Detecting multi-object anomalies utilizing a low rank sparsity model

1. A method for detecting anomalies in transportation related video footage, said method comprising:

in an offline training phase, receiving video footage at a traffic location;

in an offline training phase, extracting event encodings from said video footage received at said traffic location and collecting said event encodings into a training dictionary;

in an online detection phase, receiving at least one input video sequence captured at said traffic location or a similar traffic location;

extracting an event encoding corresponding to said at least one input video sequence;

reconstructing said event encoding with a low rank sparsity prior model applied with respect to said training dictionary; and

computing a reconstruction error between actual and reconstructed event encodings in order to determine if an event thereof is anomalous by comparing said reconstruction error with a threshold, wherein said computing said reconstruction error between said actual and reconstructed event encodings and determining if said event is anomalous includes asserting that said event is normal if the following test holds true:



y

i

-

y

^

i



2



y

i



2

<

τ

→

y

i

 wherein said y comprises a true event encoding, ŷ i comprises a reconstructed event encoding, and τ comprises a predetermined threshold.

2. The method of claim 1 wherein said event encoding comprises a trajectory of a moving object.

3. The method of claim 1 wherein said event encoding is based on spatiotemporal volume.

4. The method of claim 3 wherein reconstructing said event encoding further comprises computing with the following expression ŷ i =Aŝ i wherein ŝ i comprises a solution to a constrained convex optimization problem, and ŷ i comprises a reconstructed event encoding.

5. The method of 4 further comprising solving said constrained convex optimization problem via semi-definite programming.

6. The method of claim 1 wherein reconstructing said event encoding with said low rank sparsity prior model further comprises solving a constrained convex optimization problem in order to simultaneously minimize a rank and maximize sparsity of a reconstruction coefficient matrix subject to a constraint on reconstruction error.

7. The method of claim 6 further comprising solving the following problem:

minimize ∥S∥ S +λ∥S∥ 1

subject to ∥ Y−AS∥ F <ε

wherein S is a reconstruction coefficient matrix, Y is a matrix of input event encodings y i , A is the training dictionary, ∥ S∥ * is the nuclear norm of S, ∥S∥ 1 is the L−1 norm of S, ∥ ∥ F is the Frobenius norm of a matrix, |is a regularization parameter, and e is a predetermined threshold.

8. The method of claim 1 wherein said training dictionary comprises a plurality of event encodings, wherein each event encoding among said plurality of event encodings corresponds to at least one multiple object.

9. A system for detecting anomalies in transportation related video footage, said system comprising:

a processor; and

a non-transitory computer-usable medium embodying computer program code, said non-transitory computer-usable medium capable of communicating with said processor, said computer program code comprising instructions executable by said processor and configured for:

in an offline training phase, receiving video footage at a traffic location;

in an offline training phase, extracting event encodings from said video footage received at said traffic location and collecting said event encodings into a training dictionary;

in an online detection phase, receiving at least one input video sequence captured at said traffic location or a similar traffic location;

extracting an event encoding corresponding to said at least one input video sequence;

reconstructing said event encoding with a low rank sparsity prior model applied with respect to said training dictionary; and

computing a reconstruction error between actual and reconstructed event encodings in order to determine if an event thereof is anomalous by comparing said reconstruction error with a threshold, wherein said computing said reconstruction error between said actual and reconstructed event encodings and determining if said event is anomalous includes asserting that said event is normal if the following test holds true:



y

i

-

y

^

i



2



y

i



2

<

τ

→

y

i

⁢

 wherein said y comprises a true event encoding, ŷ i comprises a reconstructed event encoding, and τ comprises a predetermined threshold.

10. The system of claim 9 wherein said event encoding comprises a trajectory of a moving object.

11. The system of claim 9 wherein said event encoding is based on spatiotemporal volume.

12. The system of claim 9 wherein said instructions for reconstructing said event encoding with said low rank sparsity prior model, further comprises instructions configured for solving a constrained convex optimization problem in order to simultaneously minimize a rank and maximize sparsity of a reconstruction coefficient matrix subject to a constraint on reconstruction error.

13. The system of claim 12 wherein said instructions are further configured for solving the following problem:

minimize ∥S∥ * +λ∥S∥ 1

subject to ∥ Y−AS∥ F <ε

wherein S is a reconstruction coefficient matrix, Y is a matrix of input event encodings y i , A is the training dictionary, ∥ S∥ * is the nuclear norm of S, ∥S∥ 1 is the L−1 norm of S, ∥ ∥ F is the Frobenius norm of a matrix, |is a regularization parameter, and e is a predetermined threshold.

14. The system of claim 12 wherein reconstructing said event encoding further comprises computing with the following expression ŷ i =Aŝ i wherein ŝ i comprises a solution to a constrained convex optimization problem, and ŷ i comprises a reconstructed event encoding.

15. The system of 14 wherein said instructions are further configured for solving said constrained convex optimization problem via semi-definite programming.

16. The system of claim 9 wherein said training dictionary comprises a plurality of event encodings, wherein each event encoding among said plurality of event encodings corresponds to at least one multiple object.

17. A non-transitory processor-readable medium storing computer code representing instructions to cause a process for detecting anomalies in transportation related video footage, said computer code further comprising code to:

in an offline training phase, receive video footage at a traffic location;

in an offline training phase, extract event encodings from said video footage received at said traffic location and collecting said event encodings into a training dictionary;

in an online detection phase, receive at least one input video sequence captured at said traffic location or a similar traffic location;

extract an event encoding corresponding to said at least one input video sequence;

reconstruct said event encoding with a low rank sparsity prior model applied with respect to said training dictionary; and

compute a reconstruction error between actual and reconstructed event encodings in order to determine if an event thereof is anomalous by comparing said reconstruction error with a threshold, wherein said computing said reconstruction error between said actual and reconstructed event encodings and determining if said event is anomalous includes asserting that said event is normal if the following test holds true:



y

i

-

y

^

i



2



y

i



2

<

τ

->

y

i

 wherein said y comprises a true event encoding, ŷ i comprises a reconstructed event encoding, and r comprises a predetermined threshold.

18. The non-transitory processor-readable medium of claim 17 wherein:

said event encoding comprises a trajectory of a moving object;

said event encoding is based on spatiotemporal volume.