The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008
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spectral curve show fractal can be used to represent the spectral
feature to reduce dimensionality of hyper spectral image.
Finally, the application of fractal measurement of spectral
domain feature analysis is briefly discussed.
2. DATA ANALYSIS
2.1 Spectral feature of hyper spectral image
Spectral feature is the main difference of the hyper spectral
image and the common remote sensing image (Peter F, 2001;
Shu N,2001). Pixel value in each band which constructs the
spectral curve can represent the object information for image
classification. With the high resolution of spectral band, the
spectral curve can be used for feature extraction, band selection
and classification. Spectral matching method is used to identify
the object with the spectral library supporting while it is time
consuming with the vast mount of spectral data. In order to full
use the spectral information of each pixel in hyper spectral
image, the feature analysis can be done to each spectral curve to
obtain feature and form the feature image of hyper spectral data.
Thus the classification can be done with the spectral curve
feature image. Dimensionalities reduce and feature analysis is
done at the same time which can increase the processing
efficiency. The key problem of spectral feature analysis is to
extract the feature from the spectral curve.
2.2 Fractal characteristic of spectral curve
Fractal is a tool to analysis the spatial structure and spatial
complex and it obtains fast progress in the remote sensing
application. Fractal dimension is used to present the spatial
structure thus the fractal research focus on the image spatial
fractal analysis (Qiu H L; Weng Q, 2003). For the hyper
spectral image, both the spatial domain and spectral domain has
fractal characteristic. The fractal characteristic in spectral
domain is from the spectral curve as the following items:
1) Hyper spectral curve represent the object spectral imaging
course is.non-linear
Hyper spectral curve represent the object spectral imaging
course. And the object spectral imaging course is a non-linear.
As the remote sensing physical principle, spectral imaging
model is:
L i = K 1 \Fi(fyi sin dp^dQ + W' ei ■ )+ bJ (l)
Where K A is the spectral response coefficient of the sensor.
T^ is the atmosphere spectral transmittance. N^ is the solar
incident spectral energy. 6 is the solar altitude angle, p ? is
the object spectral reflectivity. Q is the solar azimuth. W eA is
the black body spectrum radiation flux density. £ A is the
object spectrum emissive, b^ is the energy of atmospheric
scattering and radiation. As the equation (1), object spectral
imaging course is a complex non-linear system. Non-linear is
the main characteristic of fractal phenomenon. Thus we can
conclude that the spectral curve has the characteristic of fractal
as the spectral imaging model.
2) Spectral curve has some statistical self-similar property
As the fractal definition of Mandelbrot in 1986, fractal is a
model which the partial is similar to the total object. Thus the
fractal has the important property that the local part of fractal
model is similar to the whole model in some sides such as the
structure, correlation. The spectral curve has the self-similar in
statistics which indicate it has the fractal characteristic. The
self-similar property of spectral curve can be represented in the
SPOT image and TM multiple image as figure 1 shown:
SPOT. 1995.Wuhan TM,1993,Wuhan
Figure 1 Self-similar property in spectral image
Figure 1 is one of the SPOT image and TM image in Wuhan
city. The two images are similar. SPOT image has the total
information of the visible spectral bands and it can be taken as
the total model. TM image is just one band of the total 7 bands
and it can be taken as a local partial model while it is quite
similar to the SPOT image. Thus we can conclude that the local
partial spectral is similar to the whole spectral and it is one of
important characteristic of fractal. As the spectral self-similar
property, the spectral curve has the characteristic of fractal
model.
3) The length of spectral curve under different measurement
unit shows exponential relation
Different objects of 30 bands MAIS images are selected to
measure the length of spectral curve under different band width.
The result is shown as table 1:
Road
Tree
Water
Band width
length
Band width
length
Band width
length
0.0152
1919.891
0.0152
1919.788
0.0151
1919.927
0.0303
959.8975
0.0303
959.8264
0.0303
959.9269
0.0455
639.9032
0.0455
639.841
0.0454
639.9231
0.0606
479.9182
0.0606
479.8622
0.0605
479.9199
0.0758
383.9039
0.0758
383.8579
0.0757
383.9047
0.091
319.8651
0.091
319.855
0.0908
319.9119
0.1061
274.1918
0.1061
274.1394
0.1059
274.1956
0.1213
239.9018
0.1213
239.8822
0.1211
239.9165
0.1365
213.2343
0.1365
213.2071
0.1362
213.2365
0.1516
191.9162
0.1516
191.8814
0.1513
191.9256
0.1668
174.4568
0.1668
174.4649
0.1665
174.4974
0.1819
159.8929
0.1819
159.8763
0.1816
159.9186
0.1971
147.6093
0.1971
147.6089
0.1967
147.6362
0.2123
137.0428
0.2123
137.0259
0.2119
137.0728
0.2274
127.9135
0.2274
127.8472
0.227
127.9143
0.2426
119.9109
0.2426
119.8937
0.2422
119.9301
0.2578
112.8496
0.2577
112.8472
0.2573
112.8621
0.2729
106.5528
0.2729
106.5297
0.2724
106.5741
0.2881
100.9874
0.2881
100.8711
0.2876
100.9878
0.3032
95.9225
0.3032
95.8372
0.3027
95.9008
0.3184
91.3273
0.3184
91.2451
0.3178
91.3375
0.3336
87.2123
0.3336
87.2308
0.333
87.2487
0.3487
83.3676
0.3487
83.2667
0.3481
83.3575
0.3639
79.901
0.3639
79.8703
0.3632
79.9195
0.3791
76.7229
0.379
76.6772
0.3784
76.7366
0.3942
73.7573
0.3942
73.7568
0.3935
73.7788
0.4094
71.0025
0.4094
70.9662
0.4086
71.0291
0.4245
68.4847
0.4245
68.3921
0.4238
68.5072
0.4397
66.1024
0.4397
66.0308
0.4389
66.0975
0.4549
63.9291
0.4548
63.871
0.454
63.9264
0.4700
61.8521
0.4700
61.8318
0.4692
61.8694
0.4852
59.8985
0.4852
59.8314
0.4843
59.9113
Table 1 Spectral Curve length under different spectral width
