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Large Area Forest Cover Assessment:
Effects of Misregistration in a Double
Sampling Approach with Coarse and
High Resolution Satellite Images
Christoph ~leinn',Berthold ~raub',Matthias ~ e e s '
Abstract When combining satellite data of considerable different spatial
resolution the effect of msregistration is one of the techcal issues to be
addressed. This simulation stud is based upon subcontract research carried
out in the framework of &e TREES roject (Tropical Ecos stem
Environment Observation by Satellites, Joint kesearch Centre, Ispra, taly).
Overall objective is a global tro ical forest cover estimate and the production
of a forest map. In a first p ase of the invent0 approach a complete
coverage by the coarsly resolving NOAA A
satellite images is
provided. To improve the forest area estimates derived from this image set a
sample of Landsat-TM scenes was selected in a second phase: In
corresppndin frames/blocks of the same eographical area forest cover
percent in
and TM was recorded. k e s e pairs of values formed the
Input variables for a calibration regression.
To assume perfect geogra hlc registration is certamly not realistic. Some
effects of rnisre istration getween the coarse and hgh resolution ima e
frames/ ixel bloc s on the resultin regression are studied in this paper in tfe
form o a simulation study. The e ects can be considerable, particularly when
small blocks of coarse resolution pixels are to be registered.
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1
INTRODUCTION AND OBJECTIVES
Global monitoring of forest cover is a current issue in the context of the
destruction of tropical forests and in the discussion about global climatic changes.
Forest cover monitoring systems are to provide sound information on state and
changes in forest cover. Satellite remote sensing plays an important role there:
NOAA AVHRR has proved to have favourable characteristics to discriminate
vegetation from other land cover and is frequently used in environmental
monitoring (Ehrlich et al. 1994). LANDSAT TM has in the 1980's developed to
be the standard high resolution sensor in many forestry applications. These two
systems have quite different characteristics with respect to temporal, spatial and
spectral resolution, in detail described in standard textbooks.
The high temporal frequency and low cost of the coarsely resolving AVHRR
(about 1 km x 1 km) is well suited to provide in a first phase a more or less
complete coverage of the region of interest. This results in an equally 'coarse'
estimation of forest cover. The estimate might then in a second phase be improved
through a sample of the much higher resolving LANDSAT TM, which is much
more detailed but also much more expensive. Regression technique is used to
1
Abteilun fQr Forstliche Biometrie, Universiat Freiburg, Werderring 6, D-79085 Freiburg,
Germany &einn@orst. um-fieiburgde)
The acronymfcp is used throughout the paper forforest cover percent
predict 'true' forest cover from the coarse information delivered by AVHRR.
'True' forest cover is assumed to be represented by the TM forest cover. In terms
of sampling theory this is a double sampling for regression approach (Cochran
1977). From an image interpretation and classification point of view the resulting
regression can be regarded as calibration fbnction.
To calculate the regression it is necessary to obtain geographically matching
pairs of map frames, one of the coarse resolution map and one of the high resolution map. This procedure is also called coregstration. Two approaches how to
calculate the regression are discussed in the literature:
(1) Coregistration of forest percentages from both data sources; an example is
found in Nelson (1989). This approach is also used in a global tropical forest
assessment in the TREES project, a general description of which can be found in
Malingreau (1993). Units to be coregistered can be areas corresponding to the size
of one single coarse resolution pixel, with only to values possib1e:O and 1, or
blocks of pixels.
(2) Coregistration of forest percentages in the high resolution image with
spectral values of coarse resolution image. Examples are found in Iverson et al.
(1989)) Paivinen and Pitkanen (1992) and Zhu and Evans (1992). In this approach
the units to be coregistered are areas of the size of one single coarse resolution
pixel.
Like all types of measurements coregistration is subject to error, too: The
problem of misregistration arises. This paper investigates in the form of a
simulation study possible effects of misregistration onto the calibration procedure.
It is an'extension of a former study presented in Kleim et al. (1995). Approach (1)
is pursued here, using blocks of pixels as registration unit.
2.
GENERAL DESCRIPTION OF MISREGISTRATION
Not many publications yet deal with the impact of misregistration in detail. One
of the few articles focuses on change detection: Townshend et al. (1992) state that
change assessments using satellite images of two different taking dates are affected
by the level of registration, depending, of course, on several factors. They finally
state that "high levels of registration must be achieved by operational monitoring
systems if there is to be reliable monitoring of global change".
Assuming perfect classification procedures, the two data sources under
consideration here (coarse and high resolution) would yield identical forest cover
estimates. A simple linear regression between the data pairs would result in the one
to one line. In reality, there are more or less significant deviations: Sensors of
different spectral and spatial resolution 'see' things in a different way. Additionally
geometric inaccuracies lead to misregistration: The block of high resolution pixels
is not exactly matching the corresponding block of coarse resolution pixels.
Perfect registration would mean that (1) the centres of the two blocks match
and that (2) their shape and (3) their alignment are the same. In Figure 1 these
factors are depicted schematically. Misregistration means that not only the high
resolution pixels in the true matching block have a chance to be registered, but also
the pixels around them. Would the amount and type of misregistration be known,
then one could calculate the probability of a pixel to be included in the registration
process of one specific block. For perfect coregistration this probability would be 1
for the pixels in the matching block, 0 elsewhere. In the presence of misregistration
the probability is high in the matching block but greater than 0 in a certain area
around.it. It is 0 only beyond the maximum misregistration distance. Under the
assumption that misregistration is an isotrope process this area is drawn in Figure 1
as a circular envelope.
Figure 1: Large circle: Area in which
the registration probability of the
pixels of the high resolution images is
greater than 0. Small circle: Area of
pixels having an inclusion probability
greater 0 for a 'rotating' displaced
block with fixed distance d and shift
Assumed that the actual registration of individual sample blocks in two different
images is a random process, misregistration leads to a bias when estimating fcp:
The expectation of the attribute (forest cover) measured in the high resolution
image is not the value of the true matching block. This adds another source of
variability (error) into the target regression between forest cover estimates of high
and coarse resolution pixel blocks.
3.
MATERIAL
Computer generated foresthon-forest (110) maps of size 9000x9000 pixels
were used to investigate the effects of misregistration. A set of 'homogeneous'
maps was created by randomly locating clusters of dots. These dots have diameters
3, 30 and 100 pixels for the map sets 1a- 1e, 2a-2e and 3a-3e, respectively. The
total fcp goes from 10% (in maps la, 2a, 3a) over 30%, 50%, 70% to 90% (in
maps le-3e). Three inhomogeneous maps (maps 4 to 6) consist of regions with
different structures. Examples of these maps at original, high resolution are given
in Figure 2, left hand side.
The high resolution maps were gradually degraded to produce coarse resolution
maps. Square pixel blocks of size n x n pixels of the original image were collapsed
to one new coarse resolution pixel, with n taking on the values 10, 25 and 50.
Depending on the forest cover within the n x n high resolution pixels the attribute
forest or non-forest was assigned to the new coarse resolution pixel. If fcp
exceeded 30%, the attribute 'forest' was assigned. In Figure 2, right hand side,
results of the degradation are shown. For the degraded maps only the 'core-region'
of 8000x8000 pixels is shown in Figure 2, the region to which the analysis is
limited. This allows for a buffer frame surrounding the analysed region, thus
facilitating the treatment of edge effects in the simulations.
Map l a (10% cover): Original resolution
Map la: Degraded (level 50, see text)
Map 3d (70% cover): Original resolution
Map 3d: Degraded (level 50, see text)
Map 4 (44.4% cover): Original resolution
Map 4: Degraded (level 50, see text)
Figure 2: Sample maps as used in the simulation study. Left hand side: Original maps of
size 900019000 pixels. For the degraded maps (right hand side) only the core-region
corresponding to 8000x8000 pixels in original resolution is depicted.
Table 1: 'Forest' cover percent in the original and degraded maps used in this study.
The fcp .values of the maps shown in Figure 2 are framed.
Map
Map
la
Degraded
10 x 10
25 x 2 5
forest cover vercent o f the total mav
10.0
13.6
12.9
3a
3b
3c
3d
3e
........................................
Map
4
Map
5
Mar,
6
Original
resolution
I
Map
I
1
10.0
30.0
50.0
70.0
90.0
44.4
I
J
5 0 x 50
1
1
10.4
10.7
30.2
30.8
51.0
5 1.6
70.6
71.5
90.6
91.1
.....................................................
48.1
50.1
I
1-
1-
5.4
11.0
31.6
53.1
92.0
The image degradation technique leads to a change in total forest cover as
illustrated in Table 1. It is a very simple technique, which probably does not mirror
very realistically the properties of two real map sets. But it was felt that this was
sufficiently realistic to investigate the general properties of misregistration. With
real data sets the differences in fcp values would be due to differences in spatial
resolution, taking date, atmospheric conditions etc. and, of course, differences in
image interpretation and classification.
METHODS
When modeling misregistration one has to make assumptions on the distance
and/or direction distribution of the deviations relative to the true location. The
registration process is modelled as purely random process here. The factors which
were included in this simulation and which were subject to variation at several
levels are listed in Table 2. Non-matching shapes of the two blocks to be are not
taken into respect in this study. For each combination of the listed factor levels a
systematic grid of coarse resolution sample blocks was superimposed onto the
original, high resolution maps. For all blocks at first the fcp of the true matching
high resolution block was determined. Then the high resolution block was
displaced 100 times according to the probability assumptions given in Table 2. For
each block, mean and standard deviation of the fcp values resulting from the 100
replications were recorded.
4.
5.
RESULTS
Statistics of the diffences between truly matching pixel block and the mean
(expectation) of the 100 simulated misregistered pixel blocks: In Figure 1 it was
illustrated that a bias is suspected when estimating the fcp as an expectation of
misregistered pixel blocks. In some results are given for the maps shown in Figure
2, for degradation level 50. The bias (mean of the dflferences for all blocks
analysed througout the whole map) is negligible for all maps investigated.
Table 2: List of factors included in the model study
Description andfacior levels
Factor
-
--
Area structure
Artificially generated maps: Some produced with a homogeneous generation process, some with several processes overlaid (heterogeneous)
Total forest cover
Total forest cover is lo%, 30%, 50%, 70% and 90% for the homogeneous
maps and 32% to 44% for the heterogeneous ones
Spatial resolution of coarse
resolution image
Side length of the square pixels of the coarse resolution maps correspond
to 10,25 and 50 pixels of the high resolution image
Forestlnm-forest rule to be
used for image degradation
M u m 'crown' cover percent in the degraded image for a pixel to be
assigned to the class 'forest' is fixed to be 30%
Block size
Coarse resolution square pixel blocks of 2,5, 10,20 pixels side length
Parameters of
misregistration
Misregistration described in Figure 1. Maximum distance is 4 pixels of
coarse resolution following a linearly decreasing pdf (mean distance =
413 = 1.333 pixels, standard deviation = J16/18 = 0.943 pixels). Isotropy
is assumed. The coregistered blocks may rotate up to f10 degrees, following a triangular probability density b c t i o n symmetric around 0 degrees.
For the single sample blocks - i.e. not using themean of the 100 replications per
block - the difference between truly matching pixel block and rnisregistered pixel
bock can be considerable. This can be seen with the range and standard deviation
of the differences as given in Table 3: For Map 3d and block size 2 x 2 the
standard deviation is about 10% fcp, having a range of differences from -41% to
+38%, meaning that one has to be aware of large variation when making blockwise
evaluations. For a block size of 10 x 10 or even 20 x 20 this variation is much less.
This variability of the differences is also a fhction of total forest cover, which
can be observed when analysing for example the sequence of maps l a to le. These
maps were generated with the same algorithm of random clustering of dots of a
diameter of 3 pixels. The difference is that Map l a was only filled up to lo%, Map
lb up to 30% and so on. Map l e has a 90% cover. In Figure 3 the standard
deviation of the differences is shown over total forest cover: The highest variability
is thus-reached with the intermediate fcp of around 50%. With a forest cover of
10% or 90% variability is much less. This relationship is a quite obvious one when
analysing the extreme cases: In the complete presence (or absence) of forest,
misregistration has no effect at all.
Calibration regression: The regression is to predict blockwise the fcp estimate
of the coarse resoution pixel blocks. Here, simple linear regression is used. Though
it would be justiied for practical reasons the intercept was not suppressed. Gwen
the situaion illustrated in Table 1 it is clear that one gets a slope coefficient
different from 1 (in most cases smaller than I), when predicting fcp of the high
resoluion map (dependent variable) using the fcp of the coarse resolution map as
independent variable. This holds even for the situation of perfect coregistration.
In analysing the regression results we are interested in two relationships:
Regression 1 under perfect coregistration and Regression 2 in the presence of
rnisregistration. In Table 4 general characteristics of the regressions are listed for
the three sample maps addressed throughout this paper. Given the same map and
the same degradation level there are considerable differences between the
coefficients of Regression 1 and Regression 2 for the small block size 2, but the
differences level out quite markedly for the largest block size 20. Intercept and
slope coefficients of the Regressions 1 and 2 are quite close for this large block
size. As Regression 1 is the 'true' regression under perfect coregistration one sees
that small block sizes lead to an incorrect calibration function and that only for
very large block sizes Regression 2 approaches the coefficients of the true
Regression 1.
Figure 3: Standard deviation of differences
between fcp of truly matching pixel block
and the mean of the 100 misregistered pixel
blocks over fcp
I
0
0
20
40
60
80
100
Total forest cover (fcp)
Table 3: Descriptive statistics of the differences between the fcp of the true matching
high resolution block and the fcp results of the 100 simulated misregistered blocks
(degradation level 50):
Block size
Mean
Std Dev
Minimum
Maximum
0.0356
-0.0931
0.1679
2
0.000246
5
0.000281
0.0103
-0.0326
0.0442
10
0.000255
0.0036
-0.0098
0.0096
20
0.000256
0.00
1
1
-0.0029
0.0031
----------------------------------------.
Map
2
0.003002
0.1017
-0.4104
0.3791
0.002945
3d
5
0.0429
-0.1661
0.1418
10
0 .002647
0.0156
-0.0417
0.0568
20
0.003288
0.0061
-0.0149
0.0177
- - - - - ---------------- --_-_-------------_.
Map
2
0.001279
0.082 1
-0.4125
0.4526
5
4
0.001563
0.0195
-0.1277
0.0690
10
0.001645
0.0080
-0.0338
0.0274
20
0.000914
0.0038
-0.01 11
0.0125
Map
1a
Differences between the coefficients of Regression 1 and Regression 2 are most
clear for map set 1, consisting of very small forest 'patches' compared to the
spatial resolution of the degraded images. This holds - as mentioned in the
preceeding paragraph - particularly for small block sizes and low total forest cover.
For larger patches and higher total fcp the effect is much smaller, though still there.
Table 4: Basic statistics of the simple linear calibration regression for three sample maps
(rmse=root mean square error, r2=coefficient of determination).
Map 3d (70% fcp in original map)
Mat, 4 (44% fct, in orieinal mat,)
For map 3d, consisting of large forest patches (diameter 100 original pixels
each) and having a total forest cover 70% this approximation is quite good even
for the small block sizes. For degradation level 10 for example the slope coefficient
is 0.9592 for block size 2 ('true' coefficient: 0.9978) and 0.9976 for block size 20,
being almost equal to the 'true' 1.0044. For Map la, consisting of very small
patches with a total cover of only about lo%, there is a considerable difference
betweeen the slope coefficient for block size 2 (0.4413) and the 'true' value of
0.7028, while for block size 20 the difference between 'misregistered' slope
(0.7416) and 'true' slope (0.7611) is small.
The differences in slope, however, do not lead to an error of estimation of
overall-fcp. This is illustrated in Table 3. The differences are leveled out by the
adverse differences in intercept: Lower slope coefficients go together with higher
intercepts. In Map l a the differences in intercept are relatively small. But one has
to consider that the vast majority of observations in this map is in the class fcp=O,
as total forest cover is only 10%. So small differences in intercept have a large
effect.
When the calibration regressions based upon misregistered blocks are used for
map production (calibrating the fcp of each coarse resolution pixel block) a clear
error is introduced. For larger fcp values the true value will be underestimated, for
very small values overestimated. Negative intercepts as they occur in Table 4 are
normally not acceptable in a calibration regression: It would mean that a forestfree coarse resolution pixel block is calibrated from an fcp of 0.0 to a negative fcp.
In our simulation study, however, the calibration regression was intentionally not
forced to be non-negative.
The root mean square error (rmse) is in most cases higher for Regression 2
what would be expected as misregistration introduces more variability. The rmse,
however, is not an adequate measure here as calculations were made using per
block the mean of the fcp of 100 simulations. Thus, if one is interested in the
variability for one single set of misregistered blocks, one would have to take
additionally into account the variability within the individual blocks.
7. CONCLUSION
Three major factors can be identified which determine the magnitude of the
misregistration effect as to this simulation study:
- Magnitude of misregistrution. The bigger the dislocation distance the bigger
the difference in fcp values registered. This obvious relation, however, must also
be seen in interacting context with the two other factors.
- Size of pixel blocks to be registered. The bigger the block size the less the
effect of misregistration For small pixel blocks the effect can be considerable. This
relation interacts very much with the third important factor, the
- spatial structure and fcp of the region of interest. For very high and very
low fcp the misregistration effect is smaller than for intermediate fcp's. If the forest
patches are large in comparison to the size of the pixel blocks to be coregistered,
the effect of misregistration on fcp estimation is smaller.
The bias of the total forest cover estimate that was suspected on the basis of
theoretical considerations could not be confirmed to be significant in this