugged terrain. The statistical, Minnaert and C-correction approaches, however, yielded an improvement of the forest classification and an impressive reduction of the visual topography effect.
1. Introduction
The overutilization of tropical forests as well as the problems of deterioration of the health of forests in mid latitudes, have warned mankind that an important ecological factor, i.e., an important natural resource is endangered and may not be so renewable as was anticipated. In recent years, much emphasis was laid on the mapping and inventorying of forests and forest damage. On a local level, colour-infrared air photographs have been used with great success, and on larger scales, be they regional, continental or even global, satellite studies show quite encouraging results. In this study the feasibility of Landsat TM forest classifications in an alpine environment is tested versus excellent ground reference data. It has been shown in the past that terrain-induced illumination variations have hindered an easy and straightforward solution of the distinction of forests versus non-forest backgrounds, and also to separate a forest into its major classes. Four methods to correct the impact of illumination have been tested in order to improve the accuracy of forest classifications. Since a correction of the atI Remote Sensing Laboratories, Department of Geography, University of Zurich-lrchel CH-8057 Zurich, Switzerland. * Present address: Jet Propulsion Laboratory, California Institute of Technology, MS 169-315, 4800 Oak Groove Drive, Pasadena, CA 91109, USA.
mospheric effects based on 5S (Tanr6 et al., 1986) did not result in a significant improvement of the forest classification (Leu, 1991), no atmospheric correction was applied in this study. 2. Basis of the study
2.1. Selection of test sites and associated ground reference data The base dataset consists of a 7-band TM scene (194-27) of 3 July, 1985. Fall, winter or spring imagery is not suited for forest classification due to the lower sun angles which cast shadows, and the fact that the foliage of the various forest types is not fully developed. Within the selected cloud-free scene, the "Beckenried" site was selected, situated in the mountainous pre-Alps of the Canton of Nidwalden in Central Switzerland. The terrain elevation in the 12.0 km by 17.5 km test site varies from 434 to 2404 m with pronounced steep slopes. For this test site the green plates, containing the class forest, of the 1 : 50,000 Swiss Federal Office topographic maps were scanned. Additionally, maps of forest stands were digitized which had been generated by the Swiss Sanasilva Project using colour-infrared air photographs at a scale of 1 : 10,000 and flown on 25 July, 1985 (353 ha) and 13 August, 1987 (572 ha). Thus, well timed ground reference information was available, which in part
ISPRS Journal of Photogrammetry and Remote Sensing, 48(4): 17-28 0924-2716/93/$06.00
© 1993 Elsevier Science Publishers B.V. All rights reserved.
]8
contained also information on forest type, degree of mixing, crown closure, growth status and vitality. The Beckenried forest area is a heterogeneous mixture of conifers and deciduous trees, there being only small patches of clearly discernible stands. Based on a study by D F V L R (1988), stands with less than 20% conifers were defined as deciduous forest, those with a ratio between 20% and 80% are called mixed forest, and stands with more than 80% conifers are referred to as coniferous forest.
ISPRS Journal of Photogrammetry and Remote Sensing
/] !
~
z
.\\,~//.
2.2. Digital elevation model (DEM) and related datasets For our test site a digital elevation model was available from the Swiss Federal Office of Topography with a resolution of 25 m in x and y and 0.1 m for elevation. It is based on the Swiss 1:25,000 topographic map "Beckenried" with a contour interval of 20 m. From this DEM datasets for slope, aspect and illumination, as well as masks for cast-shadow and self-shadow, were generated. According to Goodenough et al. (1990), slope and aspect should not be derived at a resolution higher than 4.29 times the contour interval of the source map. This requirement cannot be met in our case, since we would need a contour interval of about 6 m to reach a grid size of 25 m. Nevertheless, we considered it useful to assess the power and applicability of some of today's available correction algorithms. Basic to any ra6iometric terrain correction is the illumination. It is defined as the cosine of the incident solar angle, thus representing the proportion of the direct solar radiation hitting a pixel. The illumination is therefore depending on the relative orientation of the pixel towards the sun's actual position (see Fig. 1). All datasets used in this study have been geocoded to the rectangular coordinate system of the Swiss topographic maps. This rectification also included geometric correction of relief displacement due to variations in terrain elevation (Itten and Meyer, 1993). In contrast to the treatment of data from large field-of-view sensors such as NOAA/AVHRR, with TM geometric and radiometric corrections may be performed independently one after another (Woodham and Lee. 1985). In order to keep the Digital Numbers of the scene unchanged a nearest neighbour resam-
Figure 1. Representation of the sun's angle of incidence i and the solar zenith angle sz. piing algorithm instead of an often applied cubic convolution technique was used (Meyer, 1992). 3. Radiometric corrections
Digital Numbers (DN) representing the radiance measured by a sensor such as the Thematic Mapper and registered by its system, cannot be referred only to reflective and emission properties of the observed objects. They are influenced by additional radiometric effects. Teillet (1986) subdivides them into two major categories: sensor-induced effects and scene-related effects. Sensor-induced effects summarize technical aspects such as calibration of detectors, filtering, platform and system stability, etc. Scene-related effects include the influence of topography, atmosphere, viewing angle, adjacency effect, position of the sun and the reflectance properties of the objects. Both, sensor- and scene-related effects were treated in this study. As tested by Sandmeier (1991), however, the radiometric variance of the sensor induced effects in our scene was within a limit of ±1 DN for the detector calibration mean. The scene could therefore be left unchanged from the aspect of sensor-induced effects (NASA, 1982). Within the scene-related effects, the study focussed on the impact and correction of illumination which are described with regard to their physical soundness and their influence on classifi-
19
Volume 48, number 4, 1993
cation results, as well as on the visual appearance of the scene. Extensive tests with the atmospheric correction code 5S (Tanr6 et al., 1986) did not yield a significant improvement of the forest classification in our scene and were no longer considered. This may be due to the fairly clear weather condition during the overflight with horizontal visibilities of 25 km in the valleys and over 70 km in the mountain area (Leu, 1991). A correction of the viewing angle, a so-called path length correction, was also not necessary. The two paths limiting the rather small test site in the east-west direction differ by only 1.7 km from each other. This corresponds to 0.24% of the average path length. Therefore the influence of this effect was neglected. When processing a full TM scene, however, this factor may have to be reexamined. 3.1. Slope-aspect correction
Neglecting the atmospheric influence and the adjacency effects we can state that in the visible and near-infrared bands the direct sun radiation is the only illuminating factor. If the terrain were additionally completely flat and all objects had a Lambertian reflection characteristic, the reflected energy measured by a sensor (radiance) would only depend on the direct irradiance and the reflectance of the objects on the surface. However, most objects, including forest, have a non-Lambertian reflectance characteristic. Also the effects of topography on scene radiance cannot be neglected in an alpine region and have to be taken into account in several regards: (1) the optical thickness is elevation-dependent; (2) targets may lie in the cast-shadow of surrounding hills or mountains; (3) slopes have a brightening effect on adjacent targets (imagine a deep valley which is brightened by the reflection of snow-covered slopes); (4) the irradiance on a pixel is highly dependent on the sun-target geometry (slope-aspect effect) This study focussed on the correction of slopeaspect effects. The influence of adjacent slopes (topographic adjacency correction) and optical thickness are neglected. Also cast-shadows are not handled and are masked out since only few pixels of the test site lay in cast-shadowed areas during the time of overflight. A Lambertian reflection characteristic, however, is only assumed in one of four approaches under investigation.
3.2. A i m
An ideal slope-aspect correction removes all topographically induced illumination variation so that two objects having the same reflectance properties show the same Digital Number despite their different orientation to the sun's position. As a visible consequence the three-dimensional relief impression of a scene gets lost and the image looks flat. 3.3. Correction methods
The four following slope-aspect correction methods as described by Teillet et al. (1982) were tested: a statistic-empirical correction method, a cosine correction, and two semi-empirical methods the Minnaert method and the C-correction. They will be presented in view of their simplicity in application and their effectiveness.
-
-
3.3.1. Statistic-empirical method A statistical approach such as used in this study is based on a significant correlation between a dependent and one or several independent variables. With the help of a regression function the influence of the independent variables can be corrected. The quality of such a correction of course depends on the degree of explanation of the regression function. Assuming a linear correlation between the original band and the illumination, the influence of the direct radiation can be corrected as follows:
LH = LT -- COS(i) m -- b + LT
(1)
where: LH = radiance observed for horizontal surfa_cce; LT = radiance observed over sloped terrain; LT = average of LT for forested pixels (according to ground reference data); i = sun incidence angle in relation to the normal on a pixel (Fig. 1); m = inclination of the regression line; b = intercept of regression line. The application of eq. 1 effects a rotation of the regre____sssionline into the horizontal at the elevation of La-. A specific object is independent of cos(i) and shows the same Digital Number throughout the scene. The position of LH is secondary. Figures 2 and 3 illustrate the linear regression between the original band 2 and the illumination and between the statistic-empirical corrected band 2 and the illumination, respectively.
ISPRS Journal
20
of Photogrammetry and Remote Sensing
al., 1982). Only the part cos(i)- Ei of the total incoming irradiance Ei reaches the inclined pixel. Ei is dependent of the solar constant and the distance between sun and earth: The cosine law, however, only takes the sun's position into account in the form of the sun's zenith angle, assuming the solar constant and the distance between sun and earth to be constant for all scenes.
60 50 ,~ 40
Z
o 30
~3o
Or- . . . . .
0
r
20
40
60
80
100
ILLUMINATION ( c o s ( I ) . 100)
Figure 2. Linear regression of illumination versus original band 2 in forest according to ground reference data.
60 Q
~50
(J
~4o O
,,=,3o
~20 o
cos(sz) LT-cos(i)
LF~ =
10
I
1°l o
0
20
40
60
80
(2)
where: LH = radiance observed tbr horizontal surface; LT = radiance observed over sloped terrain; sz = sun's zenith angle; i = sun's incidence angle in relation to the normal on a pixel (Fig. 1) Thus, for the correction of slope-aspect effects with the cosine approach, only data on the sun's zenith angle and illumination are needed. The cosine correction only models the direct part of the irradiance. Weakly illuminated regions, however, receive a considerable amount of diffuse irradiance. On such areas, the cosine correction has a disproportional brightening effect. The smaller cos(i), the stronger this overcorrection is (Fig. 4). For pixels in complete self-shadow (cos(i) = 0), where a division by 0 occurs when applying eq. 2, and in faintly illuminated areas, the Digital Numbers saturate and lead to artefacts in the corrected image as can be seen in the top-right image of Fig. 8.
100
ILLUMINATION (cos(i)- 100)
Figure 3. Linear regression of illumination versus band 2 statistic-empirical corrected in forest according to ground reference data.
60
~50 3.3.2. Cosine correction The cosine correction is often applied in flat terrain to equalize illumination differences due to the different sun positions in multitemporal datasets. It is a strongly trigonometric approach based on a basic physical law assuming a Lambertian reflection characteristic of objects and neglecting the presence of an atmosphere. According to Fig. 1, the amount of irradiance reaching an inclined pixel is proportional to the cosine of the incidence angle i, where i is defined as the angle between the normal on the pixel in question and the zenith direction (Teillet et
==40 O ¢3
~E 3 o ¢/) O O
20 z
m lO
i
0
20
40 60 80 ILLUMINATION (cos(i)- 100)
100
Figure 4. Linear regression of illumination versus band 2 cosine-corrected in forest according to ground reference data.
Volume 48, number 4, 1993
21
3.3.4. C-correction
Teillet et al. (1982) describe the possibility of bringing the original data into the form LT = m cos(i) + b. This corresponds to a regression line used in the statistical-empirical approach with the original Digital Number on the ordinate and cos(i) on the abscissa. Teillet et al. (1982) now introduce a parameter c which is the quotient of b and m of the regression line. Parameter c is built in the cosine law as an additive term:
el,
840 ~ao Z
z = 20 0
z
lo
b c = -m
0 0
20
40
60
80
100
fcos(sz)_+c]
ILLUMINATION (coa (I). 100)
(5)
LIj = LT L cos(i) + c _]
Figure 5. Linear regression of illumination versus band 2 Minnaert-corrected in forest according to ground reference data.
3.3.3. Minnaert correction
The name Minnaert correction is derived from the Belgian astrophysicist Marell G.J. Minnaert (1941). In connection with his investigations of the lunar light, he modified the common cosine correction by adding a constant k: r cos(sz) ]k
LH = LT L cos(i) I
(4)
(3)
where: LH = radiance observed for horizontal surface; LT = radiance observed over sloped terrain; sz = sun's zenith angle; i = sun's incidence angle in relation to the normal on a pixel (Fig. 1); k = Minnaert constant. Parameter k has become known as the Minnaert constant and is considered to be a measure of the extent to which a surface is Lambertian, in which case k = 1. In general, k is also a function of the phase angle, but this dependence has only to be considered when using multitemporal or multisensor datasets (Teillet et al., 1982). The values of k varies between 0 and 1. The smaller the k, the weaker is the influence of the quotient in eq. 3. Especially in areas with a cos(i) near 0, k increases the denominator and prevents a division by small values. Thus one can counteract an overcorrection as obtained in the common cosine correction (Figs. 4 and 5). Parameter k can be determined empirically by linearizing eq. 3 logarithmically and estimating the slope of a linear regression.
where: c = correction parameter; m = inclination of regression line; b = intercept of regression line; LIj = radiance observed for horizontal surface; L-r = radiance observed over sloped terrain; sz = sun's zenith angle; i = sun's incidence angle in relation to the normal on a pixel (Fig. 1). According to Teillet et al. (1982) the parameter c might emulate the effect of path radiance on the slope-aspect correction, but the physical analogies are not exact. Mathematically, the effect of c is similar to that of the Minnaert constant. It increases the denominator and weakens the overcorrection of faintly illuminated pixels as a consequence (Fig. 6). Parameter c is determined with the same regression that was used in the statistical-empirical approach.
uJ I:g nO
o 0O
6
,~ 20
Z
!o
10
0 0
20
40
ILLUMINATION
60
8O
100
( c o s (I). 1 0 0 )
Figure 6. Linear regression of illumination versus band 2 Ccorrected in forest according to ground reference data.
ISPRS Journal of Photograrnmetry and Remote Sensing
22
3. 4. Overview of the./'our methods and their basic differences
4. Evaluation of slope-aspect corrections
Table 1 gives a summary on the basic characteristics of the presented slope-aspect correction methods. The parameters given in the third column are the actual correction values used in this study. They are determined empirically by estimating slope and intercept of a linear regression between illumination (cos(i) x 100) and the corresponding TM-band, as described in Sect. 3.3. Therefore, the parameters are specific to the chosen scene and test site and furthermore optimized on forests. They may not be applied to another scene or test site without adaption.
1ABLE
The usefulness of the slope-aspect corrections has been tested statistically, visually and in regard to their influence on a forest versus non-forest classification. All tests were based on the whole Beckenried test area (338,624 pixels). In general, it can be stated that only a small difference between the results of the statistical, the Minnaert and the C-method is observable. For reasons of simplicity, these three correction approaches will be grouped and called SMC-methods hereafter. The simple cosine correction, on the other hand, shows remarkable differences for the SMC correction methods and has to be treated separately.
1
Overview on the tested "slope-aspect" correction methods including parameters u s e d to correct bands 2, 4 and 5
Correction Method Statistic-empirical correction LH=L'I -cos(i)'m
Remarks
Parameters
Purely statistical approach
1112
=
0.80
based on a linear relationship
b,
-
I t) 96
between the original band and
r2~
~-
(!.42
tile illumination. G e o m e t r i c a l l y
m4
::
7(}.90
Ihe c o r r e c t i o n
b4 r2
,:
";(L59
regression line to tile horizontal
:
0.42
Io remove |he i l l u n l i n a l i n n
I]1 .~
:
fi(L~O
b5
::
I ,~.h( J
r25
::
0.48
rotates
tile
dependence.
Cosine correction L H = L 1 c o s sz)! cox (i)
Trigonometric approach taking
n('~ p a r a m e t e r s
into a c c o u t l | the p o r t i o n o f
needed
direct irradiance on lhe reclined
surface
element
Objects
are
(pixelt.
regarded
as
Lumber|tan reflectors. Minnaert correction
Varialion
(semi-empirical)
correction by introduction of a
LtI= LT
cos (sz)'lk cos ( ) I
I
of
lhe
1tl7
cosine
0.39
Minnaerl conslanl, simulating
k4
the n o n - L a m b e r | t a n behaviour
1-24
o l the earth surface. With k=l
it is u normal cosine correction.
=
(148
k5
-
fl.54
r25
=
0.42
0.37
C-correction
Modification
c2
:=
2.03
i semi-empirical)
correction by a taclor c which
t.2~
=
H,42
~,hould m o d e l lhe diffuse sky
c4
=
O.40
radiation, c ix ba~,ed on tile
1-24
=
0.42
c5
-:
031
=cos (sz) + c t.H= L,r i cos(i) + c
regression
in
o f lhe c o s i n e
the statistic
empirical approach.
I r2~'
::
Volume 48, number 4, 1993
23
4.1. Statistical analysis The dynamics of data described by the standard deviation remains more or less constant for the SMC-corrected images compared to the uncorrected original. It is much higher, however, for the cosine correction. The Pearson correlation coefficient is very high between the uncorrected original band and the SMC-corrected images (r is about 0.97) and rather low between the uncorrected original and the cosine-corrected image (r is about 0.14) in all of the three bands under investigation. As the original band shows (apart from the disturbing illumination effect) mainly target information, it seems that the SMC-corrected images have a higher degree of target information than the cosine-corrected band. Under the assumption that the level of noise is not influenced by the correction algorithms, the SMC-corrected images are expected to be more authentic than the cosinecorrected one. The correlation between the corrected images and the illumination emphasizes this impression. Figures 2, 3 and 4 depict band 2 as a function of illumination for the statistic-empirical and the cosine-corrected image in comparison with the
original image including the corresponding linear regression lines. While the statistic-empirical corrected image (and with it all other SMC-corrected images) shows more or less independence of illumination, in the cosine-corrected image (Fig. 4) a drastic overcorrection of the weakly illuminated pixels is obvious. This is due to the unrealistic assumption, basic to that correction method, that only direct irradiance is present. Especially weakly illuminated pixels with a small incidence angle i exhibit a large amount of diffuse irradiance and are therefore amplified disproportionally by the cosine correction. Mathematically, this can be explained by division of a constant (cos(sz)) through a very small number (cos(i)) which is zero for a pixel lying in its self-shadow. In this case, the result of the correction is not defined (zero-division) and leads to artefacts in the corrected image. For this reason, Teillet et al. (1982) recommends the application of the cosine correction only in cases where the incidence angles are smaller than 55 °. Table 2 summarizes inclination (m), intercept (b) and coefficient of determination r 2 of the various correlations between the original and the corrected images on the one hand and the illumination file on the other. An ideal correction of
TABLE 2
Inclination m, intercept b and coefficient of determination r z for regressions between illumination and Digital Numbers in bands 21), 42) and 5 3) (Beckenried test site, forest after ground reference data, 95,356 pixels) test site Beckenried
inclination m
intercept b
coeff, of det. r2
original I)
9.8
20.0
0.4234
statistic-empiric, corr. I) cosine corrected I)
-4.1
31.9
0.0013
-101.6
109.9
0.1676
Minnaert corrected l) C-corrected I)
0.8
27.5
0.0033
-0.7
28.9
0.0036
original 2)
76.9
30.6
0.4187
8.5
68.0
0.0087
-173.3
234.4
0.1155
4.4
91.2
0.0013
8.6
88.4
0.0063
60.3
18.6
0.4770
6.5
53.6
0.0107
-107,4
155.1
0.1049
2,5
66.6
0.0008
5.1
64.9
0.0042
statistic-empiric, corr. 2) cosine corrected 2) Minnaert corrected 2) C-corrected 2) original 3) statistic-empiric, corr. 3) cosine corrected 3) Minnaert corrected 3) C-corrected 3)
24
the illumination effect would lead to an r 2 of zero so that the zero hypothesis "the inclination of the regression line is equal to 0" could no longer be rejected. In all three analysed bands 2, 4 and 5, r 2 can be reduced by the SMC-methods by a maximum from 0,4770 in the original band 5 to 0.0008 in the Minnaert-corrected band 5. The effect of the other SMC-methods are similar in all of the three bands investigated. The success of the illumination correction can therefore be verified statistically for the SMC-methods. The r 2 values for the cosine correction are much higher though they are still smaller than those of the original bands. As Fig. 4 shows, the cosine correction leads to a regression of second degree rather than to an elimination of the regression. However, the r 2 values are quite small even for the linear regression in spite of the insufficient correction of the illumination effect.
4.2. Visual analysis A comparison between the original band 2 and the statistic-empirical corrected band 2 shows a reduction of the relief effect (Fig. 7). This leads to a loss of the three-dimensional impression in the illumination-corrected image. It becomes flat and more or less homogeneous in regions of identical objects. The appearance of forests, for instance, becomes much more independent of topography than in the original (uncorrected) bands. This visual effect is more impressive in a nearinfrared band than in a visible one. As the impact of the atmosphere is much stronger in the visible part of the electromagnetic spectrum than in the near-infrared, the influence of diffuse irradiance is much more important. Thus, especially in sparsely illuminated pixels, the effect of the illumination correction is reduced by the smearing effect of the atmosphere so that the illumination correction could only be examined properly after an atmospheric correction. As expected, the illumination correction with the SMC-methods is much more efficient than the classical cosine correction which is unsuitable in such a rugged terrain. Figure 8 (top right) demonstrates the inadequate correction of the illumination effect and the artefacts along the mountain ridges due to the zero division for pixels in selfshadow. These artefacts can be observed in the
ISPRS Journal of Photogrammetry and Remote Sensing
Minnaert and C-corrected images as well; however, the overcorrection of the cosine approach is reduced to a large amount by both the Minnaert constant and parameter c (Fig. 8). Cast-shadows are not handled with this correction method and appear dark. A special treatment of these pixels would be necessary.
4.3. Impact on classification After illumination correction it is assumed that the influence of scene-related effects is reduced in favour of the intrinsic reflection properties of objects. Therefore, an increase in classification accuracy can be expected. Based on experiences by Leu (1991), a parallel epiped algorithm was chosen to examine the effect of illumination correction on a forest versus nonforest and forest stand classification using bands 2, 4 and 5. The determination of the parallel epiped limits are fully based on ground reference information. Therefore, the classification results are not influenced by operator inaccuracies in choosing training areas. Table 3 shows the results of the classification. The classification accuracy is defined as the sum of all correctly classified pixels (be it forest and nonforest for the forest versus non-forest classification or coniferous, mixed and deciduous for the stand classification) divided by the total number of pixels in the test site. At first glance, the classification accuracies achieved by performing the radiometric corrections seem to be discouraging. It has to be kept in mind, however, that the radiometric corrections may improve the classification results in small problem regions, such as sparsely or brightly illuminated areas. For an evaluation of whether these problem regions were better classified after a correction, the achieved accuracies for no correction and slope-aspect correction were calculated for the forest versus non-forest case (Table 4) as well as for the stand/forest type classification (Table 5). The slope-aspect correction improves the accuracy of the forest versus non-forest classification in faintly illuminated areas, without having an adverse effect on the sunny areas. The rather small overall improvement of 1% is due to the fact that only 27% of the pixets are faintly illuminated having a cos(i) < 0.6. In fact, if areas having a cos(i) < 0.6 are examined, an improvement of
25
Volume 48, number 4, 1993
Figure
7. Uncorrected
band 4, Beckenried
test site (top) and statistic-empirical
corrected
band 4, Beckenried
test site (bottom).
26
ISPRS Journal of Photogrammetly and Remote Sensing
Figure 8. Detail presentation of band 4 within the Beckenried test site. Top left: statistic-empirical corrected. Top right:: cosine-corrected. Bottom left: C-corrected. Bottom right: Minnaert-corrected.
Volume 48, number 4, 1993
27
TABLE 3 Accuracies for the forest versus non-forest and forest stand classification before and after the four slope-aspect corrections classification
original,
star.- emp.
cosine
Minnaert
accuracies
uncorrected
corrected
corrected
corrected
forest versus
86.01%
87.35 %
54.87 %
58.64 %
77.95 %
C-corrected
87.60 %
86.98 %
60,40 %
61.81%
non-forest forest stands TABLE 4 Accuracies of the forest versus non-forest classification in the Beckenried test site in relation to the illumination after slope-aspect C-correction (100% = 338,624 pixels) illumination
in % of the testarea
classific, accuracy
[cos (i).100]
Beckenried
original TM bands
C-correction
10
0.56 %
53,15 %
59.18 %
+ 6.03 %
1 I to 20
0.99 %
67.86 %
68.67 %
+0.81%
21 to 30
1.91%
76.13 %
76.00 %
-0.12%
31 to 40
3.80 %
78.19 %
80.61%
+ 2.42 %
41 to 50
6.40 %
76.18 %
82.12 %
+ 5.95 %
51 to 60
7.70 %
77.00 %
82.16 %
+5.16%
61 to 70
9.59 %
81.52 %
82.45 %
+ 0.94 %
71 to 80
i2.27 %
86.06 %
84.23 %
- 1.83 %
81 to 90
41.01%
94.28 %
94.10%
-0.17%
91 to 100
15.77 %
82.64 %
84.05 %
+ 1.41%
Ito
classific, accuracy classification difference
TABLE 5 Accuracies of the stand/forest type classification in the Beckenried test site with respect to the illumination after slope-aspect C-correction (100% = 338,624 pixels) illumination
in % of the testarea
classific, accuracy
[cos (i). 100]
Beckenried
original TM bands
classific, accuracy classification C-correction
difference
10
1.79 %
60.51%
61.03 %
+0,51%
11 to 20
4.80 %
58.13 %
58.13 %
+ 0,00 %
21 to 30
11.10%
50.91%
58.18 %
+ 7.27 %
31 to 40
15.95 %
54.89 %
59.72 %
+ 4.83 %
41 to 50
20.32 %
60.86 %
61.81%
+ 0.95 %
51 to 60
14.26 %
59.91%
63.00 %
+ 3.09 %
61 to 70
9.65 %
53.23 %
63.21%
+ 9.98 %
71 to 80
8.58 %
47.38 %
60.21%
+ 12.83 %
81 to 90
9,25 %
48.91%
64.29 %
+ 15.38 %
91 to 100
429 %
44.44 %
74.57 %
+ 30.13 %
lto
average classification accuracy of approx. 5% is achieved. The reason why there is hardly any classification improvement in well illuminated areas may be that those regions dominate the test site and as a consequence the determination of the parallel epiped limits. Therefore, the classification is opti-
mized on bright areas regardless of a slope-aspect correction. In contrast, the positive influence of the slopeaspect correction on the stand/forest type classification is not only visible in the fainter illuminated parts, as found in the forest versus nonforest classification, but even more pronounced in
28
the brighter areas. Again the illumination classes which are underrepresented in the stand groundreference data are improved. A major improvement of between 10 and 30% could be achieved in the classification of stands in brightly illuminated areas with cos(i) > 0.6. Over the whole training area, a total improvement of the stand/forest type classification of 7% could be reached. In summary it can be stated, that the illumination correction markedly increases the accuracies of both the forest versus non forest, and the stand/ forest type classifications. 5. Conclusions Through the correction of scene-related radiometric effects, a classification accuracy of forests versus non-forests of almost 90% could be achieved in the Beckenried test area. The semiempirical C-correction method improved the classification accuracy of faintly illuminated areas by about 5%, while the statistical-empirical methods' improvement was inferior and the conventional cosine correction even proved to be useless for our test site. The accuracy improvement in the forest stand/ type classification using the C-correction method was between an impressive 10% and 30% for brightly illuminated areas. In the future one should concentrate more on physical models because the improvement potential of empirical and semi-empirical models is somewhat limited, and because the physical models allow for a better description of objects in nature (Woodham, 1989; Deering et al., 1990). More research is encouraged and needed on the bidirectional reflection distribution functions (BRDF) of objects, since the assumption of Lambertian surfaces is not adequate, especially for vegetated surfaces. Acknowledgements This project has greatly benefited from the experience gained in the SRSFM-Project (Swiss Remote Sensing Forest Mapping Project) at the Remote Sensing Laboratories of the Department of Geography, University of Zurich which started in 1988 and is supported by the Swiss Government, UNEP/GRID and ESA. The permission to use the digital elevation model (DHM-25), issued by the
ISPRS Journal oj Photogrammetry and Remote Sensmg
Swiss Federal Institute of "Ibpography, for this research is greatly appreciated. The results reported here are mainly based on the MSc Theses of St. Sandmeier (1991) and R. Sandmeier-Leu (1991). The geometric corrections were carried out by P. Bitter and T. Kellenberger. References DFVLR, 1988. Waldkartierung mit Satellitendaten im Kartenblatt T 0 K 200 Regensburg. Forschungsbericht Nr. 2/88, Deutsche Forschungs- und Versuchsanstalt ftir Luft- und Raumfahrt (DLR), Oberpfaffenhofen, 16 pp. Deering, D.W., Eck, T.E and Otterman, J., 1990. Bidirectional reflectances of selected desert surfaces and their threeparameter soil characterization. Agric. For. Meteorol., 52: 71-93. Goodenough, D.G., Deguise, J.-C. and Robson, M.A., 199t). Multiple expert systems for using digital terrain models. Proc. IGARSS '90 Symp., Washington, D.C., p. 961. ltten, K.I. and Meyer, P.. 1993. Geometric and Radiometric Correction of TM-Data of Mountainous Forested Areas. IEEE Transactions on Geoscience and Remote Sensing, in press. Lcu, R., 1991. Digitale Kartierung des Schweizer Waldes mit Landsat TM-Daten, Teil 13. MSc Thesis, Dept. of Geography, University of Zurich, 145 pp. Meyer, P., 1992. Empirical quality assessment: effect of resampiing on geometric and radiometric data quality using a region-based approach. Proc. IGARSS '92 Symp., Houston, Texas, pp. 1481-1483. Minnaert, N., 1941. The reciprocity principle in lunar photometry. Astrophys. J., 93: 403-410. NASA, 1982. Landsat Data Users Notes. Issue No. 23. U.S. Geological Survey, EROS Data Center, Sioux Falls, S.D. Sandmeier, St., 1991. Digitale Kartierung des Schweizer Waldes mit Landsat TM-Daten, Teil A. MSc Thesis, Dept. of Geography, University of Zurich, 144 pp. q~anr6, D., Deroo, C,, Duhaut, P., Herman, M., Morcrette, J.J., Perbos, J. and Deschamps, EY., 1986. Description of a computer code to simulate the satellite signal in the solar spectrum: the 5S code. Int. J. Remote Sensing, 11(4): 659-668. Teillet, EM., Guindon, B. and Goodenough, D.G., 1982. On the slope-aspect correction of multispectral scanner data. Can. J. Remote Sensing, 8(2): 84-106. Teillet, EM., 1986. Image correction for radiometric effects in remole sensing. Int. J. Remote Sensing, 7(12): 1637-1651. Woodham, R.J. and Lee, TK., 1985. Photometric method for radiometric correction of multispectral scanner data. Can. J. Remote Sensing, 11(2): 132-16 I. Woodham, R.J., 1989. Determining intrinsic surface reflectance in rugged terrain and changing illumination. Proc. IGARSS '89 Syrup., Vancouver, pp. 1-5. (Received August 24, 1992; revised and accepted January 5. 1993 )
17
P e t e r M e y e r 1,., K l a u s I. I t t e n 1, Tobias K e l l e n b e r g e r 1, S t e f a n S a n d m e i e r 1 and Ruth Sandmeier 1
Radiometric corrections of topographically induced effects on Landsat TM data in an alpine environment Four radiometric correction methods for the reduction of slope-aspect effects in a Landsat TM data set are tested in a mountainous test site with regard to their physical soundness and their influence on forest classification, as well as on the visual appearance of the scene. Excellent ground reference information and a fine-resolution DEM allowed precise assessment of the applicability of the methods under investigation. The results of the study presented here demonstrate the weakness of the classical cosine correction method for radiometric correction in rugged terrain. The statistical, Minnaert and C-correction approaches, however, yielded an improvement of the forest classification and an impressive reduction of the visual topography effect.
1. Introduction
The overutilization of tropical forests as well as the problems of deterioration of the health of forests in mid latitudes, have warned mankind that an important ecological factor, i.e., an important natural resource is endangered and may not be so renewable as was anticipated. In recent years, much emphasis was laid on the mapping and inventorying of forests and forest damage. On a local level, colour-infrared air photographs have been used with great success, and on larger scales, be they regional, continental or even global, satellite studies show quite encouraging results. In this study the feasibility of Landsat TM forest classifications in an alpine environment is tested versus excellent ground reference data. It has been shown in the past that terrain-induced illumination variations have hindered an easy and straightforward solution of the distinction of forests versus non-forest backgrounds, and also to separate a forest into its major classes. Four methods to correct the impact of illumination have been tested in order to improve the accuracy of forest classifications. Since a correction of the atI Remote Sensing Laboratories, Department of Geography, University of Zurich-lrchel CH-8057 Zurich, Switzerland. * Present address: Jet Propulsion Laboratory, California Institute of Technology, MS 169-315, 4800 Oak Groove Drive, Pasadena, CA 91109, USA.
mospheric effects based on 5S (Tanr6 et al., 1986) did not result in a significant improvement of the forest classification (Leu, 1991), no atmospheric correction was applied in this study. 2. Basis of the study
2.1. Selection of test sites and associated ground reference data The base dataset consists of a 7-band TM scene (194-27) of 3 July, 1985. Fall, winter or spring imagery is not suited for forest classification due to the lower sun angles which cast shadows, and the fact that the foliage of the various forest types is not fully developed. Within the selected cloud-free scene, the "Beckenried" site was selected, situated in the mountainous pre-Alps of the Canton of Nidwalden in Central Switzerland. The terrain elevation in the 12.0 km by 17.5 km test site varies from 434 to 2404 m with pronounced steep slopes. For this test site the green plates, containing the class forest, of the 1 : 50,000 Swiss Federal Office topographic maps were scanned. Additionally, maps of forest stands were digitized which had been generated by the Swiss Sanasilva Project using colour-infrared air photographs at a scale of 1 : 10,000 and flown on 25 July, 1985 (353 ha) and 13 August, 1987 (572 ha). Thus, well timed ground reference information was available, which in part
ISPRS Journal of Photogrammetry and Remote Sensing, 48(4): 17-28 0924-2716/93/$06.00
© 1993 Elsevier Science Publishers B.V. All rights reserved.
]8
contained also information on forest type, degree of mixing, crown closure, growth status and vitality. The Beckenried forest area is a heterogeneous mixture of conifers and deciduous trees, there being only small patches of clearly discernible stands. Based on a study by D F V L R (1988), stands with less than 20% conifers were defined as deciduous forest, those with a ratio between 20% and 80% are called mixed forest, and stands with more than 80% conifers are referred to as coniferous forest.
ISPRS Journal of Photogrammetry and Remote Sensing
/] !
~
z
.\\,~//.
2.2. Digital elevation model (DEM) and related datasets For our test site a digital elevation model was available from the Swiss Federal Office of Topography with a resolution of 25 m in x and y and 0.1 m for elevation. It is based on the Swiss 1:25,000 topographic map "Beckenried" with a contour interval of 20 m. From this DEM datasets for slope, aspect and illumination, as well as masks for cast-shadow and self-shadow, were generated. According to Goodenough et al. (1990), slope and aspect should not be derived at a resolution higher than 4.29 times the contour interval of the source map. This requirement cannot be met in our case, since we would need a contour interval of about 6 m to reach a grid size of 25 m. Nevertheless, we considered it useful to assess the power and applicability of some of today's available correction algorithms. Basic to any ra6iometric terrain correction is the illumination. It is defined as the cosine of the incident solar angle, thus representing the proportion of the direct solar radiation hitting a pixel. The illumination is therefore depending on the relative orientation of the pixel towards the sun's actual position (see Fig. 1). All datasets used in this study have been geocoded to the rectangular coordinate system of the Swiss topographic maps. This rectification also included geometric correction of relief displacement due to variations in terrain elevation (Itten and Meyer, 1993). In contrast to the treatment of data from large field-of-view sensors such as NOAA/AVHRR, with TM geometric and radiometric corrections may be performed independently one after another (Woodham and Lee. 1985). In order to keep the Digital Numbers of the scene unchanged a nearest neighbour resam-
Figure 1. Representation of the sun's angle of incidence i and the solar zenith angle sz. piing algorithm instead of an often applied cubic convolution technique was used (Meyer, 1992). 3. Radiometric corrections
Digital Numbers (DN) representing the radiance measured by a sensor such as the Thematic Mapper and registered by its system, cannot be referred only to reflective and emission properties of the observed objects. They are influenced by additional radiometric effects. Teillet (1986) subdivides them into two major categories: sensor-induced effects and scene-related effects. Sensor-induced effects summarize technical aspects such as calibration of detectors, filtering, platform and system stability, etc. Scene-related effects include the influence of topography, atmosphere, viewing angle, adjacency effect, position of the sun and the reflectance properties of the objects. Both, sensor- and scene-related effects were treated in this study. As tested by Sandmeier (1991), however, the radiometric variance of the sensor induced effects in our scene was within a limit of ±1 DN for the detector calibration mean. The scene could therefore be left unchanged from the aspect of sensor-induced effects (NASA, 1982). Within the scene-related effects, the study focussed on the impact and correction of illumination which are described with regard to their physical soundness and their influence on classifi-
19
Volume 48, number 4, 1993
cation results, as well as on the visual appearance of the scene. Extensive tests with the atmospheric correction code 5S (Tanr6 et al., 1986) did not yield a significant improvement of the forest classification in our scene and were no longer considered. This may be due to the fairly clear weather condition during the overflight with horizontal visibilities of 25 km in the valleys and over 70 km in the mountain area (Leu, 1991). A correction of the viewing angle, a so-called path length correction, was also not necessary. The two paths limiting the rather small test site in the east-west direction differ by only 1.7 km from each other. This corresponds to 0.24% of the average path length. Therefore the influence of this effect was neglected. When processing a full TM scene, however, this factor may have to be reexamined. 3.1. Slope-aspect correction
Neglecting the atmospheric influence and the adjacency effects we can state that in the visible and near-infrared bands the direct sun radiation is the only illuminating factor. If the terrain were additionally completely flat and all objects had a Lambertian reflection characteristic, the reflected energy measured by a sensor (radiance) would only depend on the direct irradiance and the reflectance of the objects on the surface. However, most objects, including forest, have a non-Lambertian reflectance characteristic. Also the effects of topography on scene radiance cannot be neglected in an alpine region and have to be taken into account in several regards: (1) the optical thickness is elevation-dependent; (2) targets may lie in the cast-shadow of surrounding hills or mountains; (3) slopes have a brightening effect on adjacent targets (imagine a deep valley which is brightened by the reflection of snow-covered slopes); (4) the irradiance on a pixel is highly dependent on the sun-target geometry (slope-aspect effect) This study focussed on the correction of slopeaspect effects. The influence of adjacent slopes (topographic adjacency correction) and optical thickness are neglected. Also cast-shadows are not handled and are masked out since only few pixels of the test site lay in cast-shadowed areas during the time of overflight. A Lambertian reflection characteristic, however, is only assumed in one of four approaches under investigation.
3.2. A i m
An ideal slope-aspect correction removes all topographically induced illumination variation so that two objects having the same reflectance properties show the same Digital Number despite their different orientation to the sun's position. As a visible consequence the three-dimensional relief impression of a scene gets lost and the image looks flat. 3.3. Correction methods
The four following slope-aspect correction methods as described by Teillet et al. (1982) were tested: a statistic-empirical correction method, a cosine correction, and two semi-empirical methods the Minnaert method and the C-correction. They will be presented in view of their simplicity in application and their effectiveness.
-
-
3.3.1. Statistic-empirical method A statistical approach such as used in this study is based on a significant correlation between a dependent and one or several independent variables. With the help of a regression function the influence of the independent variables can be corrected. The quality of such a correction of course depends on the degree of explanation of the regression function. Assuming a linear correlation between the original band and the illumination, the influence of the direct radiation can be corrected as follows:
LH = LT -- COS(i) m -- b + LT
(1)
where: LH = radiance observed for horizontal surfa_cce; LT = radiance observed over sloped terrain; LT = average of LT for forested pixels (according to ground reference data); i = sun incidence angle in relation to the normal on a pixel (Fig. 1); m = inclination of the regression line; b = intercept of regression line. The application of eq. 1 effects a rotation of the regre____sssionline into the horizontal at the elevation of La-. A specific object is independent of cos(i) and shows the same Digital Number throughout the scene. The position of LH is secondary. Figures 2 and 3 illustrate the linear regression between the original band 2 and the illumination and between the statistic-empirical corrected band 2 and the illumination, respectively.
ISPRS Journal
20
of Photogrammetry and Remote Sensing
al., 1982). Only the part cos(i)- Ei of the total incoming irradiance Ei reaches the inclined pixel. Ei is dependent of the solar constant and the distance between sun and earth: The cosine law, however, only takes the sun's position into account in the form of the sun's zenith angle, assuming the solar constant and the distance between sun and earth to be constant for all scenes.
60 50 ,~ 40
Z
o 30
~3o
Or- . . . . .
0
r
20
40
60
80
100
ILLUMINATION ( c o s ( I ) . 100)
Figure 2. Linear regression of illumination versus original band 2 in forest according to ground reference data.
60 Q
~50
(J
~4o O
,,=,3o
~20 o
cos(sz) LT-cos(i)
LF~ =
10
I
1°l o
0
20
40
60
80
(2)
where: LH = radiance observed tbr horizontal surface; LT = radiance observed over sloped terrain; sz = sun's zenith angle; i = sun's incidence angle in relation to the normal on a pixel (Fig. 1) Thus, for the correction of slope-aspect effects with the cosine approach, only data on the sun's zenith angle and illumination are needed. The cosine correction only models the direct part of the irradiance. Weakly illuminated regions, however, receive a considerable amount of diffuse irradiance. On such areas, the cosine correction has a disproportional brightening effect. The smaller cos(i), the stronger this overcorrection is (Fig. 4). For pixels in complete self-shadow (cos(i) = 0), where a division by 0 occurs when applying eq. 2, and in faintly illuminated areas, the Digital Numbers saturate and lead to artefacts in the corrected image as can be seen in the top-right image of Fig. 8.
100
ILLUMINATION (cos(i)- 100)
Figure 3. Linear regression of illumination versus band 2 statistic-empirical corrected in forest according to ground reference data.
60
~50 3.3.2. Cosine correction The cosine correction is often applied in flat terrain to equalize illumination differences due to the different sun positions in multitemporal datasets. It is a strongly trigonometric approach based on a basic physical law assuming a Lambertian reflection characteristic of objects and neglecting the presence of an atmosphere. According to Fig. 1, the amount of irradiance reaching an inclined pixel is proportional to the cosine of the incidence angle i, where i is defined as the angle between the normal on the pixel in question and the zenith direction (Teillet et
==40 O ¢3
~E 3 o ¢/) O O
20 z
m lO
i
0
20
40 60 80 ILLUMINATION (cos(i)- 100)
100
Figure 4. Linear regression of illumination versus band 2 cosine-corrected in forest according to ground reference data.
Volume 48, number 4, 1993
21
3.3.4. C-correction
Teillet et al. (1982) describe the possibility of bringing the original data into the form LT = m cos(i) + b. This corresponds to a regression line used in the statistical-empirical approach with the original Digital Number on the ordinate and cos(i) on the abscissa. Teillet et al. (1982) now introduce a parameter c which is the quotient of b and m of the regression line. Parameter c is built in the cosine law as an additive term:
el,
840 ~ao Z
z = 20 0
z
lo
b c = -m
0 0
20
40
60
80
100
fcos(sz)_+c]
ILLUMINATION (coa (I). 100)
(5)
LIj = LT L cos(i) + c _]
Figure 5. Linear regression of illumination versus band 2 Minnaert-corrected in forest according to ground reference data.
3.3.3. Minnaert correction
The name Minnaert correction is derived from the Belgian astrophysicist Marell G.J. Minnaert (1941). In connection with his investigations of the lunar light, he modified the common cosine correction by adding a constant k: r cos(sz) ]k
LH = LT L cos(i) I
(4)
(3)
where: LH = radiance observed for horizontal surface; LT = radiance observed over sloped terrain; sz = sun's zenith angle; i = sun's incidence angle in relation to the normal on a pixel (Fig. 1); k = Minnaert constant. Parameter k has become known as the Minnaert constant and is considered to be a measure of the extent to which a surface is Lambertian, in which case k = 1. In general, k is also a function of the phase angle, but this dependence has only to be considered when using multitemporal or multisensor datasets (Teillet et al., 1982). The values of k varies between 0 and 1. The smaller the k, the weaker is the influence of the quotient in eq. 3. Especially in areas with a cos(i) near 0, k increases the denominator and prevents a division by small values. Thus one can counteract an overcorrection as obtained in the common cosine correction (Figs. 4 and 5). Parameter k can be determined empirically by linearizing eq. 3 logarithmically and estimating the slope of a linear regression.
where: c = correction parameter; m = inclination of regression line; b = intercept of regression line; LIj = radiance observed for horizontal surface; L-r = radiance observed over sloped terrain; sz = sun's zenith angle; i = sun's incidence angle in relation to the normal on a pixel (Fig. 1). According to Teillet et al. (1982) the parameter c might emulate the effect of path radiance on the slope-aspect correction, but the physical analogies are not exact. Mathematically, the effect of c is similar to that of the Minnaert constant. It increases the denominator and weakens the overcorrection of faintly illuminated pixels as a consequence (Fig. 6). Parameter c is determined with the same regression that was used in the statistical-empirical approach.
uJ I:g nO
o 0O
6
,~ 20
Z
!o
10
0 0
20
40
ILLUMINATION
60
8O
100
( c o s (I). 1 0 0 )
Figure 6. Linear regression of illumination versus band 2 Ccorrected in forest according to ground reference data.
ISPRS Journal of Photograrnmetry and Remote Sensing
22
3. 4. Overview of the./'our methods and their basic differences
4. Evaluation of slope-aspect corrections
Table 1 gives a summary on the basic characteristics of the presented slope-aspect correction methods. The parameters given in the third column are the actual correction values used in this study. They are determined empirically by estimating slope and intercept of a linear regression between illumination (cos(i) x 100) and the corresponding TM-band, as described in Sect. 3.3. Therefore, the parameters are specific to the chosen scene and test site and furthermore optimized on forests. They may not be applied to another scene or test site without adaption.
1ABLE
The usefulness of the slope-aspect corrections has been tested statistically, visually and in regard to their influence on a forest versus non-forest classification. All tests were based on the whole Beckenried test area (338,624 pixels). In general, it can be stated that only a small difference between the results of the statistical, the Minnaert and the C-method is observable. For reasons of simplicity, these three correction approaches will be grouped and called SMC-methods hereafter. The simple cosine correction, on the other hand, shows remarkable differences for the SMC correction methods and has to be treated separately.
1
Overview on the tested "slope-aspect" correction methods including parameters u s e d to correct bands 2, 4 and 5
Correction Method Statistic-empirical correction LH=L'I -cos(i)'m
Remarks
Parameters
Purely statistical approach
1112
=
0.80
based on a linear relationship
b,
-
I t) 96
between the original band and
r2~
~-
(!.42
tile illumination. G e o m e t r i c a l l y
m4
::
7(}.90
Ihe c o r r e c t i o n
b4 r2
,:
";(L59
regression line to tile horizontal
:
0.42
Io remove |he i l l u n l i n a l i n n
I]1 .~
:
fi(L~O
b5
::
I ,~.h( J
r25
::
0.48
rotates
tile
dependence.
Cosine correction L H = L 1 c o s sz)! cox (i)
Trigonometric approach taking
n('~ p a r a m e t e r s
into a c c o u t l | the p o r t i o n o f
needed
direct irradiance on lhe reclined
surface
element
Objects
are
(pixelt.
regarded
as
Lumber|tan reflectors. Minnaert correction
Varialion
(semi-empirical)
correction by introduction of a
LtI= LT
cos (sz)'lk cos ( ) I
I
of
lhe
1tl7
cosine
0.39
Minnaerl conslanl, simulating
k4
the n o n - L a m b e r | t a n behaviour
1-24
o l the earth surface. With k=l
it is u normal cosine correction.
=
(148
k5
-
fl.54
r25
=
0.42
0.37
C-correction
Modification
c2
:=
2.03
i semi-empirical)
correction by a taclor c which
t.2~
=
H,42
~,hould m o d e l lhe diffuse sky
c4
=
O.40
radiation, c ix ba~,ed on tile
1-24
=
0.42
c5
-:
031
=cos (sz) + c t.H= L,r i cos(i) + c
regression
in
o f lhe c o s i n e
the statistic
empirical approach.
I r2~'
::
Volume 48, number 4, 1993
23
4.1. Statistical analysis The dynamics of data described by the standard deviation remains more or less constant for the SMC-corrected images compared to the uncorrected original. It is much higher, however, for the cosine correction. The Pearson correlation coefficient is very high between the uncorrected original band and the SMC-corrected images (r is about 0.97) and rather low between the uncorrected original and the cosine-corrected image (r is about 0.14) in all of the three bands under investigation. As the original band shows (apart from the disturbing illumination effect) mainly target information, it seems that the SMC-corrected images have a higher degree of target information than the cosine-corrected band. Under the assumption that the level of noise is not influenced by the correction algorithms, the SMC-corrected images are expected to be more authentic than the cosinecorrected one. The correlation between the corrected images and the illumination emphasizes this impression. Figures 2, 3 and 4 depict band 2 as a function of illumination for the statistic-empirical and the cosine-corrected image in comparison with the
original image including the corresponding linear regression lines. While the statistic-empirical corrected image (and with it all other SMC-corrected images) shows more or less independence of illumination, in the cosine-corrected image (Fig. 4) a drastic overcorrection of the weakly illuminated pixels is obvious. This is due to the unrealistic assumption, basic to that correction method, that only direct irradiance is present. Especially weakly illuminated pixels with a small incidence angle i exhibit a large amount of diffuse irradiance and are therefore amplified disproportionally by the cosine correction. Mathematically, this can be explained by division of a constant (cos(sz)) through a very small number (cos(i)) which is zero for a pixel lying in its self-shadow. In this case, the result of the correction is not defined (zero-division) and leads to artefacts in the corrected image. For this reason, Teillet et al. (1982) recommends the application of the cosine correction only in cases where the incidence angles are smaller than 55 °. Table 2 summarizes inclination (m), intercept (b) and coefficient of determination r 2 of the various correlations between the original and the corrected images on the one hand and the illumination file on the other. An ideal correction of
TABLE 2
Inclination m, intercept b and coefficient of determination r z for regressions between illumination and Digital Numbers in bands 21), 42) and 5 3) (Beckenried test site, forest after ground reference data, 95,356 pixels) test site Beckenried
inclination m
intercept b
coeff, of det. r2
original I)
9.8
20.0
0.4234
statistic-empiric, corr. I) cosine corrected I)
-4.1
31.9
0.0013
-101.6
109.9
0.1676
Minnaert corrected l) C-corrected I)
0.8
27.5
0.0033
-0.7
28.9
0.0036
original 2)
76.9
30.6
0.4187
8.5
68.0
0.0087
-173.3
234.4
0.1155
4.4
91.2
0.0013
8.6
88.4
0.0063
60.3
18.6
0.4770
6.5
53.6
0.0107
-107,4
155.1
0.1049
2,5
66.6
0.0008
5.1
64.9
0.0042
statistic-empiric, corr. 2) cosine corrected 2) Minnaert corrected 2) C-corrected 2) original 3) statistic-empiric, corr. 3) cosine corrected 3) Minnaert corrected 3) C-corrected 3)
24
the illumination effect would lead to an r 2 of zero so that the zero hypothesis "the inclination of the regression line is equal to 0" could no longer be rejected. In all three analysed bands 2, 4 and 5, r 2 can be reduced by the SMC-methods by a maximum from 0,4770 in the original band 5 to 0.0008 in the Minnaert-corrected band 5. The effect of the other SMC-methods are similar in all of the three bands investigated. The success of the illumination correction can therefore be verified statistically for the SMC-methods. The r 2 values for the cosine correction are much higher though they are still smaller than those of the original bands. As Fig. 4 shows, the cosine correction leads to a regression of second degree rather than to an elimination of the regression. However, the r 2 values are quite small even for the linear regression in spite of the insufficient correction of the illumination effect.
4.2. Visual analysis A comparison between the original band 2 and the statistic-empirical corrected band 2 shows a reduction of the relief effect (Fig. 7). This leads to a loss of the three-dimensional impression in the illumination-corrected image. It becomes flat and more or less homogeneous in regions of identical objects. The appearance of forests, for instance, becomes much more independent of topography than in the original (uncorrected) bands. This visual effect is more impressive in a nearinfrared band than in a visible one. As the impact of the atmosphere is much stronger in the visible part of the electromagnetic spectrum than in the near-infrared, the influence of diffuse irradiance is much more important. Thus, especially in sparsely illuminated pixels, the effect of the illumination correction is reduced by the smearing effect of the atmosphere so that the illumination correction could only be examined properly after an atmospheric correction. As expected, the illumination correction with the SMC-methods is much more efficient than the classical cosine correction which is unsuitable in such a rugged terrain. Figure 8 (top right) demonstrates the inadequate correction of the illumination effect and the artefacts along the mountain ridges due to the zero division for pixels in selfshadow. These artefacts can be observed in the
ISPRS Journal of Photogrammetry and Remote Sensing
Minnaert and C-corrected images as well; however, the overcorrection of the cosine approach is reduced to a large amount by both the Minnaert constant and parameter c (Fig. 8). Cast-shadows are not handled with this correction method and appear dark. A special treatment of these pixels would be necessary.
4.3. Impact on classification After illumination correction it is assumed that the influence of scene-related effects is reduced in favour of the intrinsic reflection properties of objects. Therefore, an increase in classification accuracy can be expected. Based on experiences by Leu (1991), a parallel epiped algorithm was chosen to examine the effect of illumination correction on a forest versus nonforest and forest stand classification using bands 2, 4 and 5. The determination of the parallel epiped limits are fully based on ground reference information. Therefore, the classification results are not influenced by operator inaccuracies in choosing training areas. Table 3 shows the results of the classification. The classification accuracy is defined as the sum of all correctly classified pixels (be it forest and nonforest for the forest versus non-forest classification or coniferous, mixed and deciduous for the stand classification) divided by the total number of pixels in the test site. At first glance, the classification accuracies achieved by performing the radiometric corrections seem to be discouraging. It has to be kept in mind, however, that the radiometric corrections may improve the classification results in small problem regions, such as sparsely or brightly illuminated areas. For an evaluation of whether these problem regions were better classified after a correction, the achieved accuracies for no correction and slope-aspect correction were calculated for the forest versus non-forest case (Table 4) as well as for the stand/forest type classification (Table 5). The slope-aspect correction improves the accuracy of the forest versus non-forest classification in faintly illuminated areas, without having an adverse effect on the sunny areas. The rather small overall improvement of 1% is due to the fact that only 27% of the pixets are faintly illuminated having a cos(i) < 0.6. In fact, if areas having a cos(i) < 0.6 are examined, an improvement of
25
Volume 48, number 4, 1993
Figure
7. Uncorrected
band 4, Beckenried
test site (top) and statistic-empirical
corrected
band 4, Beckenried
test site (bottom).
26
ISPRS Journal of Photogrammetly and Remote Sensing
Figure 8. Detail presentation of band 4 within the Beckenried test site. Top left: statistic-empirical corrected. Top right:: cosine-corrected. Bottom left: C-corrected. Bottom right: Minnaert-corrected.
Volume 48, number 4, 1993
27
TABLE 3 Accuracies for the forest versus non-forest and forest stand classification before and after the four slope-aspect corrections classification
original,
star.- emp.
cosine
Minnaert
accuracies
uncorrected
corrected
corrected
corrected
forest versus
86.01%
87.35 %
54.87 %
58.64 %
77.95 %
C-corrected
87.60 %
86.98 %
60,40 %
61.81%
non-forest forest stands TABLE 4 Accuracies of the forest versus non-forest classification in the Beckenried test site in relation to the illumination after slope-aspect C-correction (100% = 338,624 pixels) illumination
in % of the testarea
classific, accuracy
[cos (i).100]
Beckenried
original TM bands
C-correction
10
0.56 %
53,15 %
59.18 %
+ 6.03 %
1 I to 20
0.99 %
67.86 %
68.67 %
+0.81%
21 to 30
1.91%
76.13 %
76.00 %
-0.12%
31 to 40
3.80 %
78.19 %
80.61%
+ 2.42 %
41 to 50
6.40 %
76.18 %
82.12 %
+ 5.95 %
51 to 60
7.70 %
77.00 %
82.16 %
+5.16%
61 to 70
9.59 %
81.52 %
82.45 %
+ 0.94 %
71 to 80
i2.27 %
86.06 %
84.23 %
- 1.83 %
81 to 90
41.01%
94.28 %
94.10%
-0.17%
91 to 100
15.77 %
82.64 %
84.05 %
+ 1.41%
Ito
classific, accuracy classification difference
TABLE 5 Accuracies of the stand/forest type classification in the Beckenried test site with respect to the illumination after slope-aspect C-correction (100% = 338,624 pixels) illumination
in % of the testarea
classific, accuracy
[cos (i). 100]
Beckenried
original TM bands
classific, accuracy classification C-correction
difference
10
1.79 %
60.51%
61.03 %
+0,51%
11 to 20
4.80 %
58.13 %
58.13 %
+ 0,00 %
21 to 30
11.10%
50.91%
58.18 %
+ 7.27 %
31 to 40
15.95 %
54.89 %
59.72 %
+ 4.83 %
41 to 50
20.32 %
60.86 %
61.81%
+ 0.95 %
51 to 60
14.26 %
59.91%
63.00 %
+ 3.09 %
61 to 70
9.65 %
53.23 %
63.21%
+ 9.98 %
71 to 80
8.58 %
47.38 %
60.21%
+ 12.83 %
81 to 90
9,25 %
48.91%
64.29 %
+ 15.38 %
91 to 100
429 %
44.44 %
74.57 %
+ 30.13 %
lto
average classification accuracy of approx. 5% is achieved. The reason why there is hardly any classification improvement in well illuminated areas may be that those regions dominate the test site and as a consequence the determination of the parallel epiped limits. Therefore, the classification is opti-
mized on bright areas regardless of a slope-aspect correction. In contrast, the positive influence of the slopeaspect correction on the stand/forest type classification is not only visible in the fainter illuminated parts, as found in the forest versus nonforest classification, but even more pronounced in
28
the brighter areas. Again the illumination classes which are underrepresented in the stand groundreference data are improved. A major improvement of between 10 and 30% could be achieved in the classification of stands in brightly illuminated areas with cos(i) > 0.6. Over the whole training area, a total improvement of the stand/forest type classification of 7% could be reached. In summary it can be stated, that the illumination correction markedly increases the accuracies of both the forest versus non forest, and the stand/ forest type classifications. 5. Conclusions Through the correction of scene-related radiometric effects, a classification accuracy of forests versus non-forests of almost 90% could be achieved in the Beckenried test area. The semiempirical C-correction method improved the classification accuracy of faintly illuminated areas by about 5%, while the statistical-empirical methods' improvement was inferior and the conventional cosine correction even proved to be useless for our test site. The accuracy improvement in the forest stand/ type classification using the C-correction method was between an impressive 10% and 30% for brightly illuminated areas. In the future one should concentrate more on physical models because the improvement potential of empirical and semi-empirical models is somewhat limited, and because the physical models allow for a better description of objects in nature (Woodham, 1989; Deering et al., 1990). More research is encouraged and needed on the bidirectional reflection distribution functions (BRDF) of objects, since the assumption of Lambertian surfaces is not adequate, especially for vegetated surfaces. Acknowledgements This project has greatly benefited from the experience gained in the SRSFM-Project (Swiss Remote Sensing Forest Mapping Project) at the Remote Sensing Laboratories of the Department of Geography, University of Zurich which started in 1988 and is supported by the Swiss Government, UNEP/GRID and ESA. The permission to use the digital elevation model (DHM-25), issued by the
ISPRS Journal oj Photogrammetry and Remote Sensmg
Swiss Federal Institute of "Ibpography, for this research is greatly appreciated. The results reported here are mainly based on the MSc Theses of St. Sandmeier (1991) and R. Sandmeier-Leu (1991). The geometric corrections were carried out by P. Bitter and T. Kellenberger. References DFVLR, 1988. Waldkartierung mit Satellitendaten im Kartenblatt T 0 K 200 Regensburg. Forschungsbericht Nr. 2/88, Deutsche Forschungs- und Versuchsanstalt ftir Luft- und Raumfahrt (DLR), Oberpfaffenhofen, 16 pp. Deering, D.W., Eck, T.E and Otterman, J., 1990. Bidirectional reflectances of selected desert surfaces and their threeparameter soil characterization. Agric. For. Meteorol., 52: 71-93. Goodenough, D.G., Deguise, J.-C. and Robson, M.A., 199t). Multiple expert systems for using digital terrain models. Proc. IGARSS '90 Symp., Washington, D.C., p. 961. ltten, K.I. and Meyer, P.. 1993. Geometric and Radiometric Correction of TM-Data of Mountainous Forested Areas. IEEE Transactions on Geoscience and Remote Sensing, in press. Lcu, R., 1991. Digitale Kartierung des Schweizer Waldes mit Landsat TM-Daten, Teil 13. MSc Thesis, Dept. of Geography, University of Zurich, 145 pp. Meyer, P., 1992. Empirical quality assessment: effect of resampiing on geometric and radiometric data quality using a region-based approach. Proc. IGARSS '92 Symp., Houston, Texas, pp. 1481-1483. Minnaert, N., 1941. The reciprocity principle in lunar photometry. Astrophys. J., 93: 403-410. NASA, 1982. Landsat Data Users Notes. Issue No. 23. U.S. Geological Survey, EROS Data Center, Sioux Falls, S.D. Sandmeier, St., 1991. Digitale Kartierung des Schweizer Waldes mit Landsat TM-Daten, Teil A. MSc Thesis, Dept. of Geography, University of Zurich, 144 pp. q~anr6, D., Deroo, C,, Duhaut, P., Herman, M., Morcrette, J.J., Perbos, J. and Deschamps, EY., 1986. Description of a computer code to simulate the satellite signal in the solar spectrum: the 5S code. Int. J. Remote Sensing, 11(4): 659-668. Teillet, EM., Guindon, B. and Goodenough, D.G., 1982. On the slope-aspect correction of multispectral scanner data. Can. J. Remote Sensing, 8(2): 84-106. Teillet, EM., 1986. Image correction for radiometric effects in remole sensing. Int. J. Remote Sensing, 7(12): 1637-1651. Woodham, R.J. and Lee, TK., 1985. Photometric method for radiometric correction of multispectral scanner data. Can. J. Remote Sensing, 11(2): 132-16 I. Woodham, R.J., 1989. Determining intrinsic surface reflectance in rugged terrain and changing illumination. Proc. IGARSS '89 Syrup., Vancouver, pp. 1-5. (Received August 24, 1992; revised and accepted January 5. 1993 )