Method and system for fuzzy clustering of images

• US 7,260,263 B1
• Filed: 08/31/2004
• Issued: 08/21/2007
• Est. Priority Date: 03/28/2001
• Status: Expired due to Fees

• Current Assignee: AT&T Corporation (AT&T, Inc.)
• Original Assignee: AT&T Corporation (AT&T, Inc.)
• Inventors: Jafarkhani, Hamid, Tarokh, Vahid
• Primary Examiner(s): Bali; Vikkram
• Application Number:
  US10/930,253
• Time in Patent Office: 1,085 Days
• Field of Search: 382115-128, 382/181, 382/224, 382/225, 358/3.17, 704/245, 348/700
• US Class Current: 382/225
• CPC Class Codes: G06F 18/2323 based on graph theory, e.g. minimum spanning trees [MST] or graph cuts

Abstract

An approach to clustering a set of images based on similarity measures employs a fuzzy clustering paradigm in which each image is represented by a node in a graph. The graph is ultimately partitioned into subgraphs, each of which represent true clusters among which the various images are distributed. The partitioning is performed in a series of stages by identifying one true cluster at each stage, and removing the nodes belonging to each identified true cluster from further consideration so that the remaining, unclustered nodes may then be grouped. At the beginning of each such stage, the nodes that remain to be clustered are treated as all belonging to a single candidate cluster. Nodes are removed from this single candidate cluster in accordance with similarity and connectivity criteria, to arrive at a true cluster. The member nodes of this true cluster are then removed from further consideration, prior to the next stage in the process.

Claims

1. An apparatus for clustering a set of N images into P final clusters, where N and P are integers, comprising:

means for calculating at least one similarity measure S_ij between members of each possible pair of images, wherein S_ij represents the similarity measure between the ith and jth images with i and j being image indices and S_i,j=S_j,i;

means for calculating a total connectivity value for each of the images remaining to be clustered, a total connectivity value for each image being defined as a sum of a function f of the similarity measures associated with that image;

means for identifying, from among said images remaining to be clustered, a maximum total connectivity value t_max corresponding to an image I_max, image I_max belonging to a current cluster C which initially includes all images remaining to be clustered;

means for removing, from the current cluster C, at least one image based on at least one of its similarity measure with image I_max and its total connectivity value within current cluster C;

means for adding, to current cluster C, images having a similarity measure that is grater than a threshold T3 with any image currently in C;

means for calculating, for each image within current cluster C, a total connectivity value based on those images within C;

means for removing, from current cluster C, those images having a total connectivity value less than some threshold T4, wherein said total connectivity value calculating step and said image removing step are repeated until no further images are removed to thereby establish current cluster C as one of the final clusters; and

means for removing all images in current cluster C from further consideration, wherein one or more of said calculating steps, said identifying step, said removing steps, and said adding step are repeating until all N images are assigned to a final cluster.

2. The apparatus of claim 1, further comprising:

means for applying a non-linear function to each similarity measure, prior to calculating the total connectivity value.

3. The apparatus of claim 2, wherein the non-linear function is a transcendental function.

4. The apparatus of claim 3, wherein the transcendental function is a hyperbolic tangent.

5. The apparatus of claim 4, wherein each similarity measure S_i,j is transformed according to the formula tanh(5×

S_i,j) prior to calculating a total connectivity value.

6. The apparatus of claim 1, wherein the function f is the identify function.

7. The apparatus of claim 1, wherein the function f is a nonlinear function.

8. The apparatus of claim 1, wherein said at least one image removing means removes at least one image from the current cluster based on its similarity measure with image I_max, and then at least one other image is removed from the current cluster based on its total connectivity value within the current cluster.

9. The apparatus of claim 1, wherein said at least one image removing means removes at least one image from the current cluster based on its total connectivity value within the current cluster, and then at least one other image is removed from the current cluster based on its similarity measure with image I_max.

10. The apparatus of claim 1, wherein said at least one image removing means removes images having a similarity measure with I_max that is less than some threshold T1 from the current cluster.

11. The apparatus of claim 1, wherein said at least one image removing means removes a number N1 images having the N1 lowest similarity measures with I_max from the current cluster.

12. The apparatus of claim 1, wherein said at least one image removing means removes images having a total connectivity value which differs from t_max by more than some threshold T2 from the current cluster.

13. The apparatus of claim 12, wherein images have a similarity measure with I_max that is less than some threshold T1 are removed from the current cluster.

14. The apparatus of claim 13, wherein at least one image is removed from the current cluster based on its similarity measure with image I_max and then at least one other image is removed from the current cluster based on its total connectivity value within the current cluster.

15. The apparatus of claim 12, wherein a number N1 images having the N1 lowest similarity measures with I_max are removed from the current cluster.

16. The apparatus of claim 15, wherein at least one image is removed from the current cluster based on its similarity measure with image I_max and then at least one other image is removed from the current cluster based on its total connectivity value within current cluster.

17. An apparatus for clustering a set of N items into P final clusters, where N and P are integers, comprising:

means for calculating at least one similarity measure S_i,j between members of each possible pair of items, wherein S_i,j represents the similarity measure between the ith and jth items with i and j being items indices and S_i,j=S_j,i;

means for calculating a total connectivity value for each of the items remaining to be clustered, a total connectivity value for each item being defined as a sum of a function f of the similarity measures associated with that item;

means for identifying, from among said items remaining to be clustered, a maximum total connectivity value t_max corresponding to an item I_max, item I_max belonging to a current cluster C which initially includes all items remaining to be clustered;

means for removing, from the current cluster C, at least one item based on at least one of its similarity measure with item I_max and its total connectivity value within current cluster C;

means for adding, to current cluster C, items having a similarity measure that is greater than a threshold T3 with any item currently in C;

means for calculating, for each item within current cluster C, a total connectivity value based on those items within C;

means for removing, from current cluster C, those items having a total connectivity value less than some threshold T4, wherein said total connectivity value calculating step and said item removing step are repeated until no further items are removed to thereby establish current cluster C as one of the final clusters; and

means for removing all items in current cluster C from further consideration, wherein one or more of said calculating steps, said identifying step, said removing steps, and said adding step are repeating until all N items are assigned to a final cluster.

18. A computer-readable medium having stored thereon a plurality of instructions, the plurality of instructions including instructions which, when executed by a processor, cause the processor to perform the steps of a method for clustering a set of N images into P final clusters, where N and P are integers comprising of:

(a) calculating at least one similarity measure S_i,j between members of each possible pair of images, wherein S_i,j represents the similarity measure between the ith and jth images with i and j being image indices and S_i,j=S_j,i;

(b) calculating a total connectivity value for each of the images remaining to be clustered, a total connectivity value for each image being defined as a sum of a function f of the similarity measures associated with that image;

(c) identifying, from among said images remaining to be clustered, a maximum total connectivity value t_max corresponding to an image I_max, image I_max belonging to a current cluster C which initially includes all images remaining to be clustered;

(d) removing, from the current cluster C, at least one image based on at least one of its similarity measure with image I_max and its total connectivity value within current cluster C;

(e) adding, to current cluster C, images having a similarity measure that is greater than a threshold T3 with any image currently in C;

(f) calculating, for each image within current cluster C, a total connectivity value based on those images within C;

(g) removing from current cluster C, those images having a total connectivity value less than some threshold T4;

(h) repeating steps (f) and (g) until no further images are removed to thereby establish current cluster C as one of the final clusters;

(i) removing all images in current cluster C from further consideration; and

(j) repeating steps (b)-(i) until all N images are assigned to a final cluster.

19. The computer-readable medium of claim 18, comprising the step of applying a non-linear function to each similarity measure, prior to calculating the total connectivity value.

20. The computer-readable medium of claim 19, wherein the non-linear function is a transcendental function.

21. The computer-readable medium of claim 20, wherein the transcendental function is a hyperbolic tangent.

22. The computer-readable medium of claim 21, wherein each similarity measure S_i,j is transformed according to the formula tanh(5×

S_i,j) prior to calculating a total connectivity value.

23. The computer-readable medium of claim 18, wherein the function f is the identify function.

24. The computer-readable medium of claim 18, wherein the function f is a nonlinear function.

25. The computer-readable medium of claim 18, wherein in step (d), at least one image is removed from the current cluster based on its similarity measure with image I_max, and then at least one other image is removed from the current cluster based on its total connectivity value within the current cluster.

26. The computer-readable medium of claim 18, wherein in step (d), at least one image is removed from the current cluster based on its total connectivity value within the current cluster, and then at least one other image is removed from the current cluster based on its similarity measure with image I_max.

27. The computer-readable medium of claim 18, wherein in step (d), images having a similarity measure with I_max that is less than some threshold T1 are removed from the current cluster.

28. The computer-readable medium of claim 27, wherein in step (d), a number N1 images having the N1 lowest similarity measures with I_max are removed from the current cluster.

29. The computer-readable medium of claim 18, wherein in step (d), images having a total connectivity value which differs from t_max by more than some threshold T2 are removed from the current cluster.

30. The computer-readable medium of claim 29, wherein images having a similarity measure with I_max that is less than some threshold T1 are removed from the current cluster.

31. The computer-readable medium of claim 30, wherein at least one image is removed from the current cluster based on its similarity measure with image I_max and then at least one other image is removed from the current cluster based on its total connectivity value within the current cluster.

32. The computer-readable medium of claim 29, wherein a number N1 images having the N1 lowest similarity measures with I_max are removed from the current cluster.

33. The computer-readable medium of claim 32, wherein at least one image is removed from the current cluster based on its similarity measure with image I_max and then at least one other image is removed from the current cluster based on its total connectivity value within current cluster.

34. A computer-readable medium having stored thereon a plurality of instructions, the plurality of instructions including instructions which, when executed by a processor, cause the processor to perform the steps of a method for clustering a set of N items into P final clusters, where N and P are integers comprising of:

(a) calculating at least one similarity measure S_i,j between members of each possible pair of items, wherein S_i,j represents the similarity measure between the ith and jth items with i and j being item indices and S_i,j=S_j,i;

(b) calculating a total connectivity value for each of the items remaining to be clustered, a total connectivity value for each item being defined as a sum of a function f of the similarity measures associated with that item;

(c) identifying, from among said items remaining to be clustered, a maximum total connectivity value t_max corresponding to an item I_max, item I_max belonging to a current cluster C which initially includes all items remaining to be clustered;

(d) removing, from the current cluster C, at least one item based on at least one of its similarity measure with item I_max and its total connectivity value within current cluster C;

(e) adding, to current cluster C, items having a similarity measure that is greater than a threshold T3 with any item currently in C;

(f) calculating, for each item within current cluster C, a total connectivity value based on those items within C;

(g) removing, from current cluster C, those items having a total connectivity value less than some threshold T4;

(h) repeating steps (f) and (g) until no further items are removed to thereby establish current cluster C as one of the final clusters;

(i) removing all items in current cluster C from further consideration; and

(j) repeating steps (b)-(i) until all N items are assigned to a final cluster.