EcoTraffic

A Spatiotemporal Entropy & Eco-Dynamics Estimation Framework Using Computer Vision

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📌 Overview

EcoTraffic transforms roadside video into a set of environment-aware motion disorder metrics using:

• Object detection (YOLOv8)
• Motion tracking (Kalman + SORT assignment)
• Velocity time-series modeling
• Shannon entropy of velocity distributions
• Kinetic energy variance
• Per-cell spatiotemporal entropy fields
• Eco-dynamics proxies (efficiency + CO₂ trend estimate)

This project fits directly into the theme Automotive × Object Detection × Environment by converting simple video into interpretable environmental indicators of traffic flow.

Unlike classical CV projects, EcoTraffic does not focus on detection accuracy. Detection is merely a measurement layer. The core idea is physical modeling of traffic motion through entropy and kinetic dispersion.

All metrics are logged into frame_metrics.csv, enabling deep time-series analysis and environmental trend estimation.

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📐 Theoretical Framework

1. Velocity Distribution Estimation

Using tracked vehicle centroids:

$$ v_i(t) = \sqrt{(x_i(t)-x_i(t-\Delta t))^2 + (y_i(t)-y_i(t-\Delta t))^2} $$

A rolling global velocity window of size ( W = 200 ) (as in the code) forms an empirical PDF:

$$ p_t(v) = \frac{\text{hist}(v_{t-W:t})}{\sum \text{hist}} $$

This distribution evolves over time and serves as the basis for entropy and energy statistics.

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2. Motion Entropy (Global Shannon Entropy)

$$ S(t) = -\sum_{v} p_t(v) \log(p_t(v)) $$

Interpretation:

• High entropy → diverse velocities → unstable traffic → stop-go turbulence
• Low entropy → uniform movement → stable traffic flow

Your code computes this exactly via a histogram over recent velocity magnitudes.

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3. Kinetic Energy Dispersion

For each instantaneous speed:

$$ E_i(t) = \frac{1}{2} v_i(t)^2 $$

Then global variance:

$$ \sigma_E^2(t) = \textrm{Var}(E_i(t)) $$

This reflects motion turbulence and “jerkiness” in the flow.

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4. Spatiotemporal Grid Entropy (Local Disorder Field)

The frame is divided into a grid:

• Width = 16 cells
• Height = 9 cells
• Each cell stores up to 100 recent speeds

For each cell ( c ):

$$ S_c = -\sum_{v} p_c(v)\log p_c(v) $$

Producing a 2D entropy heatmap (not displayed in the output video but computed internally).

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5. Eco-Dynamic Models

These models are deliberately simplified proxies (as you wrote in code).

Efficiency Estimate

$$ \eta(t) = \alpha e^{-\beta S(t)} + \gamma $$

Used constants:

ALPHA = 1.0
BETA = 1.0
GAMMA = 0.0

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CO₂ Trend Estimate (Proxy)

$$ E_{\text{CO₂}}(t) = k_1 \sigma_E^2(t) + k_2 S(t) + k_3 $$

These are not physical CO₂ units, only a trend signal combining turbulence & disorder.

The code uses:

K1 = 1.0
K2 = 0.5
K3 = 0.0

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⚙️ System Architecture

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🧩 Implementation Breakdown

Module	Description
Detection	YOLOv8-l (only for bounding boxes)
Tracking	Kalman Filter (x, y, vx, vy) + Hungarian assignment
Velocity Modeling	Δx-Δy displacement per frame
Entropy	Shannon entropy on histogram of last 200 velocities
Energy Dispersion	Variance of kinetic energies
Grid Entropy	Local cell-wise velocity entropy map
Eco-Dynamics	Efficiency + CO₂ trend proxy
Statistics	Pearson, Spearman, ANOVA, Mann-Whitney

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📊 Output Metrics (Per Frame)

Exported to frame_metrics.csv:

Column	Meaning
frame	Frame index
entropy	Shannon entropy ( S(t) )
sigma_E2	Kinetic energy variance
efficiency	( \eta(t) )
E_co2	CO₂ trend estimate
n_tracks	Number of active objects
mean_speed_frame	Avg. instantaneous per-frame speed

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📈 Statistical Analysis (Built-in)

1. Pearson & Spearman Correlations

The correlation analysis yielded:

$$ \begin{aligned} \rho_{\text{Pearson}}= -0.0151, \rho_{\text{Spearman}}= -0.0407. \end{aligned} $$

$$ \text{Both correlations indicate no linear or monotonic relationship between entropy and the CO}_2 \text{ proxy.} $$

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2. ANOVA Across Segments

$$ \begin{aligned} F_{\text{entropy}}= 2.4889,\quad p = 0.1149, F_{\text{CO}_2}= 2.0452,\quad p = 0.1529. \end{aligned} $$

$$ \text{Neither metric shows statistically significant differences across temporal segments.} $$

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3. Mann–Whitney U Tests

$$ \begin{aligned} p_{\text{entropy}}= 0.6577, p_{\text{CO}_2}= 0.0003. \end{aligned} $$

$$ \text{Entropy shows no significant difference, while the CO}_2 \text{ proxy exhibits a strong segment-level difference.} $$

🎥 Output

1. Annotated Processed Video

/outputs/eco_entropy_output.mp4

→ Shows bounding boxes, track IDs, entropy, σE², efficiency, CO₂.

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2. Entropy Time-Series Plot

3. CO₂ Estimate Time-Series Plot

4. Kinetic Energy Variance Plot

5. Efficiency Plot

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📁 Logs

All numerical results are saved into:

frame_metrics.csv

This CSV is the primary dataset for downstream analytics and environmental insights.

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🚀 Key Contributions

• A thermodynamics-inspired modeling of traffic flow
• Direct extraction of environment-related signals from plain video
• Integration of object detection + tracking + information theory
• A practical framework for environmental mobility analytics
• Full reproducibility with a single Python file

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⚠ Limitations

• Speeds are in pixels/frame, not physical units
• CO₂ output is a proxy, not physically calibrated
• Single-camera perspective may cause occlusions
• Entropy computed only on velocity magnitude, not directional fields
• Grid entropy computed but not rendered visually in the output video (by design)

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📚 Conclusion

EcoTraffic reframes traffic analysis as a non-equilibrium dynamical system, combining:

• entropy modeling
• kinetic energy variance
• stochastic velocity distributions
• eco-dynamic proxies
• segment-wise statistical tests