Crowd Detection Using Grid-Based Pigeonhole Principle
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Solution Overview
Problem
Existing location tracking systems face significant hardware and computational burdens when detecting crowds in real-time, as the sweep-line approach requires quadratic increases in storage and runtime with the number of objects being tracked, making it unsuitable for large-scale implementations.
Innovation Solution
A method using a two-dimensional grid with predetermined spacing to define active grid points, where each object's location is compared to these points, and updates are processed to determine crowd formation by checking if four or more objects are within a specific threshold, employing the pigeonhole principle to limit hardware and computational requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the sweep-line approach is used for crowd detection, then measurement precision is improved, but device complexity increases quadratically with the number of objects
Solution Approach 1:
The patent divides the continuous spatial domain into discrete grid cells with predetermined spacing. Each grid point represents a discrete location where crowd detection can be performed independently. This segmentation transforms the continuous sweep-line problem into discrete grid-based operations, reducing computational complexity from quadratic to linear while maintaining detection precision through appropriate grid spacing selection.
Solution Approach 2:
The patent introduces a discrete grid dimension overlaying the continuous spatial domain. By mapping objects to grid points and using grid-based indexing, the system transforms the continuous 2D spatial problem into a discrete grid structure problem. This dimensional transformation enables efficient storage and querying using hash tables or arrays indexed by grid coordinates, reducing hardware requirements while maintaining detection accuracy.
2Measurement precision
If the sweep-line approach is used for crowd detection, then measurement precision is improved, but productivity decreases due to quadratic runtime increase
Solution Approach 1:
The continuous sweep-line operation is segmented into discrete grid cell operations. Instead of processing all objects across the entire area continuously, the system divides the space into grid cells and processes each cell independently. This segmentation reduces the runtime from O(n²) to O(n) by limiting comparisons to objects within the same or adjacent grid cells, thereby improving processing speed while maintaining detection precision.
Solution Approach 2:
The patent performs preliminary actions by pre-establishing the grid structure and pre-computing grid point locations before actual crowd detection begins. Objects are pre-mapped to grid points based on their coordinates. This preliminary grid-based organization eliminates the need for continuous pairwise comparisons during runtime, significantly improving processing speed while maintaining the precision of crowd detection through the predetermined grid spacing.
3Measurement precision
If the sweep-line approach is used for crowd detection, then measurement precision is improved, but loss of time increases due to quadratic computational requirements
Solution Approach 1:
The computational time is reduced by segmenting the problem into discrete grid cell operations. Instead of performing O(n²) comparisons across all objects, the system performs O(n) operations by processing each object once and placing it in the appropriate grid cell. This segmentation dramatically reduces computational time while maintaining detection precision through the predetermined grid spacing that ensures all relevant objects are captured in adjacent cells.
Solution Approach 2:
The patent uses grid points as simplified copies or representatives of spatial locations. Instead of processing all pairwise object relationships, the system creates a grid-based copy of the spatial structure and maps objects to these grid points. This copying approach reduces computational time from quadratic to linear by eliminating redundant comparisons while maintaining measurement precision through the predetermined grid spacing that preserves spatial relationships.
Data Source
AI summary
A method and computer system for detecting crowds in a location tracking system utilizes a grid and the pigeonhole principle to minimize an amount of hardware, memory and/or processing capability required in the location tracking system. In particular, an amount of storage required to determine whether a location update has resulted in a crowd grows only linearly, rather than quadratically, with the number of objects being tracked because a number of active grid points will be, at most, four times the number of objects being tracked. By determining whether an individual active grid point is within a crowd area, the computational time required for detecting a crowd within this crowd area is independent from the total number of objects being tracked.