Multiscale detection of local image structures

1. A method for detection of local image structures represented as clusters in a joint-spatial range domain, comprising:

receiving an input image made having one or more clusters in a joint-spatial range domain, and each of the one or more clusters having a corresponding mode;

receiving a set of analysis matrices;

selecting through each one of the analysis matrices,

using the selected analysis matrix to partition the input image into the one or more clusters and their corresponding modes, and

computing a mean, μ, and a local covariance matrix Σ for each of the corresponding modes of each of the one or more clusters;

building a mode tree with at least one branch having a plurality of leaves, each leaf representing a respective one of the modes and the corresponding cluster, and

cycling through each branch of the mode tree and selecting at least one of the one or more clusters corresponding to the modes represented by the plurality of leaves, wherein each selected cluster has a stable mean and stable covariance matrix across the set of analysis matrices, and each of the selected clusters is indicative of a local image structure.

2. A method as defined in claim 1 , wherein the step of using the selected analysis matrix to partition the input image comprises:

computing a plurality of mean shift vectors using the selected analysis matrix; and

partitioning the input image into the one or more clusters using the plurality of mean shift vectors, the selected analysis matrix and a mean shift procedure.

3. A method as defined in claim 2 , wherein the step of computing a plurality of mean shift vectors using the selected analysis matrix comprises calculating each mean shift vector using the following equation

m

⁡

(

x

;

H

)

=

∑

i

⁢

w

x

i

⁡

(

x

;

H

)

⁢

x

i

∑

i

⁢

w

x

i

⁡

(

x

;

H

)

-

x

where m(x, H) is the mean shift vector calculated at a point vector x of the input image, H is the selected analysis matrix, vector x i represents a data point that makes up the input image, i is an index representing all the data points in the input image, w xi (x, H)=Φ(x−x i , H)v(x i ), Φ is the D-dimensional Gausian kernel, and v(x i ) is a weight associated with the point x i .

4. A method as defined in claim 3 , wherein v(x i )=1.

5. A method as defined in claim 1 , wherein the set of analysis matrices comprises:

the matrices H k , where H k =(h k ) 2 *I, k is an index, I is the identity matrix, and h k is varied between two values.

6. A method as defined in claim 5 , where h k is varied on a logarithmic scale by a constant step.

7. A method as defined in claim 1 wherein, the mean, μ, and the local covariance matrix Σ are computed by calculating

min

∑

∈

PDS

trace

⁢

[

(

A

T

⁢

H

-

T

⁢

∑

-

B

T

)

T

⁢

(

A

T

⁢

H

-

T

-

B

T

⁢

∑

-

1

)

]

where, Σ is a Positive Definite Symmetric local covariance matrix, H is the selected analysis matrix, A is a matrix of at least one mean shift vector at a point x, and B is a matrix of at least one vector calculated by subtracting the point x and the mean shift vectors at point x from the mean μ.

8. A method as defined in claim 1 , wherein the step of selecting through each one of the analysis matrices, using the selected analysis matrix to partition the input image, and computing a mean μ and a local covariance matrix Σ for each of the corresponding modes, further comprises the step of associating to each of the data points of each of the one or more clusters with the position x, the mean μ and the covariance matrix Σ of the mode of each of the one or more clusters.

9. A method as defined in claim 1 , wherein

each leaf also having the mean μ and the covariance matrix Σ associated with the mode wherein the step of selecting at least one of the one or more clusters comprises;

selecting each branch of the mode tree one at a time, and for each selected branch

defining a set of Gausian distributions p 1 . . . p K from the corresponding(μ1,Σ1) . . . (μK, ΣK) associated with each one of the leaves that make up the branch;

selecting the (μ,Σ) corresponding to a stable distribution of p 1 . . . p K ; and

selecting the cluster associated with the stable mean μ and the stable covariance Σ.

10. A method as defined in claim 9 wherein, selecting the (μ,Σ) corresponding to a stable distribution of p 1 . . . p K comprises:

selecting the (μ,Σ) corresponding to a minimum Jensen-Shannon divergence between neighboring Gausian distributions calculated using

JS

⁡

(

p

1

⁢

⁢

…

⁢

⁢

p

J

)

=

⁢

1

2

⁢

log

⁢

⁢



1

J

⁢

∑

j

=

1

J

⁢

Σ

j



∐

j

=

1

J

⁢



Σ

j



J

+

⁢

1

2

⁢

∑

j

=

1

J

⁢

(

μ

j

-

μ

)

T

⁢

(

∑

j

=

1

J

⁢

Σ

j

)

-

1

⁢

(

μ

j

-

μ

)

where p 1 . . . p J are the neighboring Gausian distributions, J is the number of the neighboring Gausian Distributions, vector μ J is the mean associated with the Gausian distribution, matrix Σ J is the covariance of the Gausian distribution and the vector μ representing the average of all the means associated with the neighboring Gausian distributions.

11. A method as defined in claim 10 wherein one neighboring Gausian Distribution is used.

12. A program storage device readable by machine, tangibly embodying a program of instructions executable by the machine to perform a method for detection of local image structures represented as clusters in a joint-spatial range domain, the method comprising:

receiving an input image made having one or more clusters in a joint-spatial range domain, and each of the one or more clusters having a corresponding mode;

receiving a set of analysis matrices;

selecting through each one of the analysis matrices,

using the selected analysis matrix to partition the input image into the one or more clusters and their corresponding modes, and

computing a mean, μ, and a local covariance matrix Σ for each of the corresponding modes of each of the one or more clusters;

building a mode tree with at least one branch having a plurality of leaves, each leaf representing a respective one of the modes and the corresponding cluster, and

cycling through each branch of the mode tree and selecting at least one of the one or more clusters corresponding to the modes represented by the plurality of leaves,

wherein each selected cluster has a stable mean and stable covariance matrix across the set of analysis matrices, and each of the selected clusters is indicative of a local image structure.

13. A program storage device as defined in claim 12 , wherein the step of using the selected analysis matrix to partition the input image comprises:

computing a plurality of mean shift vectors using the selected analysis matrix; and

partitioning the input image into the one or more clusters using the plurality of mean shift vectors, the selected analysis matrix and a mean shift procedure.

14. A program storage device as defined in claim 13 , wherein the step of computing a plurality of mean shift vectors using the selected analysis matrix comprises calculating each mean shift vector using the following equation

m

⁡

(

x

;

H

)

=

Σ

i

⁢

w

x

i

⁡

(

x

;

H

)

⁢

x

i

Σ

i

⁢

w

x

i

⁡

(

x

;

H

)

-

x

where m(x, H) is the mean shift vector calculated at a point vector x of the input image, H is the selected analysis matrix, vector x i represents a data point that makes up the input image, i is an index representing all the data points in the input image, w xi (x, H)=Φ(x−x i , H)v(x i ), Φ is the D-dimensional Gausian kernel, and v(x i ) is a weight associated with the point x i .

15. A program storage device as defined in claim 14 , wherein v(x i )=1.

16. A program storage device as defined in claim 12 , wherein the set of analysis matrices comprises:

the matrices H k , where H k =(h k ) 2 *I, k is an index, I is the identity matrix, and h k is varied between two values.

17. A program storage device as defined in claim 16 , where h k is varied on a logarithmic scale by a constant step.

18. A program storage device as defined in claim 12 , wherein the mean, μ, and the local covariance matrix Σ are computed by calculating

min

Σ

∈

PDS

⁢

trace

⁡

[

(

A

T

⁢

H

-

T

⁢

⁢

Σ

-

B

T

)

T

⁢

(

A

T

⁢

H

-

T

-

B

T

⁢

⁢

Σ

-

1

)

]

where, Σ is a Positive Definite Symmetric local covariance matrix, H is the selected analysis matrix, A is a matrix of at least one mean shift vector at a point x, and B is a matrix of at least one vector calculated by subtracting the point x and the mean shift vectors at point x from the mean μ.

19. A program storage device as defined in claim 12 , wherein the step of selecting through each one of the analysis matrices, using the selected analysis matrix to partition the input image, and computing a mean μ and a local covariance matrix Σ for each of the corresponding modes, further comprises the step of associating to each of the data points of each of the one or more clusters with the position x, the mean μ and the covariance matrix Σ of the mode of each of the one or more clusters.

20. A program storage device as defined in claim 12 , wherein

each leaf also having the mean μ and the covariance matrix Σ associated with the mode, wherein the step of selecting at least one of the one or more clusters, comprises:

selecting each branch of the mode tree one at a time, and for each selected branch

defining a set of Gausian distributions p 1 . . . p K from the corresponding (μ1, Σ1) . . . (μK, ΣK) associated with each one of the leaves that make up the branch;

selecting the (μ,Σ) corresponding to a stable distribution of p 1 . . . p K ; and

selecting the cluster associated with the stable mean μ arid the stable covariance Σ.

21. A program storage device as defined in claim 20 , wherein, selecting the (μ,Σ) corresponding to a stable distribution of p 1 . . . p K comprises:

selecting the (μ,Σ) corresponding to a minimum Jensen-Shannon divergence between neighboring Gausian distributions calculated using

JS

⁡

(

p

1

⁢

⁢

…

⁢

⁢

p

J

)

=

⁢

1

2

⁢

log

⁢

⁢



1

J

⁢

∑

j

=

1

J

⁢

Σ

j



∐

j

=

1

J

⁢



Σ

j



J

+

⁢

1

2

⁢

∑

j

=

1

J

⁢

(

μ

j

-

μ

)

T

⁢

(

∑

j

=

1

J

⁢

Σ

j

)

-

1

⁢

(

μ

j

-

μ

)

where p 1 . . . p J are the neighboring Gausian distributions, J is the number of the neighboring Gausian Distributions, vector μ J is the mean associated with the Gausian distribution, matrix Σ J is the covariance of the Gausian distribution and the vector μ representing the average of all the means associated with the neighboring Gausian distributions.

22. A method as defined in claim 21 wherein one neighboring Gausian Distribution is used.