Methods and systems for predicting flow of crowds from limited observations
First Claim
1. A system for determining states of flow of objects in a scene, wherein the objects include one or a combination of an animal, a machine, a fluid, a material or an electrical current, the system 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 historical training data including flow of objects in the scene and a non-parametric operator specifying time-varying dynamics of training states of flow of the objects in the scene, wherein the non-parametric operator includes a set of operator eigenvalues and a set of operator modes that determine a set of complete modes for the states of the flow of the objects at all sample points in the set of sample points of the scene, and wherein the non-parametric 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;
an input interface in communication with the at least one sensor, to acquire the current measured states of the flow of the objects at the observed sample points of the scene;
a processor in communication with the memory and the input interface, configured to estimate, using the non-parametric operator and the current measured states at the subset of observed sample points along with the states of the flow of the objects at the subset of unobserved sample points of the scene, the estimated future states at the subset of observed sample points and at the subset of unobserved sample points, to ascertain 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
18 Claims
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1. A system for determining states of flow of objects in a scene, wherein the objects include one or a combination of an animal, a machine, a fluid, a material or an electrical current, the system 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 historical training data including flow of objects in the scene and a non-parametric operator specifying time-varying dynamics of training states of flow of the objects in the scene, wherein the non-parametric operator includes a set of operator eigenvalues and a set of operator modes that determine a set of complete modes for the states of the flow of the objects at all sample points in the set of sample points of the scene, and wherein the non-parametric 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; an input interface in communication with the at least one sensor, to acquire the current measured states of the flow of the objects at the observed sample points of the scene; a processor in communication with the memory and the input interface, configured to estimate, using the non-parametric operator and the current measured states at the subset of observed sample points along with the states of the flow of the objects at the subset of unobserved sample points of the scene, the estimated future states at the subset of observed sample points and at the subset of unobserved sample points, to ascertain 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)
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13. A method for determining states of flow of objects in a scene, wherein the objects include one or a combination of an animal, a machine, a fluid, a material or an electrical current, 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 historical training data including flow of objects in the scene and a non-parametric operator specifying time-varying dynamics of training states of flow of the objects in the scene, wherein the non-parametric operator includes a set of operator eigenvalues and a set of operator modes that determine a set of complete modes for the states of the flow of the objects at all sample points in the set of sample points of the scene, and wherein the non-parametric 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; acquiring the current measured states of the flow of the objects at the observed sample points of the scene via an input interface in communication with the at least one sensor; estimating, by a processor in communication with the memory and the input interface, and using the non-parametric operator and the current measured states at the subset of observed sample points along with the states of the flow of the objects at the subset of unobserved sample points of the scene, the estimated future states at the subset of observed sample points and at the subset of unobserved sample points, to ascertain 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 (14, 15)
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16. 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, wherein the objects include one or a combination of an animal, a machine, a fluid, a material or an electrical current, 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 historical training data including flow of objects in the scene and a non-parametric operator specifying time-varying dynamics of training states of flow of the objects in the scene, wherein the non-parametric operator includes a set of operator eigenvalues and a set of operator modes that determine a set of complete modes for the states of the flow of the objects at all sample points in the set of sample points of the scene, and wherein the non-parametric 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, wherein the non-parametric operator is a data dependent operator that directly estimates the states of the flow without requiring parameters to represent motion; acquiring the current measured states of the flow of the objects at the observed sample points of the scene via an input interface in communication with the at least one sensor; estimating, by a processor in communication with the memory and the input interface, and using the non-parametric operator and the current measured states at the subset of observed sample points along with the states of the flow of the objects at the subset of unobserved sample points of the scene, the estimated future states at the subset of observed sample points and at the subset of unobserved sample points, to ascertain 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 (17, 18)
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Specification