Determining Intensity Similarity in Low-Light Conditions Using the Poisson-Quantization Noise Model
A Poisson-quantization noise model for modeling noise in low-light conditions is described. In one aspect, image information is received. A Poisson-quantization noise model is then generated from a Poisson noise model and a quantization noise model. Poisson-quantization noise is then estimated in the image information using the Poisson-quantization noise model.
1 . A computer-readable media having computer-program instructions executable by a processor for:
receiving image information;
generating a Poisson-quantization noise model from a Poisson noise model and a quantization noise model;
estimating Poisson-quantization noise in the image information using the Poisson—quantization noise model;
determining an intensity similarity function using the Poisson-quantization noise model; and
finding pixel correspondence using the intensity similarity function.
2 . The computer-readable media as recited in claim 1 , wherein receiving comprises receiving at least two frames of image information.
3 . The computer-readable media as recited in claim 1 , wherein the Poisson noise model comprises:
p
(
k
,
λ
,
Q
)
=
∑
i
=
q
k
q
k
+
1
-
1
λ
i
i
!
-
λ
wherein k represents an intensity level, λ represents an intensity source, and Q represents quantization.
4 . The computer-readable media as recited in claim 1 , wherein the intensity similarity function comprises:
d
(
k
,
l
,
Q
)
=
min
λ
{
-
ln
(
P
(
k
,
l
,
λ
,
Q
)
)
}
=
-
ln
P
(
k
,
l
,
λ
^
,
Q
)
=
-
ln
{
-
2
λ
^
(
∑
i
=
q
k
q
k
+
1
-
1
λ
^
i
i
)
(
∑
j
=
q
l
q
l
+
1
-
1
λ
^
j
j
!
)
}
,
wherein k and l represent two intensity observations, λ represents an intensity source, P represents a joint probability, {circumflex over (λ)} represents an intensity source maximizing the joint probability P, and Q represents quantization.
5 . The computer-readable media as recited in claim 1 , wherein determining comprises finding a maximum joint probability that that two intensity observations k and l share the same intensity source.
6 . The computer-readable media as recited in claim 5 , wherein finding comprises performing a dichotomic search over the first derivative of the joint probability to find {circumflex over (λ)} corresponding to minima for the convex function −ln(P).
7 . The computer-readable media as recited in claim 5 , wherein finding comprises one of performing a gradient descent, and performing a Newton-Raphson descent to find the optimal {circumflex over (λ)}.
8 . A computing device comprising:
a processor; and
a memory coupled to the processor, the memory comprising computer-program instructions executable by the processor for:
receiving image information;
generating a Poisson-quantization noise model from a Poisson noise model and a quantization noise model;
estimating Poisson-quantization noise in the image information using the Poisson-quantization noise model;
determining an intensity similarity function using the Poisson-quantization noise model; and
finding pixel correspondence using the intensity similarity function.
9 . The device of claim 8 , wherein receiving comprises receiving at least two frames of image information.
10 . The device of claim 8 , wherein the Poisson noise model comprises:
p
(
k
,
λ
,
Q
)
=
∑
i
=
q
k
q
k
+
1
-
1
λ
i
i
!
-
λ
wherein k represents an intensity level, λ represents an intensity source, and Q represents quantization.
11 . The device of claim 8 , wherein generating comprises combining the Poisson noise model and the quantization noise model.
12 . The device of claim 8 , wherein the intensity similarity function comprises:
d
(
k
,
l
,
Q
)
=
min
λ
{
-
ln
(
P
(
k
,
l
,
λ
,
Q
)
)
}
=
-
ln
P
(
k
,
l
,
λ
^
,
Q
)
=
-
ln
{
-
2
λ
^
(
∑
i
=
q
k
q
k
+
1
-
1
λ
^
i
i
)
(
∑
j
=
q
l
q
l
+
1
-
1
λ
^
j
j
!
)
}
,
wherein k and l represent two intensity observations, λ represents an intensity source, P represents a joint probability, {circumflex over (λ)} represents an intensity source maximizing the joint probability P, and Q represents quantization.
13 . The device of claim 8 , wherein determining comprises finding a maximum joint probability that two intensity observations k and l share the same intensity source.
14 . The device of claim 13 , wherein finding comprises performing a dichotomic search over the first derivative of the joint probability to find {circumflex over (λ)} corresponding to minima for the convex function −ln(P).
15 . The device of claim 13 , wherein finding comprises one of performing a gradient descent, and performing a Newton-Raphson descent to find the optimal {circumflex over (λ)}.
16 . A computing device comprising:
a processor;
a Poisson-quantization noise modeling module executable on the processor to estimate Poisson quantization noise;
an intensity similarity measure module executable on the processor to determine an intensity similarity function based on the estimated Poisson quantization noise; and
a pixel correspondence module for finding pixel correspondence between image frames based on the intensity similarity function.
17 . The computing device of claim 16 , wherein the Poisson-quantization noise modeling module estimates Poisson quantization noise using a Poisson-quantization noise model comprising:
p
(
k
,
λ
,
Q
)
=
∑
i
=
q
k
q
k
+
1
-
1
λ
i
i
!
-
λ
,
wherein k represents an intensity level, λ represents an intensity source, Q represents quantization, and q k represents the minimum number of electrons to produce an intensity level of k.
18 . The computing device of claim 16 , wherein the Poisson-quantization noise module estimates quantization parameters for two image frames.
19 . The computing device of claim 16 , wherein the intensity similarity function comprises:
d
(
k
,
l
,
Q
)
=
min
λ
{
-
ln
(
P
(
k
,
l
,
λ
,
Q
)
)
}
=
-
ln
P
(
k
,
l
,
λ
^
,
Q
)
=
-
ln
{
-
2
λ
^
(
∑
i
=
q
k
q
k
+
1
-
1
λ
^
i
i
)
(
∑
j
=
q
l
q
l
+
1
-
1
λ
^
j
j
!
)
}
wherein k and l represent two intensity observations, λ represents an intensity source, P represents a joint probability, {circumflex over (λ)} represents an intensity source maximizing the joint probability P, Q represents quantization, and q k represents the minimum number of electrons to produce an intensity level of k.
20 . The computing device of claim 16 , wherein the computing device is used to improve images in one of night vision, medical imaging, underwater imaging, microscopic imaging and astronomical imaging.