SimpleTIR: Trajectory Filtering in Real-Time Tracking

• Trajectory filtering is a set of spatio-temporal processes that remove noisy, fragmented, or unreliable segments to produce clean, continuous object trajectories.
• The methodology combines multi-feature matching (distance, area, shape, and color) with Kalman filter-based state prediction and correction for efficient track association.
• The system is computationally lightweight and scalable, with empirical results demonstrating robust performance in varied surveillance scenarios.

Trajectory filtering, in the context of SimpleTIR, refers to the set of spatio-temporal post-processing operations applied to sequence-based tracking outputs with the goal of removing noisy, fragmented, or unreliable trajectory segments and fusing those belonging to the same moving object. This approach integrates straightforward feature-based association with low-complexity prediction models and global lifecycle management to achieve robust, real-time multi-object tracking. The canonical methodology, established in "Robust Mobile Object Tracking Based on Multiple Feature Similarity and Trajectory Filtering" (Chau et al., 2011), provides a foundation for more recent, scalable filtering strategies and ongoing development in resource-constrained surveillance applications.

1. Multi-Feature Measurement and Association

SimpleTIR leverages a combination of four spatial features—distance, area, shape ratio, and color histogram—to perform frame-to-frame object association:

• Distance Feature: The displacement between bounding box centers, normalized by the anticipated maximum motion $D_{max}$. The local similarity for candidate $i, j$ is:

$$LS_1 = \max\left(0, 1 - \frac{d}{D_{max} \cdot m}\right)$$

where $d$ is center distance and $m$ is the frame gap.

• Area Feature: Relative bounding box area, measured as:

$$LS_2 = \frac{\min(W_i H_i, W_j H_j)}{\max(W_i H_i, W_j H_j)}$$

• Shape Ratio Feature: Aspect ratio match:

$$LS_3 = \frac{\min(W_i/H_i, W_j/H_j)}{\max(W_i/H_i, W_j/H_j)}$$

• Color Histogram Feature: The averaged similarity of color histogram bins:

$$LS_4 = \frac{1}{n} \sum_{k=1}^n \frac{\min(H_i(k), H_j(k))}{\max(H_i(k), H_j(k))}$$

These similarities are linearly weighted and fused, with global similarity $GS$ as:

$$GS = \begin{cases} \frac{\sum_{i=1}^4 w_i LS_i}{\sum_{j=1}^4 w_j} & LS_1 > 0 \ 0 & \text{otherwise} \end{cases}$$

Object pairs are associated if $GS > T_1$, enabling robust matching in the presence of varying illumination and partial occlusion.

2. State Prediction and Correction through Kalman Filtering

SimpleTIR employs a standard linear Kalman filter to extrapolate object states between frames. The process comprises:

• Estimation: The Kalman filter predicts object position and size:

$s_t^- = \Phi \cdot s_{t-1}^+$

• Measurement: The feature-based association yields a "measured state" $MS_t$.
• Correction: The filter blends the estimate ($ES_t$) and measurement ($MS_t$) by

$$CS_t = \begin{cases} w \cdot MS_t + (1-w) \cdot ES_t & \text{if measurement available} \ \text{prev } MS & \text{otherwise} \end{cases}$$

with $w$ typically set high (e.g., $w=0.7$) to favor data-driven correction. This mechanism is both lightweight and robust to moderate deviations from linear motion, elegantly combining model-based prediction with feature-based data association.

3. Global Trajectory Filtering: Lifecycle Management

The trajectory filtering ("global tracker") module addresses fragmentation caused by occlusions and detection failures and suppresses spurious tracks:

• Trajectory Fusion: When detections are missing for a few frames ("waiting state"), the last known state is maintained. If re-detection occurs within a predetermined window, fragmented segments are concatenated into a single trajectory.
• Noise Removal: Trajectories are filtered via temporal and spatial constraints:
  • Early termination: A trajectory is closed if the last matched frame $F_l$ satisfies $F_l < F_c - \min(N_r, T_2)$, where $F_c$ is current frame, $N_r$ is the number of frames with a match, $T_2$ is a delay threshold.
  • Short Trajectories: Reject trajectories with total time $T < T_3$ or maximum displacement $d_{max} < T_4$ (spatial threshold).
  • Waiting Time Fraction: If the ratio $T_w/T \geq T_5$ (waiting to total lifetime), the trajectory is suppressed.

Criterion	Equation	Purpose
Early termination	$F_l < F_c - \min(N_r, T_2)$	Fragment merging
Short lifespan	$T < T_3$	Outlier pruning
Small displacement	$d_{max} < T_4$	False alarm rejection
Excess waiting	$T_w / T \geq T_5$	Unstable track filtering

This approach meticulously filters out unreliable detections while preserving valid, but intermittently broken, tracks.

4. Computational Efficiency and Scalability

SimpleTIR is optimized for real-time operation. Feature extraction and matching are computationally light; the Kalman filter and global tracker logic involve lightweight linear algebra and rule-based updates. Empirical results show that, neglecting the detector’s cost, full tracking—including feature similarity, Kalman prediction, and trajectory filtering—can reach over 50 fps (and up to 641 fps) on moderately sized video frames, making the system well-suited for deployment in high-throughput surveillance scenarios (Chau et al., 2011).

Thresholds ($T_1$–$T_5$) may require empirical tuning to balance fragmentation tolerance and false positive rejection for a particular application. However, no explicit off-line learning or scene calibration is required.

5. Empirical Evaluation and Limitations

In the ETISEO multi-camera tracking benchmark, SimpleTIR outperforms or equals contemporary state-of-the-art algorithms on core metrics:

• $M_1$ (Tracking Time): Fraction of well-tracked object time.
• $M_2$ (ID Persistence): Ratio of unique reference IDs to matched tracked objects.
• $M_3$ (ID Confusion): Number of references per tracker (lower is better).
• $\bar{M}$: Aggregate performance metric (average of $M_1$–$M_3$).

The method exhibits robustness across both indoor and outdoor scenes and under weak/strong illumination, a direct consequence of multi-feature similarity and post-hoc trajectory filtering rather than reliance on contextual priors or calibration.

However, performance may degrade for highly nonlinear object dynamics or when sophisticated appearance descriptors would be essential to distinguish targets in dense crowds—a consequence of using elementary motion and color features. The system's effectiveness is also dependent upon appropriate parameter selection for spatial thresholds and waiting time.

Future improvements, as identified in the original work, include the introduction of automatically learned thresholds and potentially more advanced appearance or motion descriptors, but at the cost of increased model complexity and tuning requirements.

6. Summary and Theoretical Underpinnings

SimpleTIR exemplifies a pragmatic, principle-driven trajectory filtering pipeline that explicitly incorporates multi-feature similarity, Kalman-based prediction/correction, and rule-based global management. Its trajectory filtering mechanism is realized through a global tracker that fuses fragmented tracks and removes unreliable ones according to well-defined spatio-temporal heuristics. As a result, it enables robust, real-time tracking across diverse surveillance settings without recourse to scene-dependent models or computationally intensive association schemes. The design philosophy and empirical successes have shaped subsequent lightweight tracking pipelines and remain relevant reference points for contemporary real-time trajectory filtering system design.