Method of determining alignment of images in high dimensional feature space
View Patent ↗A method determines alignment of images in high dimensional feature space. The method comprises registering a source image of a reference modality to a target image of a second modality with an algorithm based upon a measure of information affinity present in both of the source and target image to create a registered image. Next, a plurality of feature vector are extracted from the registered image for each of the source and target images and attributes of the joint distribution of feature vector are captured using an entropic graph spanning the features. Edge lengths are between proximal feature vectors are extracted from the entropic graph and a similarity measure of one of an α-divergence estimate or an α-affinity estimate is constructed based upon these edge lengths to quantify whether the source and target image are sufficiently registered.
1. A method of determining alignment of decorelating images in high dimensional feature space, said method comprising:
simultaneously registering a source image of a reference modality to a plurality of target images of a second modality with an algorithm based upon a measure of information affinity present in both of the source and target images to create a registered image;
extracting a plurality of feature vectors from the registered image for each of the source and target images;
plotting a distribution of the feature vectors on an entropic graph;
determining edge lengths between the feature vectors from the entropic graph; and
determining a similarity measure of one of an α-divergence estimate or an α-affinity estimate based upon these edge lengths to indicate whether the source and target images are sufficiently registered.
2. A method as set forth in claim 1 wherein the entropic graph is further defined as a minimal graph spanning the feature vectors that minimizes a function of the total edge length of the minimal graph and that approximates the α-affinity or α-divergence of the distribution of the feature vectors.
3. A method as set forth in claim 1 wherein the entropic graph is further defined as based upon one of a minimum spanning tree (MST) or a k-nearest neighbor graph (k-NNG), a Steiner tree, a Delaunay triangulation, or a traveling salesman problem (TSP).
4. A method as set forth in claim 1 further comprising the step of re-deforming the source image into the target images with a different algorithm to shorten the edge lengths from the entropic graph thereby improving the similarity measure therebetween.
5. A method as set forth in claim 1 wherein the reference modality is further defined as different than the second modality.
6. A method as set forth in claim 1 wherein each of the feature vectors represent at least two feature dimensions.
7. A method as set forth in claim 1 wherein each of the feature vectors represent more than two feature dimensions.
8. A method as set forth in claim 1 wherein the step of determining the similarity measure is further defined as utilizing at least one of an α-mutual information (α-MI), an α-geometric-arithmetic (α-GA) divergence, and a Henze-Penrose (HP) divergence.
9. A method as set forth in claim 8 wherein the α-MI is further defined by the general formula:
α
MI
=
D
α
(
f
g
)
=
1
α
-
1
log
∫
f
α
(
x
,
y
)
f
1
-
α
(
x
)
f
1
-
α
(
y
)
ⅆ
x
ⅆ
y
wherein f and g are densities,
α ε (0,1) 1 ,
f(x,y) is a joint density, and
g(x,y) is a product of marginals f(x)f(y).
10. A method as set forth in claim 8 wherein the α-GA divergence is further defined by the general formula:
α
D
GA
(
f
,
g
)
=
D
α
(
pf
+
qg
f
p
g
q
)
=
1
α
-
1
log
∫
(
pf
(
z
)
+
qg
(
z
)
)
α
(
f
p
(
z
)
g
q
(
z
)
)
1
-
α
ⅆ
z
wherein f and g are densities,
α ε (0,1) 1 ,
p and q=1−p are weights;
p ε [0,1],
f(x,y) is a joint density, and
g(x,y) is a product of marginals f(x)f(y).
11. A method as set forth in claim 8 wherein the HP divergence is further defined by the general formula:
D
HP
(
f
g
)
=
∫
p
2
f
2
(
z
)
+
q
2
g
2
(
z
)
pf
(
z
)
+
qg
(
z
)
ⅆ
z
wherein f and g are densities,
p and q=1−p are weights;
p ε [0,1],
f(x,y) is a joint density, and
g(x,y) is a product of marginals f(x)f(y).
12. A method of determining alignment of decorelating images in high dimensional feature space, said method comprising:
simultaneously registering more than two images comprising at least a source image of a reference modality to target images of a second modality with an algorithm based upon a measure of mutual information present in both of the source and target images to create a registered image;
extracting a plurality of feature vectors from the registered image for each of the source and target images;
determining edge lengths between proximal feature vectors from an entropic graph; and
determining a similarity measure of one of an α-divergence estimate or an α-affinity estimate based upon these edge lengths with at least one of an α-mutual information (α-MI), an α-geometric-arithmetic (α-GA) divergence, and a Henze-Penrose (HP) divergence.
13. A method as set forth in claim 12 wherein the α-MI is further defined by the general formula:
α
MI
=
D
α
(
f
g
)
=
1
α
-
1
log
∫
f
α
(
x
,
y
)
f
1
-
α
(
x
)
f
1
-
α
(
y
)
ⅆ
x
ⅆ
y
wherein f and g are densities,
α ε (0,1) 1 ,
f(x,y) is a joint density, and
g(x,y) is a product of marginals f(x)f(y).
14. A method as set forth in claim 12 wherein the α-GA divergence is further defined by the general formula:
α
D
GA
(
f
,
g
)
=
D
α
(
pf
+
qg
f
p
g
q
)
=
1
α
-
1
log
∫
(
pf
(
z
)
+
qg
(
z
)
)
α
(
f
p
(
z
)
g
q
(
z
)
)
1
-
α
ⅆ
z
wherein f and g are densities,
α ε (0,1) 1 ,
p and q=1−p are weights;
p ε [0,1],
f(x,y) is a joint density, and
g(x,y) is a product of marginals f(x)f(y).
15. A method as set forth in claim 12 wherein the HP divergence is further defined by the general formula:
D
HP
(
f
g
)
=
∫
p
2
f
2
(
z
)
+
q
2
g
2
(
z
)
pf
(
z
)
+
qg
(
z
)
ⅆ
z
wherein f and g are densities,
p and q=1−p are weights;
p ε [0,1],
f(x,y) is a joint density, and
g(x,y) is a product of marginals f(x)f(y).
16. A method as set forth in claim 12 wherein the entropic graph is further defined as based upon one of a minimum spanning tree (MST) or a k-nearest neighbor graph (k-NNG).
17. A computer readable recording medium storing an executable control program for executing a method of determining alignment of decorelating images in high dimensional feature space, said method comprising:
simultaneously registering more than two images with an algorithm based upon a measure of information affinity present in the images to create a registered image;
extracting a plurality of feature vectors from the registered image for each of the source and target images;
determining edge lengths between proximal feature vectors from an entropic graph; and
determining a similarity measure of one of an α-divergence estimate or an α-affinity estimate based upon these edge lengths to indicate whether the source and target images are sufficiently registered.
18. A method as set forth in claim 17 wherein the entropic graph is further defined as based upon one of a minimum spanning tree (MST), a k-nearest neighbor graph (k-NNG), a Steiner tree, a Delaunay triangulation, or a traveling salesman problem (TSP).
19. A method as set forth in claim 17 wherein the step of determining the similarity measure is further defined as utilizing at least one of an α-mutual information (α-MI), an α-geometric-arithmetic (α-GA) divergence, and a Henze-Penrose (HP) divergence.