Probabilistic Object Counting with Track Uncertainty
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Solution Overview
Problem
Existing object counters do not account for the uncertainty of whether a track has crossed a predefined counting zone, leading to a lack of confidence in passage count values and triggered events.
Innovation Solution
A method that calculates a success probability for each moving object crossing a predefined curve using a time-dependent probability density function, providing both an expected value and variance of the number of objects that crossed the curve, incorporating filtering algorithms like Kalman or particle filters to track objects and account for measurement errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional object counting methods are used, then the counting process is simple and fast, but the reliability of the count is low due to unaccounted spatial uncertainty
Solution Approach 1:
The patent transforms the binary count parameter into a probabilistic parameter by calculating success probabilities pi for each track. Instead of simply incrementing a counter when a track crosses a line, the system now computes the probability that each track successfully crossed, taking into account the spatial uncertainty of the track. This parameter transformation resolves the contradiction by providing reliable counts through probabilistic assessment while maintaining computational feasibility.
Solution Approach 2:
The patent replaces the mechanical deterministic counting approach with a probabilistic computational model. Instead of using simple geometric intersection tests, the system employs probability density functions to model track uncertainty and computes expected values and variances. This substitution of mechanical methods with probabilistic computation resolves the contradiction between reliability and complexity by providing statistically sound results through mathematical modeling.
2Measurement precision
If spatial uncertainty is taken into account, then the confidence of passage count value improves, but the computational complexity increases
Solution Approach 1:
The patent segments the overall counting problem into independent per-track assessments. Instead of computing uncertainty for the entire count simultaneously, the system evaluates each track's success probability independently by examining whether the track's probability density function indicates crossing the counting zone. This segmentation resolves the contradiction by breaking down the complex computational task into manageable independent evaluations, improving measurement precision while controlling computational complexity through modular processing.
Solution Approach 2:
The patent introduces new parameters (success probability pi, expected value, variance) to quantify confidence in passage counts. By transforming the simple count into a probabilistic framework with measurable confidence indicators, the system provides measurement precision in terms of expected values and uncertainties. This parameter transformation resolves the contradiction by making confidence quantifiable through statistical parameters rather than qualitative assessment.
3Measurement precision
If probabilistic tracking is used, then the accuracy of object position is improved, but the simplicity of counting operation is reduced
Solution Approach 1:
The patent extracts the uncertainty characterization from the tracking process and separates it into a distinct probabilistic assessment step. The tracking system generates probability density functions that capture positional uncertainty, and then the counting operation independently evaluates these functions to determine success probabilities. This extraction resolves the contradiction by isolating the complex probabilistic reasoning from the simple counting operation, maintaining ease of operation while improving measurement precision through dedicated uncertainty analysis.
Data Source
AI summary
A method for counting a number of moving objects that cross at least one predefined curve in a scene comprises making detections of positions of one or more moving objects in the scene, tracking the positions of the moving objects over time based on the detections to produce one or more corresponding tracks, wherein each track is described by a time dependent probability density function, calculating, for each moving object, a success probability pi that the moving object succeeded to cross the at least one predefined curve in the scene, wherein the success probability is calculated by using the time dependent probability density function describing the track of the moving object, and calculating an expected value and a variance of a number of moving objects that crossed the at least one predefined curve by summing success probabilities pi and summing products pi(1−pi) of success and corresponding failure probabilities, respectively.