<s>
The	O
Oren	B-Algorithm
–	I-Algorithm
Nayar	I-Algorithm
reflectance	I-Algorithm
model	I-Algorithm
,	O
developed	O
by	O
Michael	O
Oren	O
and	O
Shree	O
K	O
.	O
Nayar	O
,	O
is	O
a	O
reflectivity	O
model	O
for	O
diffuse	O
reflection	O
from	O
rough	O
surfaces	O
.	O
</s>
<s>
In	O
computer	B-Application
vision	I-Application
and	O
computer	O
graphics	O
,	O
the	O
diffuse	O
component	O
is	O
often	O
assumed	O
to	O
be	O
Lambertian	O
.	O
</s>
<s>
This	O
model	O
for	O
diffuse	O
reflection	O
was	O
proposed	O
by	O
Johann	O
Heinrich	O
Lambert	O
in	O
1760	O
and	O
has	O
been	O
perhaps	O
the	O
most	O
widely	O
used	O
reflectance	O
model	O
in	O
computer	B-Application
vision	I-Application
and	O
graphics	O
.	O
</s>
<s>
Since	O
photo	O
receptors	O
of	O
the	O
retina	O
and	O
pixels	B-Algorithm
in	O
a	O
camera	O
are	O
both	O
finite-area	O
detectors	O
,	O
substantial	O
macroscopic	O
(	O
much	O
larger	O
than	O
the	O
wavelength	O
of	O
incident	O
light	O
)	O
surface	O
roughness	O
is	O
often	O
projected	O
onto	O
a	O
single	O
detection	O
element	O
,	O
which	O
in	O
turn	O
produces	O
an	O
aggregate	O
brightness	O
value	O
over	O
many	O
facets	O
.	O
</s>
<s>
The	O
Oren	B-Algorithm
–	I-Algorithm
Nayar	I-Algorithm
reflectance	I-Algorithm
model	I-Algorithm
,	O
developed	O
by	O
Michael	O
Oren	O
and	O
Shree	O
K	O
.	O
Nayar	O
in	O
1993	O
,	O
predicts	O
reflectance	O
from	O
rough	O
diffuse	O
surfaces	O
for	O
the	O
entire	O
hemisphere	O
of	O
source	O
and	O
sensor	O
directions	O
.	O
</s>
<s>
It	O
also	O
has	O
important	O
implications	O
for	O
human	O
vision	O
and	O
computer	B-Application
vision	I-Application
problems	O
,	O
such	O
as	O
shape	B-Algorithm
from	I-Algorithm
shading	I-Algorithm
,	O
photometric	B-Algorithm
stereo	I-Algorithm
,	O
etc	O
.	O
</s>
<s>
The	O
surface	O
roughness	O
model	O
used	O
in	O
the	O
derivation	O
of	O
the	O
Oren-Nayar	B-Algorithm
model	I-Algorithm
is	O
the	O
microfacet	O
model	O
,	O
proposed	O
by	O
Torrance	O
and	O
Sparrow	O
,	O
which	O
assumes	O
the	O
surface	O
to	O
be	O
composed	O
of	O
long	O
symmetric	O
V-cavities	O
.	O
</s>
<s>
In	O
the	O
Oren	B-Algorithm
–	I-Algorithm
Nayar	I-Algorithm
reflectance	I-Algorithm
model	I-Algorithm
,	O
each	O
facet	O
is	O
assumed	O
to	O
be	O
Lambertian	O
in	O
reflectance	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
(	O
i.e.	O
,	O
all	O
facets	O
in	O
the	O
same	O
plane	O
)	O
,	O
we	O
have	O
,	O
and	O
,	O
and	O
thus	O
the	O
Oren-Nayar	B-Algorithm
model	I-Algorithm
simplifies	O
to	O
the	O
Lambertian	O
model	O
:	O
</s>
<s>
Here	O
is	O
a	O
real	O
image	O
of	O
a	O
matte	O
vase	O
illuminated	O
from	O
the	O
viewing	O
direction	O
,	O
along	O
with	O
versions	O
rendered	O
using	O
the	O
Lambertian	O
and	O
Oren-Nayar	B-Algorithm
models	I-Algorithm
.	O
</s>
<s>
It	O
shows	O
that	O
the	O
Oren-Nayar	B-Algorithm
model	I-Algorithm
predicts	O
the	O
diffuse	O
reflectance	O
for	O
rough	O
surfaces	O
more	O
accurately	O
than	O
the	O
Lambertian	O
model	O
.	O
</s>
<s>
Here	O
are	O
rendered	O
images	O
of	O
a	O
sphere	O
using	O
the	O
Oren-Nayar	B-Algorithm
model	I-Algorithm
,	O
corresponding	O
to	O
different	O
surface	O
roughnesses	O
(	O
i.e.	O
</s>
