Anomalous change detection in imagery
View Patent ↗A distribution-based anomaly detection platform is described that identifies a non-flat background that is specified in terms of the distribution of the data. A resampling approach is also disclosed employing scrambled resampling of the original data with one class specified by the data and the other by the explicit distribution, and solving using binary classification.
1. A method for identifying pixels in co-registered first and second images that correspond to anomalous changes within the images, comprising:
selecting said first and second images for comparison;
writing sample (x,y) pairs to represent a pixel at a specified location in the first and second image;
wherein x represents the pixel from the first image, and y represents the corresponding pixel from the second image;
estimating P(x);
wherein P(x) comprises the distribution of pixels in the first image;
estimating P(y);
wherein P(y) comprises the distribution of pixels in the second image;
estimating P(x,y);
wherein P(x,y) comprises the distribution of (x,y) values in the first and second images; and
computing for every (x,y) pair the ratio of f(x,y)=P(x,y)/[P(x)P(y)].
2. A method as recited in claim 1 , further comprising:
selecting as anomalous changes the pixels (x,y) for which f(x,y) is smaller than a predetermined threshold.
3. A method as recited in claim 2 , wherein at least one of P(x) and P(y) are non-uniform distributions.
4. A method as recited in claim 3 , wherein
P
(
x
)
=
∫
P
(
x
,
y
)
ⅆ
y
and P(y) is a constant,
wherein P(y) corresponds to a uniform background.
5. A method as recited in claim 2 , wherein both P(x) and P(y) are non-uniform distributions.
6. A method as recited in claim 5 , wherein
P
(
x
)
=
∫
P
(
x
,
y
)
ⅆ
y
and
P
(
y
)
=
∫
P
(
x
,
y
)
ⅆ
x
.
7. A method as recited in claim 2 , further comprising directly modeling f(x,y).
8. A method as recited in claim 7 , wherein directly modeling f(x,y) comprises assuming P(x,y), P(x), and P(y) are Gaussian distributions.
9. A method as recited in claim 8 , further comprising:
computing the quadratic function
[
x
2
y
2
]
K
(
x
y
)
;
wherein the matrix K is given by
K
=
(
X
C
T
C
Y
)
-
1
-
(
X
0
0
Y
)
-
1
.
10. A method for identifying anomalous changes in co-registered first and second images, comprising:
selecting said first and second images for comparison;
writing sample (x,y) pair to represent a pixel at a specified location in the first and second image;
wherein x represents the pixel from the first image, and y represents the corresponding pixel from the second image;
generating a new image pair (X′,Y′) by scrambling the pixels in the first and second images;
generating a normal set of (x,y) points in the original image and a background set of (x,y′) points obtained from the scrambled image pair; and
computing f(x,y) by distinguishing the normal set from the background set through binary classification.
11. A method as recited in claim 10 , further comprising:
selecting as anomalous changes the pixels (x,y) for which f(x,y) is smaller than a predetermined threshold.
12. A method as recited in claim 11 , further comprising:
assigning parameters to the normal and background datasets set to classify the data.
13. A method as recited in claim 12 , further comprising:
assigning a greater weight on the normal dataset than the background dataset.
14. A method as recited in claim 10 , wherein f(x,y) is computed with a binary classification scheme.
15. A method for identifying anomalous changes in co-registered first and second images, comprising:
selecting said first and second images for comparison;
writing sample (x,y) pair to represent a pixel at a specified location in the first and second image;
wherein x represents the pixel from the first image, and y represents the corresponding pixel from the second image;
estimating the distribution of pixels in the first image;
estimating the distribution of pixels in the second image;
estimating the distribution of (x,y) values in the first and second images; and
computing for every (x,y) pair the ratio of the distribution of (x,y) values in the first and second images divided by the product of the distribution of pixels in the first image and the distribution of pixels in the second image.
16. A method as recited in claim 15 , further comprising:
assigning a threshold value to the computed data; and
selecting as anomalous changes the pixels (x,y) for which f(x,y) is smaller than the assigned threshold.
17. A method as recited in claim 15 , wherein at least one of the distribution of pixels in the first image and distribution of pixels in the second image are non-uniform distributions.
18. A method as recited in claim 15 , wherein both the distribution of pixels in the first image and distribution of pixels in the second image are non-uniform distributions.
19. A method as recited in claim 15 , wherein at least one of distribution of pixels in the first image, the distribution of pixels in the second image and the distribution of (x,y) values in the first and second images are estimated as Gaussian distributions.
20. A method as recited in claim 19 , wherein the distribution of pixels in the first image, the distribution of pixels in the second image and the distribution of (x,y) values in the first and second images are estimated as Gaussian distributions.
21. A method as recited in claim 15 :
wherein the distribution of pixels in the first image comprises
P
(
x
)
=
∫
P
(
x
,
y
)
ⅆ
y
;
and
wherein distribution of pixels in the second image comprises
P
(
y
)
=
∫
(
x
,
y
)
ⅆ
x
.
22. A method as recited in claim 15 :
wherein the distribution of pixels in the first image comprises
P
(
x
)
=
∫
P
(
x
,
y
)
ⅆ
y
;
and wherein distribution of pixels in the second image comprises a constant, uniform distribution.
23. A system for identifying anomalous changes in first and second images, comprising:
a first set of image data;
a second set of image data;
said first and second image data sets having sample (x,y) pairs representing a pixel at a specified location in the first and second image;
wherein x represents the pixel from the first image, and y represents the corresponding pixel from the second image;
means for computing a relationship between data in the first set and data in the second set based on a non-uniform distribution of data in the first set of image data and second set of image data; and
means for selecting data from the computed relationship falling within a threshold value as an anomalous change.
24. A system as recited in claim 23 , wherein the means for computing the relationship is configured to generate a new image data set by scrambling the pixels in the original data set of the first and second images, and distinguish the scrambled data set from the original data set with a binary classification scheme.
25. A system as recited in claim 23 , wherein the means for computing the relationship is configured to estimate the distribution of pixels and (x,y) values in the first and second images and calculate a ratio of the distribution of (x,y) values in the first and second images divided by the product of the distribution of pixels in the first image and the distribution of pixels in the second image.