KDMD Operator for Crowd Flow Reconstruction from Sparse Video
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Solution Overview
Problem
Existing methods face challenges in accurately predicting and segmenting crowd flows from limited observations, particularly in dense crowd scenarios, as they struggle to identify and segment low-dimensional dynamical structures within chaotic crowd behaviors.
Innovation Solution
The implementation of a kernel dynamic mode decomposition (KDMD) operator that learns scene dynamics from training data, allowing for the estimation of flow parameters at unobserved points by projecting observed flows onto KDMD bases, thereby reconstructing complete crowd flows with limited spatial observations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional flow detection methods are used in dense crowd scenarios, then complete scene coverage is achieved, but measurement precision deteriorates due to chaotic behaviors and inability to identify low-dimensional dynamical structures
Solution Approach 1:
The patent transforms the detection approach by changing from direct flow parameter measurement to measuring projection parameters onto learned dynamical structures. This parameter transformation enables precise flow detection in dense crowds by projecting complex crowd motions onto low-dimensional manifolds that capture essential dynamics, thereby improving measurement precision without proportionally increasing system complexity
Solution Approach 2:
The patent introduces learned dynamical structures as intermediaries between sensors and flow parameters. These structures serve as a mediating layer that processes raw sensor data and extracts meaningful flow information, enabling precise measurement while keeping the detection system manageable in complexity
2Measurement precision
If more sensors are deployed to improve flow detection accuracy, then measurement precision improves, but device complexity and cost increase
Solution Approach 1:
The patent segments the flow detection problem into two parts: (1) learning dynamical structures from training data, and (2) projecting observed motions onto these structures. This segmentation allows the system to achieve high measurement precision with fewer sensors by leveraging the learned structures to infer unobserved flow characteristics
Solution Approach 2:
The patent creates virtual copies of flow information by projecting observed motions onto learned dynamical structures. This copying mechanism allows the system to reconstruct complete flow fields from partial observations, achieving high measurement precision without deploying a dense sensor network
3Reliability
If traditional methods process video texture for motion vectors, then motion detection capability is maintained, but privacy protection is compromised
Solution Approach 1:
The patent extracts only the essential motion information (projection parameters onto dynamical structures) while leaving out identifying visual features. This extraction approach maintains measurement precision by capturing key motion characteristics while removing privacy-sensitive information, thereby protecting individual privacy without sacrificing flow detection accuracy
4Measurement precision
If complete scene observation is implemented, then flow measurement accuracy improves, but loss of time and computational resources increases
Solution Approach 1:
The patent applies partial action by observing only a subset of the scene and using learned dynamical structures to infer the complete flow field. This approach achieves accurate complete flow field estimation without the time and computational cost of observing and processing the entire scene, thereby reducing loss of time while maintaining measurement precision
Data Source
AI summary
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.