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Aggregation Over Time

Learn Aggregation Over Time for free with explanations, exercises, and a quick test (for Computer Vision Engineer).

Published: January 5, 2026 | Updated: January 5, 2026

Who this is for

  • Computer Vision Engineers building streaming or video systems (CCTV, sports, retail, autonomous robotics).
  • Data scientists converting frame-by-frame model outputs into stable, actionable signals.
  • Engineers optimizing latency and reducing flicker in real-time UIs.

Prerequisites

  • Basic understanding of detection/segmentation/classification outputs (scores, boxes, labels).
  • Comfort with arrays, loops, and simple math (means, argmax).
  • Familiarity with tracking or ID association is helpful but not required.

Why this matters

Frame-level predictions are noisy. Temporal aggregation turns jittery per-frame outputs into stable signals you can trust.

  • Retail: avoid counting the same shopper multiple times as they move through frames.
  • Traffic: stabilize “red/green” light state to prevent rapid switching due to glare.
  • Sports: confirm a play event (e.g., goal) over several frames before alerting.
  • Safety: keep the “PPE not worn” alert steady with hysteresis to reduce alarm fatigue.

Concept explained simply

Temporal aggregation combines predictions across time so the final decision is less sensitive to momentary noise.

  • Smoothing scores: average or exponentially weight recent frames.
  • Voting: choose the most frequent label within a time window.
  • Track-level aggregation: merge per-frame detections along a track and decide once for the whole trajectory.
  • Hysteresis: different thresholds to turn an alert on vs. off, reducing flicker.

Mental model

Think of your model as a noisy sensor and the aggregator as a gentle damper. It resists quick flips unless evidence persists long enough.

Core techniques

Exponential Moving Average (EMA)

EMA_t = α·x_t + (1−α)·EMA_{t−1}. Lower α means more smoothing (and more latency).

  • Use for score stabilization (e.g., class probability, keypoint coordinates).
  • Initialization: set EMA_0 to the first observation to reduce warm-up bias.
Sliding window pooling
  • Mean/median over last N frames for scores.
  • Majority vote for class labels within a centered or causal window.
Hysteresis thresholds
  • Turn ON when score ≄ T_on; turn OFF when score < T_off (with T_off < T_on).
  • Great for alerts and UI indicators to avoid flicker.
Track-level aggregation
  • Associate detections across frames (tracking) to form a tubelet per object.
  • Aggregate per-tube scores (mean, max, median) and decide once.
  • Prevents double counting and stabilizes per-object attributes.
Temporal NMS / de-duplication
  • Merge overlapping detections across nearby frames based on IoU and time.
  • Keep highest-confidence representative or average coordinates.

Worked examples

1) EMA smoothing for a binary alert

Goal: stabilize a “helmet worn” score from 0–1.

  • Scores: [0.2, 0.9, 0.8, 0.3, 0.85], α=0.4; initialize with first value.
  • EMA: [0.2000, 0.4800, 0.6080, 0.4848, 0.6309]
  • Plain threshold 0.5 → alerts: [F, F, T, F, T]
  • Hysteresis (T_on=0.55, T_off=0.45) → alerts: [F, F, T, T, T] (less flicker)
When to use
  • Score-like outputs that benefit from inertia.
  • Real-time dashboards where small oscillations are distracting.

2) Majority vote over a sliding window

Goal: stabilize an action label across frames.

  • Labels per frame: [Cat, Cat, Dog, Cat, Dog, Dog, Dog], window size=3 (causal or centered).
  • Centered majority result: [Cat, Cat, Cat, Dog, Dog, Dog, Dog]
  • Optional minimum-run constraint (≄2 frames) prevents single-frame flips.
When to use
  • Discrete labels with occasional misclassifications.
  • Scenarios where a small delay is acceptable for stability.

3) Track-level decision for object attributes

Goal: for each tracked person, decide if they carry a backpack.

  1. Associate per-frame detections into tracks (IDs).
  2. Collect the attribute score per frame within each track.
  3. Aggregate with median or mean of top-k scores.
  4. Apply hysteresis at the track level to set final attribute.

Outcome: one reliable decision per person, not bouncing frame-by-frame.

How to build temporal aggregation

  1. Define the decision surface: what should be stable (score, label, count, attribute)?
  2. Choose a method: EMA for scores, majority for labels, track-level for object-wise decisions.
  3. Select window/α to balance smoothness vs. latency.
  4. Add hysteresis or minimum-run constraints to suppress flicker.
  5. Monitor latency budget (e.g., must respond < 300 ms?). Prefer causal windows/EMA.
  6. Evaluate: measure false flips per minute and average decision delay.

Exercises

These mirror the tasks below in the Exercises panel. Everyone can take them; only logged-in users get saved progress.

Exercise 1: EMA smoothing and hysteresis

Given scores [0.2, 0.9, 0.8, 0.3, 0.85], α=0.4, initialize EMA with the first value.

  • Compute the EMA sequence.
  • Apply plain threshold 0.5.
  • Apply hysteresis with T_on=0.55, T_off=0.45.
Exercise 2: Majority vote with minimum run

Labels: [Cat, Cat, Dog, Cat, Dog, Dog, Dog]; window=3 (centered). Compute stabilized labels, then enforce minimum run length of 2 frames.

  • Checklist: Did you initialize EMA properly?
  • Checklist: Are your windows causal/centered consistently?
  • Checklist: Did hysteresis reduce flicker without missing true events?

Common mistakes

  • Too-long windows → sluggish response. Self-check: measure delay between true change and reported change.
  • Inconsistent window alignment (centered vs. causal) → off-by-one decisions. Self-check: confirm timestamps used per decision.
  • Ignoring warm-up bias in EMA. Self-check: compare early EMA to raw values and allow a short warm-up.
  • Mixing objects in aggregation (no tracking) → double counts. Self-check: aggregate per track ID.
  • Not handling dropped frames → irregular timing. Self-check: use timestamps and time-based windows when frame rate varies.
  • Using same thresholds for on/off → flicker. Self-check: introduce hysteresis and compare flip rate.

Practical projects

  • Traffic-light state stabilizer: EMA on class probabilities + hysteresis for UI lamp.
  • Retail people counter: track-level counting with temporal de-duplication across entrance frames.
  • Sports highlight marker: sliding window vote for “celebration” action with minimum-run constraint.
  • Keypoint smoother: EMA on pose keypoints to reduce jitter in real-time overlays.

Learning path

  1. Day 1: Implement EMA on a saved score sequence; test thresholds and hysteresis.
  2. Day 2: Add majority vote and compare to EMA on the same data.
  3. Day 3: Build simple track association (IoU+nearest) and aggregate attributes per track.
  4. Day 4: Measure latency vs. stability; tune α/window and hysteresis gaps.

Next steps

  • Add adaptive windows: shrink on high confidence, expand on low confidence.
  • Explore Hidden Markov smoothing or temporal CRFs for structured labels.
  • Introduce time-based windows (ms) for variable FPS streams.

Mini challenge

Design a stabilizer for a “person present” overlay that must flip in under 300 ms but never flicker more than once per 10 seconds. Specify:

  • Your method (EMA, vote, hysteresis) and parameters.
  • Expected latency and how you measured it.
  • Flip-rate metric and how you tuned thresholds.

Quick test information

Everyone can take the quick test below; only logged-in users get saved progress.

Practice Exercises

2 exercises to complete

Instructions

Scores: [0.2, 0.9, 0.8, 0.3, 0.85]. Set α=0.4. Initialize EMA with the first value. Then:

  • Compute EMA for all frames.
  • Apply plain threshold 0.5 to produce boolean alerts.
  • Apply hysteresis with T_on=0.55, T_off=0.45.
Expected Output
EMA ≈ [0.2000, 0.4800, 0.6080, 0.4848, 0.6309]; Plain@0.5: [F, F, T, F, T]; Hysteresis(0.55/0.45): [F, F, T, T, T]

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