Methods and Systems for Predicting Flow of Crowds from Limited Observations
First Claim
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1. A system for determining states of flow of objects in a scene, comprising:
- at least one sensor to measure the states of the flow at observed sample points of the scene, wherein the scene contains a set of sample points having subsets of observed and unobserved sample points;
a memory to store an operator specifying time-varying dynamics of training states of flow of the objects in the scene, wherein the operator is trained to determine an estimated future state of the states of flow of the objects at a sample point in the scene, as a function of current measured states of the states of flow of the objects at the set of sample points in the scene;
a processor in communication with the memory, configured to estimate, using the operator and the measured states at the subset of observed sample points, the states of the flow of the objects at the subset of unobserved sample points of the scene, such that the estimated future states at the subset of observed sample points are consistent with the measured states at the subset of observed sample points; and
an output interface in communication with the processor, configured for outputting the states of the flow at the set of unobserved sample points of the scene, so as to assist in a management of managing states of flow of objects in the scene.
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Abstract
Systems and methods for determining flows by acquiring a video of the flows with a camera, wherein the flows are pedestrians in a scene. The video includes a set of frames, wherein motion vectors are extracted from each frame in the set, and a data matrix is constructed from the motion vectors in the set of frames. A low rank Koopman operator can be determined from the data matrix and a spectrum of the low rank Koopman operator can be analyzed to determine a set of Koopman modes. Then, the frames are segmented into independent flows according to a clustering of the Koopman modes.
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Citations
20 Claims
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1. A system for determining states of flow of objects in a scene, comprising:
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at least one sensor to measure the states of the flow at observed sample points of the scene, wherein the scene contains a set of sample points having subsets of observed and unobserved sample points; a memory to store an operator specifying time-varying dynamics of training states of flow of the objects in the scene, wherein the operator is trained to determine an estimated future state of the states of flow of the objects at a sample point in the scene, as a function of current measured states of the states of flow of the objects at the set of sample points in the scene; a processor in communication with the memory, configured to estimate, using the operator and the measured states at the subset of observed sample points, the states of the flow of the objects at the subset of unobserved sample points of the scene, such that the estimated future states at the subset of observed sample points are consistent with the measured states at the subset of observed sample points; and an output interface in communication with the processor, configured for outputting the states of the flow at the set of unobserved sample points of the scene, so as to assist in a management of managing states of flow of objects in the scene. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14)
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15. A method for determining states of flow of objects in a scene, comprising:
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acquiring measured states of the flow at observed sample points of the scene generated by at least one sensor, wherein the scene contains a set of sample points having subsets of observed and unobserved sample points; using a memory having stored thereon an operator specifying time-varying dynamics of training states of flow of the objects in the scene, wherein the operator is trained to determine an estimated future state of the states of flow of the objects at a sample point in the scene, as a function of current measured states of the states of flow of the objects at the set of sample points in the scene; estimating, by a processor in communication with the memory, and using the operator and the measured states at the subset of observed sample points, the states of the flow of the objects at the subset of unobserved sample points of the scene, such that the estimated future states at the subset of observed sample points are consistent with the measured states at the subset of observed sample points; and outputting, via an output interface in communication with the processor, the states of the flow at the set of unobserved sample points of the scene, so as to assist in a management of managing states of flow of objects in the scene. - View Dependent Claims (16, 17)
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18. A non-transitory computer readable storage medium embodied thereon a program executable by a computer for performing a method, the method for determining states of flow of objects in a scene, the method comprising:
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acquiring measured states of the flow at observed sample points of the scene generated by at least one sensor, wherein the scene contains a set of sample points having subsets of observed and unobserved sample points; using a memory having stored thereon an operator specifying time-varying dynamics of training states of flow of the objects in the scene, wherein the operator is trained to determine an estimated future state of the states of flow of the objects at a sample point in the scene, as a function of current measured states of the states of flow of the objects at the set of sample points in the scene; estimating, by a processor in communication with the memory, and using the operator and the measured states at the subset of observed sample points, the states of the flow of the objects at the subset of unobserved sample points of the scene, such that the estimated future states at the subset of observed sample points are consistent with the measured states at the subset of observed sample points; and outputting, via an output interface in communication with the processor, the states of the flow at the set of unobserved sample points of the scene, so as to assist in a management of managing states of flow of objects in the scene. - View Dependent Claims (19, 20)
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Specification