Abstract

We provide experimental data confirming the power-law spatial-correlation model of radiance statistics for a wide range of natural terrains and in two IR wave bands. We analyze imagery of four terrains that was acquired from an airborne sensor in both midwave and long-wave bands. Data are presented on the region of the correlation-model parameter space occupied by natural terrains.

© 1998 Optical Society of America

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References

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  1. D. C. Bertilone, R. S. Caprari, S. Angeli, G. N. Newsam, “Spatial statistics of natural terrain imagery I: non-Gaussian IR backgrounds and long-range correlations,” Appl. Opt. 36, 9167–9176 (1997).
    [CrossRef]
  2. N. Ben-Yosef, K. Wilner, S. Simhoney, G. Feigin, “Measurement and analysis of 2-D infrared natural background,” Appl. Opt. 24, 2109–2113 (1985).
    [CrossRef] [PubMed]
  3. T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1992).
    [CrossRef]
  4. I. Procaccia, “Fractal structures in turbulence,” J. Statis. Phys. 36, 649–664 (1984).
    [CrossRef]
  5. D. L. Ruderman, “Origins of scaling in natural images,” Vision Res. 37, 3385–3398 (1997).
    [CrossRef]
  6. The eucalypts covering terrain 1 are primarily E. miniata, E. tetrodonta, and E. nesophila, whereas for terrain 2 they are E. papuana and E. polycarpa. The projected foliage cover from trees greater than 10 m tall is 30%–69% for terrain 1 and 10%–29% for terrain 2.
  7. We have chosen to report only the data in the horizontal direction, as it is the least affected by the motion of the aircraft. In the time required for a single horizontal line scan, the aircraft moves a distance corresponding to only a few percent of the ground resolution.

1997 (2)

1985 (1)

1984 (1)

I. Procaccia, “Fractal structures in turbulence,” J. Statis. Phys. 36, 649–664 (1984).
[CrossRef]

Angeli, S.

Ben-Yosef, N.

Bertilone, D. C.

Caprari, R. S.

Feigin, G.

Newsam, G. N.

Procaccia, I.

I. Procaccia, “Fractal structures in turbulence,” J. Statis. Phys. 36, 649–664 (1984).
[CrossRef]

Ruderman, D. L.

D. L. Ruderman, “Origins of scaling in natural images,” Vision Res. 37, 3385–3398 (1997).
[CrossRef]

Simhoney, S.

Vicsek, T.

T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1992).
[CrossRef]

Wilner, K.

Appl. Opt. (2)

J. Statis. Phys. (1)

I. Procaccia, “Fractal structures in turbulence,” J. Statis. Phys. 36, 649–664 (1984).
[CrossRef]

Vision Res. (1)

D. L. Ruderman, “Origins of scaling in natural images,” Vision Res. 37, 3385–3398 (1997).
[CrossRef]

Other (3)

The eucalypts covering terrain 1 are primarily E. miniata, E. tetrodonta, and E. nesophila, whereas for terrain 2 they are E. papuana and E. polycarpa. The projected foliage cover from trees greater than 10 m tall is 30%–69% for terrain 1 and 10%–29% for terrain 2.

We have chosen to report only the data in the horizontal direction, as it is the least affected by the motion of the aircraft. In the time required for a single horizontal line scan, the aircraft moves a distance corresponding to only a few percent of the ground resolution.

T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1992).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Sample image from each of the ensembles. The number of images in each ensemble is (a) MW1, 90 images; (b) LW1, 90 images; (c) MW2, 96 images; (d) LW2, 96 images; (e) MW3, 124 images; (f) LW3, 124 images; (g) MW4, 88 images; and (h) LW4, 96 images.

Fig. 2
Fig. 2

Log–log plots of the autocovariance in the horizontal direction for (a) terrains 1 and 2 and (b) terrains 3 and 4. The solid curves show the experimental data; the dashed–dotted curves show the best fit of the model given by Eq. (1). The important physical parameters of the model are the length scale b and the exponent 2ν. The best-fit parameter values are MW1: b = 0.44 m, ν = 0.09; LW1: b = 0.68 m, ν = 0.09; MW2: b = 0.96 m, ν = 0.18; LW2: b = 1.02 m, ν = 0.17; MW3: b = 4.43 m, ν = 0.14; LW3: b = 2.89 m, ν = 0.14; MW4: b = 1.34 m, ν = 0.16; LW4: b = 0.87 m, ν = 0.17.

Fig. 3
Fig. 3

Best-fit parameter values plotted as points on the two-dimensional b - ν parameter space. The MW results are plotted as circles and the LW results as crosses. The error bars associated with parameter b correspond to the ground resolution of the sensor. Results for terrain 4 are not included because the data are not well fitted by the model, whereas results from an earlier study in the MW band (Ref. 1) are included.

Equations (1)

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C r = a b 2 + r 2 ν .

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