the stereoscopic approach: fundamental assumptions: lambertian reflection from the surface the...
Post on 21-Dec-2015
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The stereoscopic approach:
Fundamental assumptions: Lambertian reflection from the surface
The difference between measured radiances at two view-angles can be used as a proxy for relative surface roughness
Fundamentals:
For a given pixel, surface-reflected solar irradiance L (Wm-2sr-1) at a given view angle can be approximated as:
)1()(1
)( shesol fRSIL (1)
)1()(1
)1()(1
)(
)(
)(
)(
2
1
2
1
shesol
shesol
fRSI
fRSI
L
L
The ratio between L at 1 and L at 2 is then:
(2)
Isol – incident solar irradiation (Wm-2) Re- surface reflectivity
S- down-welling sky irradiance (Wm-2) fsh- effective shade fraction
)1(
)1(
)(
)(
)(
)(
2
1
2
1
sh
sh
f
f
L
L
(3)
Atmospheric effects:
Isol – incident solar irradiation (Wm-2) Re- surface reflectivity S- path radiance (Wm-2sr-1)
S- down-welling sky irradiance (Wm-2) fsh- effective shade fraction () – atmospheric transmissivity
Per pixel, the ratio between at-sensor surface-reflected solar irradiance values L (Wm-2sr-1) at view angles 1 and 2 can be approximated as:
)()()(
)()()(
222
111
2
1
)1()(1
)1()(1
SfRSI
SfRSI
L
L
shesol
shesol
(5)
)()()( )1()(1
1
SfRSIL shesol (4)Can be removed using ‘dark object subtract’
Becomes a multiplicative scaling actor
)(
)(
)(
)(
2
1
2
1
2
1
)1(
)1(
sh
sh
f
f
L
L Assuming a laterally ~homogeneous atmosphere at the image scale (1) / (2) can be regarded as constant for the whole image.
Assuming a laterally ~homogeneous atmosphere at the image scale (1) / (2) can be regarded as constant for the whole image.
Atmospheric effects:
Isol – incident solar irradiation (Wm-2) Re- surface reflectivity S- path radiance (Wm-2sr-1)
S- down-welling sky irradiance (Wm-2) fsh- effective shade fraction () – atmospheric transmissivity
)(
)(
)(
)(
2
1
2
1
2
1
)1(
)1(
sh
sh
f
f
L
L
- can be regarded as a proxy for relative surface roughness between
similarly sloping pixels within a single image.
incorporates roughness variations at all sub-pixel scales
is independent of surface composition
fairly insensitive to atmospheric effects
)(
)(
2
1
L
L
%2)()( minmax)0(
)30(
)0(
)30( o
o
o
o
surface
atmosphere30°
Atmospheric transmissivity is a function of path length