Principal components transformations was applied to a Walnut Creek, Texas subscene to reduce the dimensionality of the multispectral sensor data. This transformation was also applied to a LANDSAT 3 MSS subscene of the same area acquired in a different season and year. Results of both procedures are tabulated and allow for comparisons between TM and MSS data. The TM correlation matrix shows that visible bands 1 to 3 exhibit a high degree of correlation in the range 0.92 to 0.96. Correlation for bands 5 to 7 is 0.93. Band 4 is not highly correlated with any other band, with corrections in the range 0.13 to 0.52. The thermal band (6) is not highly correlated with other bands in the range 0.13 to 0.46. The MSS correlation matrix shows that bands 4 and 5 are highly correlated (0.96) as are bands 6 and 7 with a correlation of 0.92

Ford, G. E.

English

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https://ntrs.nasa.gov/search.jsp?R=19840018029 2020-03-20T22:05:27+00:00Z
IQuarterly Status and Technical Progress Report
Landsat-D Thematic Mapper Image Dimensionality
Reduction and Geometric Correction Accuracy
NASA Contract Number NAS5-27571
	 '^	 dG ^'6 j
19pir
Principal Investigator
Gary E. Ford
^A^''^ J6J	 Department of Electrical and Comp-_er Engineering
University of California, Davis
0	 J^	 G{i^	 Davis, California 95616	 +N,
CO /Q	 " ^ (EB4-10149) LANDSAT—D TdEMATIC MAPPER IMAGE 	 N84-26097
"' 	 DIRENSICNALITY REDUCTION AND GEOMFTBICc	 81l ^,^^	 :; ^OHREC':ION ACCURACY Quarterly Sta,as
Technical Proqress Eeport, 3 Dec. 1983 —	 Unclas
3 Mar. 1984 (California Univ.) 7 p	 G3/43 00149
G£
"^^ J	 For the period: December 3, 1983 to March 3, 1984
i
s
1. Problems
The progress of the investigation has been impeded during this reporting
period by the heavy teaching and graduate advising load of the principal
investigator. Approval has been obtained to take a leave of absence to devote
full time to this project for the remainder of the contract period.
2. Accomplishments
The thematic mapper scene that is the most useful in our investigation
was received during the reporting period. This is a scene from path 27, row
39 of central Texas (Scene ID E-40193-16315, acquired January 25, 1983),
covering the Walnut Creek watershed east of Austin, Texas. We have studied
tnis watershed previously for the U.S. Army Corps of Engineers (Ford, et al.,
1983) using MSS data. We have a substantial collection of ground truth data
fo r this study area, including color infrared aerial photography, USGS topo-
graphic maps, and ti,, results of manual and computer classification studies.
We have made a preliminary study of a 1024 by 1024 subscene of this
image, centered on Austin, Texas.	 The ranges of intensity values in all of
the TM bands were found to he
	
greater than those we had
- 2 -
observed in the other TM image avai.able to us, a February 2, 1983 acquisition
centered near Sacramento, California. Since both of these images were
acquired during the winter months, the low sun angle would be expected to
produce low dynamic ranges. However, we are unable to provide an explanation
as to why there is such a disparity between the two images, acquired just
seven days apart. We observed a 50% increase in standard deviation in the
intensities in bands 1, 2, 3, 5, and 7; no change in band 4; and a 25% de-
crease in band 6. The decrease in the thermal band is probably due to the low
percentage of water in the Texas image. Due to the heavy rainfall in
California during the 1982-83 winter, the study area of interest to us on the
Sacramento River was extensively flooded on the date of acquisition of the
image and we are unable to perform a classification study on this image.
While the late January date is not the optimum for a classification study of
the Walnut Creek watershed, an interactive analysis of the image shows that
the major land use classes exhibit spectral separation.
Principal components transformation has been applied to the Walnut Creek
subscene to reduce the dimensionality of the multispectral sensor data. The
results are summarized in Table 1. For comparison purposes, we have also
applied this transformation to a Landsat 3 MSS subscene of the same area. The
MSS scene was acquired in a different season and year (May 1978), but the
results, as summarized in Table 2, allow for comparisons between TM and MSS
data.
The correlation matrices indicate the pairwise correlation of the
spectral components. The TM correlation matrix shows that visible bands 1-3
exhibit a high degree o f correlation, in the range 0.92 to 0.96. While it
might be expected that the reflective infrared bands 4, 5, and 7 would be
highly correlated, this is only true for bands 5=7, where the correlation is
0.93. Band 4 is not highly cur elated with any other band, with correlations
in the range 0.13 to 0.52. Similarly, the thermal band 6 is not highly
correlated with other bands, with correlations in the range 0.13 to 0.46. 	 It
should be noted that bands 1-3 exhibit a moderate degree of correlation with
bands 5 and 7, with correlations in the range 0.63 to 0.83. These results are
significantly different than those we reported for the Sacramento subscene in
our project report for the period June 3, 1983 to September 3, 1983. This is
a further indication that the Sacramento scene is not representative of data
from the TM sensor.
The MSS correlation matrix shows that the visible bands (4 and 5) are
highly correlated (0.96), as are the reflective infrared bands (6 and 7),
with a correlation of 0.92. On the basis of this comparison between TM and
MSS data, we are unable to support the expectation that there would be lower
correlation among the TM spectral components than has been observed for the
MSS spectral components.
The principal components transformation matrix is composed of the normal-
ized eigenvectors of the covariance matrix ordered by eigenvalues. The
weights used t) generate a transformed coiiponent are given in the columns
mp
URIGINAL PAGE 18
- 3 -	 OF POOR QUALITY
of the eigenvector matrices in tables 1 and 2. The first transformed compo-
nent of the TM data is a weighted average of the seven spectral components.
These weights are approximately proportional to the standard deviations of the
spectral intensities. The second transformed component is roughly the sum of
bands 1-4 minus the sum of bands 5-7. The third component is roughly band 4
minus bands 1-3 and 7, with negligible weights given to bands 5 and 6. Band 4
dominates this transformed component due to its relatively low correlation
with all other bands. Again, these conclusions differ significantly from
those based on the Sacramento scene.
For the MSS data, the first transformed component is
average of the four original components, with the weights
to standard deviations of the spectral intensities. This
referred to as the brightness component since it is a sum
ponents. The second transformed component is roughly the
the visible and reflective infrared components. It has b
the greenness component, as it exhibits a strong response
again a weighted
roughly proportional
component has been
of the original com-
difference between
een referred to as
to vegetation.
If the data is represented by L transformed components of the original
N components, where L<N, then the mean-squared error of the representation
is given by the sum of the N-L eigenvalues of the components not included in
the representation. The percent variance in any transformed component is
given by the ratio of the eigenvalue for that component to the sum of the
eigenvalues. For the TM image, it is seen that nearly 80% of the variance
is contained in the first transformed component. Transformed components 2
and 3 represent 9.7% and 7.9% of the variance, respectively. The variance
in the remaining components is at or below 1%. Representing the image by
the first three components maintains 97.4% of the variance in the original
seven components. For the MSS data, 98.6% of the variance is contained in
the first two transformed components. The results in both cases support
the statement by Gnanadesikan (1977) that at least 95% of the variance will
be contained in the first three transformed components.
The results for the TM data are in close agreement with those reported
by Bernstein and Lotspiech (1983). Working with a subscene of the San
Francisco Bay acquired on December 31, 1982, they also performed principal
component processing to reduce the dimensionality of the data. Their data
exhibited lower spectral standard deviations, possibly due to the even lower
sun angles at that time of the year. 	 The correlation results are similar,
with two exceptions. The correlations between bands 4 and 5 and bands 4 and
7 are higher than that observed for the Texas scene, at 0.88 and 0.81,
respectively. The thermal data in band 6 has a small negative correlation
with bands 2-5 and 7, which was not observed in the Texas scene. Both of
these differences are probably due to the large amount of water in the San
Francisco Bay scene. Due to the observed differences in the correlation
matrix, the weights used in forming the second and third transformed
components differ considerably from those observed for the Texas scene.
The principal :onponants transforma!ion of the Texas image is also in
close agreement with the preli •ninary formja'3t i on of the thematic mapper
- 4 -
tasseled cap transformation developed by Crist (19f1). The first principal
component is similar to the brightness feature, which is also a weighted
average. The second principal component is similar to Crist's third compo-
nent, tentatively termed wetness, in that the weights are positive for origi-
nal bands 1 to 4 and negative for bands 5 and 7. The second principal compo-
nent is similar to Crist's greenness component, with a large positive weight
for band 4, negative weights for bands 1-3 and 7, and a small weight for band
5. Thus, the physical interpretation given by Crist may apply to the Texas
scene.
References:
(1) Berstein, R. and Lotspiech, J. B. (1983). "Landsat-4 thematic mapper
sensor evaluation and advanced information extraction experiments,"
Proceedings of the Eighth Pecora Memorial Remote Sensing Symposium
(preprint copy).
(2) Crist, E. P. (1983). "The thematic mapper tasseled cap -- a preliminary
formulation," Proceedings of the 1983 Machine Processing of Remotely
Sensed Data Symposium, pp 357-364.
(3) Ford, G. E., Algazi, V. R., and Meyer, D. I. (1983).
	
"A ncninteractive
procedure for land use determination," Remote Sensing of Environment,
vol. 13, pp 1-16.
(4) Gnanadesikan, R. (1977). Methods for Statistical Data Analysis of Multi-
variate Observations, New York: Wiley.
3. Significant Results
The significant results obtained this quarter are those involving
principal components analysis, as reported in section 2.
4. Publications
No publications were released during this period.
5. Recommendations
No recommendations are made concerning changes relating to maximum
utilization of the Landsat-D system.
I
l
ORIGINAL PAGE 19
OF POOR QUALITY
- 5 -
6. Funds Expended
Salary - Research Assistant
Employment Benefits
Clerical
Computer Time
1
i
i
28.54
9.906
0.7515
0.7791
0.8333
0.4288
0.9273
0.4445
1.0000
-0.2811
0.9218
-0.2533
-0.0486
0.0200
-0.0100
-0.0230
1.13
0.17
100. (1
Band 7
i
ORIGWAL PAVE 79
OF POOR QUALITY
- 6 -
Table 1. TM Principal Compcnents Transformation
MEANS
11.46
8.897
1.0000
0.9574
0.9273
0.4420
0.6370
0.1701
0.7515
0.3052
0.1807
0.2887
0.2208
0.7543
0.0520
0.4128
529.48
79.8
79.8
Band 1
28.63 31.97 41.88 61.89 102.48
STANDARD DEVIATION
5.042 7.630 8.663 17.878 2.826
CORRELATION MATRIX
0.9574 0.9273 0.4420 0.6370 0.1701
1.0000 0.9478 0.5174 0.6803 0.2070
0.9468 1.0000 0.4885 0.7463 0.2646
0.5174 0.4885 1.0000 0.5236 0.1345
0.6803 0.7463 0.5236 1.0000 0.4666
0.2070 0.2646 0.1345 0.4666 1.0000
0.7791 0.8333 0.4288 0.9273 0.4445
EIGENVECTORS
0.6309 -0.2189 -0.2135 0.1062 -0.5668
0.3275 -0.0664 -0.0200 0.0635 0.0392
0.3996 -0.1475 0.0267 0.1526 0.8044
0. ?289 0.9320 0.1518 -O.0	 22 -0.0305
-0.5177 0.0196 -0.3745 0.1472 -0.0191
-•0.1092 -0.0310 0.5739 0.7965 -0.1434
-0.0521 -0.2364 0.6787 -0.5491 -0.0913
EIGENVALUES
64.35 52.60 6.76 5.40 3.83
PERCENT VARIANCE
	
IN TRANSFORMED COMPONENTS
9.7 7.9 1.02 0.81 0.58
CUMULATIVE PERCENT VARIANCE	 IN TRANSFORMED COMPONENTS
89.5 97.4 98.4 99.2 99.3
Band 2 Band	 3 Band	 4 Band 5 Band 6
ORIGINAL PAGE 1`9
- 7 -	 Of POOR QUALITY
Table 2. MSS Principal Components Transformation
MEANS
25.48 28.10 52.87 26.17
STANDARD DEVIATION
5.621 8.852 9.455 4.992
CORRELATION MATRIX
1.0000 0.9616 0.5484 0.2529
0.9616 1.0000 0.5170 0.2186
0.5484 0.5170 1.0000 0.9164
0.2529 0.2186 0.9164 1.0000
EIGENVECTORS
0.3780 0.3490 0.7900 0.3335
0.5886 0.6052 -0.5349 -0.0336
0.6618 -0.5525 0.1337 -0.2683
0.2696 -0.4546 -0.2683 0.8054
EIGENVALUES
162.15 59.18 1.72 1.21
PERCENT VARIANCE IN TRANSFORMED COMPONENTS
72.3 26.3 0.77 0.54
CUMULATIVE PERCENT VARIANCE IN TRANSFORMED COMPONENTS
72.3 98.6 99.5 100.0
Band	 1(4) Band	 2(5) Band	 3(6) Band	 4(7)


LANDSAT-D Thematic Mapper image dimensionality reduction and geometric correction accuracy

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