C)
b) detection.
arge windows
lack in detec-
ong bloom are
red component
le by a simple
he values from
'ts in the envi-
1 the areas ex-
1tioned in sec-
ment map, for
in any image;
izon. We limit
iile the vehicle
| solid angle of
» fill the holes.
as with no sky
be reduced by
tance by solv-
n the data term
; mainly affect
nselves for the
vironment map
: at the time of
c model to re-
used model is
arameters a, b,
] the sun posi-
ince. However,
atial frequency
ds. The detec-
ickground blue
ls proposed by
„> 0.2 (2)
ield correction,
| performed by
results as long
:neously in the
d by the radio-
he bloom effect
r field of view,
'stimated Perez
Figure 6: Original image (top) and difference between the esti-
mated Perez model and the blue sky pixels (homogeneous white
areas are those not detected as blue sky; the display settings are
chosen for enhancing contrast).
3.3 Using the parametric model to correct the environment
map
In order to reduce the influence of radiometric artifacts, we pro-
pose to use a correction based on an estimated Perez model. We
select images that do not have the sun in the hemisphere in front
of the camera, so they are only little affected by radiometric arti-
facts, thus their radiometry is reliable. The parameters L;, a, b, c,
d, e are estimated with these selected images. We then compute
the difference between the blue sky pixels of the original images
and the corresponding reconstructed values with the Perez model.
This difference, computed independently for each channel, does
not fit a simple parametric model (see figure 6). Indeed, this dif-
ference is due to radiometric artifacts (noisy and hard to model in
a physical way), but also to the misfit of the Perez model in the
presence of heterogeneous veil. We assume that images classified
a priori as having artifacts only suffer from a veil (i.e. an additive
constant, estimated as their mean error). They are thus corrected
by subtracting their mean error. The complete processing algo-
rithm is summarized in figure 7.
4 RESULTS
41 Environment maps
Using 13 images, the environment maps computed with the dif-
ferent techniques presented in 3 are shown on figure 8. The Perez
model is estimated with only 7 reliable images. The per-channel
corrections computed from the estimated Perez model slightly at-
tenuates the discontinuities in the stitching process, mostly by
correcting the red values, that tends to be increased by artifacts.
Though the Perez model is visually nice, it is probably more ac-
curate for the later simulated light to take into accounts the effect
of clouds. We can notice that this dataset is particularly tricky,
because the sun itself is masked by clouds; the overexposed ar-
eas inside these clouds cannot be filled by the values of the Perez
model.
The influence of the quality of this sky radiance estimation on the
light signal is discussed in the next section (4.2).
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B3, 2012
XXII ISPRS Congress, 25 August - 01 September 2012, Melbourne, Australia
Images
bd X
| Detection of blue sky
i dnreHableimages —
( Sky pixels A / Blue sky ' ^! Selected blue
rm p pixels … Sky pixels |
| Perez model |
us |
: Model parameters :
i s
; Per-image ;
additive correction
Ls ataatet see
Environment map
"u with holes -
| interpolation |
“ Complete '
“environment map
Figure 7: The steps of the proposed algorithm.
4.2 Influence on the simulated light
The purpose of the sky radiance reconstruction is to use physically-
based methods for extracting information form the pixels of the
images. The estimation of the reflectance of the materials of the
scene is an important step for these methods, and is usually per-
formed by minimizing the difference between acquired images
and simulated images with unknown reflectances (Coubard et al.,
2011). So the influence of the environment map on the simu-
lated light is very important to know. That is why we compare
the simulated signal in a simple urban scene (a street lined with
buildings), with several estimated environment maps, to quantify
the impact of their inaccuracy. The light is simulated by ray-
tracing, with a code based on LuxRender (Pharr and Humphreys,
2004). The maximum number of interreflections between objects
is set to 2, and the simulation is made for the red channel. The
radiance computed with the three environment maps presented in
section 4.1 is given for two points of the scene (figure 9).
The Perez model clearly underestimates the total light scattered
by the sun, because it doe not taken into account the clouds, that
are usually brighter than blue sky. This underestimation is about
20% with respect to the environment map computed by aggrega-
tion of all sky pixels. In a scene of urban canyon, the scattered
radiance is the main contribution to total radiance in the shadows
(e.g. point B on figure 9), with the same order of magnitude than
reflected radiance (Martinoty, 2005). This would lead in our case
to a maximal error with an order of magnitude of 10% on the total
sensor signal.
5 CONCLUSION AND FUTURE WORK
In this paper, we propose an approach for retrieving the sky radi-
ance from every direction of the upper hemisphere of an outdoor
scene, using panoramic images. The radiometric issues inher-
ent to CCD sensors are hard to modelize and correct. A method
