Optimal multi-class classifier threshold-offset estimation with particle swarm optimization for visual object recognition

1. A system for multi-class classifier threshold-offset estimation for visual object recognition, the system comprising:

one or more processors and a memory having instructions such that when the instructions are executed, the one or more processors perform operations of:

receiving an input image comprising a set of input features;

training a classifier for each pair of a plurality of object classes M;

generating a set of classification responses r based on the set of input features;

computing a multi-class receiver-operating-characteristics (ROC) curve for a set of threshold-offsets x;

computing an objective function of classification performance f(x) from the ROC curve;

optimizing the objective function of classification performance f(x) through particle swarm optimization to generate a set of optimized threshold-offsets x;

applying the set of optimized threshold-offsets x to the set of classification responses r to generate a set of classification responses r′; and

comparing each classification response in the set of classification responses r′ to a predetermined value to classify the set of input features as belonging to an object class.

2. The system for multi-class classifier threshold-offset estimation as set forth in claim 1 , wherein the set of classification responses r is a set of M(M−1)/2 classification responses, where r=[r 12 r 13 r 14 . . . r 1m r 23 r 24 . . . r 2m r 34 . . . r (m-1)m ], and each subscript denotes an object class.

3. The system for multi-class classifier threshold-offset estimation as set forth in claim 2 , wherein r′=r+x, where x=(t 12 , t 13 , t 14 , . . . , t 1M , . . . ), and where t denotes a threshold-offset.

4. The system for multi-class classifier threshold-offset estimation as set forth in claim 3 , wherein the system further performs operation of:

generating a vote designating the set of input features as belonging to one object class of each pair of the plurality of object classes M or the other to generate a set of votes;

collecting the set of votes to determine which object class of the plurality of object classes M received a majority of the set of votes;

classifying the set of input features as belonging to the object class receiving the majority of the set of votes.

5. The system for multi-class classifier threshold-offset estimation as set forth in claim 4 , wherein the system further performs operations of:

extracting an area under the ROC curve (AUC) to determine a true-positive (TP) rate for a given false-positive rate; and

defining the objective function as:

f 1 ( x )= AUC 1 ( r ′( x ))+ AUC 2 ( r ′( x ))+ AUC 3 ( r ′( x ))+ . . . ,

wherein each subscript denotes an object class.

6. The system for multi-class classifier threshold-offset estimation as set forth in claim 4 , wherein the system further performs operations of:

extracting an area under the ROC curve (AUC) to determine a true-positive (TP) rate for a given false-positive rate; and

defining the objective function as:

f 2 ( x )= AUC 1 ( r ′( x ))* AUC 2 ( r ′( x ))* AUC 3 ( r ′( x ))* . . . ,

wherein each subscript denotes an object class and * denotes multiplication.

7. The system for multi-class classifier threshold-offset estimation as set forth in claim 4 , wherein the system further performs operations of:

extracting an area under the ROC curve (AUC) to determine a true-positive (TP) rate for a given false-positive rate; and

defining the objective function as:

f 3 ( x )= TP 1 ( r ′( x ))+ TP 2 ( r ′( x ))+ TP 3 ( r ′( x ))+ . . . ,

wherein each subscript denotes an object class.

8. The system for multi-class classifier threshold-offset estimation as set forth in claim 4 , wherein the system further performs operations of:

extracting an area under the ROC curve (AUC) to determine a true-positive (TP) rate for a given false-positive rate; and

defining the objective function as:

f 4 ( x )= TP 1 ( r ′( x ))* TP 2 ( r ′( x ))* TP 3 ( r ′( x ))* . . . ,

wherein each subscript denotes an object class and * denotes multiplication.

9. A computer-implemented method for multi-class classifier threshold-offset estimation for visual object recognition, comprising an act of:

causing a data processor to execute instructions stored on a memory such that upon execution, the data processor performs operations of:

receiving an input image comprising a set of input features;

training a classifier for each pair of a plurality of object classes M;

generating a set of classification responses r based on the set of input features;

computing a multi-class receiver-operating-characteristics (ROC) curve for a set of threshold-offsets x;

computing an objective function of classification performance f(x) from the ROC curve;

optimizing the objective function of classification performance f(x) through particle swarm optimization to generate a set of optimized threshold-offsets x;

applying the set of optimized threshold-offsets x to the set of classification responses r to generate a set of classification responses r′; and

comparing each classification response in the set of classification responses r′ to a predetermined value to classify the set of input features as belonging to an object class.

10. The method for multi-class classifier threshold-offset estimation as set forth in claim 9 , wherein the set of classification responses r is a set of M(M−1)/2 classification responses, where r=[r 12 r 13 r 14 . . . r 1m r 23 r 24 r 2m r 34 . . . r (m-1)m ], and each subscript denotes an object class.

11. The method for multi-class classifier threshold-offset estimation as set forth in claim 10 , wherein r′=r+x, where x=(t 12 , t 13 , t 14 , . . . , t 1M , . . . ), and where t denotes a threshold-offset.

12. The method for multi-class classifier threshold-offset estimation as set forth in claim 11 , further comprising an act of:

generating a vote designating the set of input features as belonging to one object class of each pair of the plurality of object classes M or the other to generate a set of votes;

collecting the set of votes to determine which object class of the plurality of object classes M received a majority of the set of votes;

classifying the set of input features as belonging to the object class receiving the majority of the set of votes.

13. The method for multi-class classifier threshold-offset estimation as set forth in claim 12 , further comprising acts of:

extracting an area under the ROC curve (AUC) to determine a true-positive (TP) rate for a given false-positive rate; and

defining the objective function as:

f 1 ( x )= AUC 1 ( r ′( x ))+ AUC 2 ( r ′( x ))+ AUC 3 ( r ′( x ))+ . . . ,

wherein each subscript denotes an object class.

14. The method for multi-class classifier threshold-offset estimation as set forth in claim 12 , further comprising acts of:

extracting an area under the ROC curve (AUC) to determine a true-positive (TP) rate for a given false-positive rate; and

defining the objective function as:

f 2 ( x )= AUC 1 ( r ′( x ))* AUC 2 ( r ′( x ))* AUC 3 ( r ′( x ))* . . . ,

wherein each subscript denotes an object class and * denotes multiplication.

15. The method for multi-class classifier threshold-offset estimation as set forth in claim 12 , further comprising acts of:

extracting an area under the ROC curve (AUC) to determine a true-positive (TP) rate for a given false-positive rate; and

defining the objective function as:

f 3 ( x )= TP 1 ( r ′( x ))+ TP 2 ( r ′( x ))+ TP 3 ( r ′( x ))+ . . . ,

wherein each subscript denotes an object class.

16. The method for multi-class classifier threshold-offset estimation as set forth in claim 12 , further comprising acts of:

extracting an area under the ROC curve (AUC) to determine a true-positive (TP) rate for a given false-positive rate; and

defining the objective function as:

f 4 ( x )= TP 1 ( r ′( x ))* TP 2 ( r ′( x ))* TP 3 ( r ′( x ))* . . . ,

wherein each subscript denotes an object class and * denotes multiplication.

17. A computer program product for multi-class classifier threshold-offset estimation for visual object recognition, the computer program product comprising: computer-readable instruction means stored on a non-transitory computer-readable medium that are executable by a computer having a processor for causing the processor to perform operations of:

receiving an input image comprising a set of input features;

training a classifier for each pair of a plurality of object classes M;

generating a set of classification responses r based on the set of input features;

computing a multi-class receiver-operating-characteristics (ROC) curve for a set of threshold-offsets x;

computing an objective function of classification performance f(x) from the ROC curve;

optimizing the objective function of classification performance f(x) through particle swarm optimization to generate a set of optimized threshold-offsets x;

applying the set of optimized threshold-offsets x to the set of classification responses r to generate a set of classification responses r′; and

comparing each classification response in the set of classification responses r′ to a predetermined value to classify the set of input features as belonging to an object class.

18. The computer program product for multi-class classifier threshold-offset estimation as set forth in claim 17 , wherein the set of classification responses r is a set of M(M−1)/2 classification responses, where r=[r 12 r 13 r 14 . . . r 1m r 23 r 24 . . . r 2m r 34 . . . r (m-1)m ], and each subscript denotes an object class.

19. The computer program product for multi-class classifier threshold-offset estimation as set forth in claim 18 , wherein r′=r+x, where x=(t 12 , r 13 , t 14 , . . . t 1M , . . . ), and where t denotes a threshold-offset.

20. The computer program product for multi-class classifier threshold-offset estimation as set forth in claim 19 , further comprising instruction means for causing the processor to perform an operation of:

generating a vote designating the set of input features as belonging to one object class of each pair of the plurality of object classes M or the other to generate a set of votes;

collecting the set of votes to determine which object class of the plurality of object classes M received a majority of the set of votes;

classifying the set of input features as belonging to the object class receiving the majority of the set of votes.

21. The computer program product for multi-class classifier threshold-offset estimation as set forth in claim 20 , further comprising instruction means for causing the processor to perform operations of:

extracting an area under the ROC curve (AUC) to determine a true-positive (TP) rate for a given false-positive rate; and

defining the objective function as:

f 1 ( x )= AUC 1 ( r ′( x ))+ AUC 2 ( r ′( x ))+ AUC 3 ( r ′( x ))+ . . . ,

wherein each subscript denotes an object class.

22. The computer program product for multi-class classifier threshold-offset estimation as set forth in claim 20 , further comprising instruction means for causing the processor to perform operations of:

extracting an area under the ROC curve (AUC) to determine a true-positive (TP) rate for a given false-positive rate; and

defining the objective function as:

f 2 ( x )= AUC 1 ( r ′( x ))* AUC 2 ( r ′( x ))* AUC 3 ( r ′( x ))* . . . ,

wherein each subscript denotes an object class and * denotes multiplication.

23. The computer program product for multi-class classifier threshold-offset estimation as set forth in claim 20 , further comprising instruction means for causing the processor to perform operations of:

extracting an area under the ROC curve (AUC) to determine a true-positive (TP) rate for a given false-positive rate; and

defining the objective function as:

f 3 ( x )= TP 1 ( r ′( x ))+ TP 2 ( r ′( x ))+ TP 3 ( r ′( x ))+ . . . ,

wherein each subscript denotes an object class.

24. The computer program product for multi-class classifier threshold-offset estimation as set forth in claim 20 , further comprising instruction means for causing the processor to perform operations of:

extracting an area under the ROC curve (AUC) to determine a true-positive (TP) rate for a given false-positive rate; and

defining the objective function as:

f 4 ( x )= TP 1 ( r ′( x ))* TP 2 ( r ′( x ))* TP 3 ( r ′( x ))* . . . ,

wherein each subscript denotes an object class and * denotes multiplication.