Depth Accuracy & Performance

The LooperRobotics Insight 9 utilizes active stereo vision based on triangulation. The fundamental relationship between depth (Z) and disparity (d) is defined as:

$Z=\frac{f\cdot B}{d}$

Where:

• Z: Depth (meters)
• f: Focal length (pixels) after rectification
• B: Baseline (meters) between the left and right optical centers
• d: Disparity (pixels), the shift of a feature point between left and right images

Depth is inversely proportional to disparity. A larger baseline (B) and focal length (f) result in higher sensitivity to depth changes, especially at long range.

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2. Theoretical Error Model #

Depth accuracy decreases quadratically with distance. By applying a first-order Taylor expansion to the depth equation, we derive the theoretical depth error (ΔZ):

$\Delta Z \approx -\frac{Z^2}{fB} \cdot \Delta d$

Key Implications:

• $\Delta Z \propto Z^2$ : Error grows with the square of the distance.
• $\Delta Z \propto \frac{1}{fB}$ : A larger f×B product (Focal Length × Baseline) directly reduces error. The Insight 9’s 100mm baseline provides significantly higher geometric stability than standard 50mm baseline cameras.
• $\Delta Z \propto \Delta d$ : If Δd = 1 pixel, long-distance depth error can reach the centimeter level or larger; if Δd = 0.1 pixel (sub-pixel accuracy), the error can be reduced by an order of magnitude.

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3. Critical Design Parameters #

The Insight 9 is engineered to balance near-field safety with long-range precision.

3.1 Focal Length (f) #

• Impact: A larger focal length increases the disparity for a given depth, making the system less sensitive to quantization noise.
• Insight 9 Spec: Optimized for mid-to-long range precision while maintaining a wide FOV for navigation.

3.2 Baseline (B) #

• Impact: The baseline determines the effective triangulation range. A wider baseline increases the geometric “resolution” of depth.
• Insight 9 Spec:100mm. This is 2x wider than standard consumer depth cameras, ensuring robustness at distances >5 meters.

3.3 Minimum Depth Range (Z_min) #

The minimum measurable distance is constrained by the maximum disparity search range (d_max) and physical occlusion.

$Z_{min}=\frac{fB}{d_{max}}$

• Insight 9 Configuration:
  • Focal Length (f): 304 pixels
  • Baseline (B): 0.1 meters
  • Max Disparity (d_max): 163 pixels
  • Result: Z_min ≈ 0.19 meters.

3.4 Summary of Optical Trade-offs #

Configuration	Design Goal	Depth Accuracy Profile	Min Distance	Typical Use Case
Low f + Small B	Near-field safety	Good at <2m, poor at long range	Very Close	Obstacle Avoidance
Mid f + Mid B	Balanced	Stable at 5–10m	Medium	Sensor Fusion
Insight 9 (High f + Large B)	Long-range Precision	High accuracy at >10m	0.19m	vSLAM, Logistics

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4. The “Oscillation” Phenomenon #

In real-world testing, depth error does not increase monotonically. It often exhibits a periodic “oscillation” or “staircase effect.”

Why this happens:

1. Discrete Sampling: Disparity is calculated on a pixel grid. Even with sub-pixel refinement, the estimation tends to “lock” onto integer or half-integer values.
2. Quantization: As an object moves away, the true disparity decreases continuously, but the calculated disparity jumps between discrete levels.
3. Result: When the true disparity aligns perfectly with the pixel grid, the error is near zero. When it falls between pixels, quantization error peaks.

Note: At very long ranges (>8m), disparity becomes very small (<4 pixels), and the oscillation transitions into random noise dominated by sensor signal-to-noise ratio.

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5. Benchmark: Insight 9 vs. RealSense D435i/D455 #

We conducted a side-by-side accuracy test to validate the Insight 9’s long-range capabilities against industry-standard sensors.

5.1 Test Setup #

• Environment: Indoor, stable lighting.
• Target: High-texture calibration board, perpendicular to the optical axis.
• Range: 0.5m to 10.10m (0.2m intervals).
• Methodology: ROI extraction, outlier removal (top/bottom 5%), and median calculation over 10 consecutive frames.

5.2 Device Specifications #

Device	Resolution	Baseline (B)	Focal Length (f)	f × B Factor
RealSense D435	848×480	50mm	424 px	~21.2
RealSense D455	848×480	95mm	433 px	~41.1
Insight 9	544×640	100mm	304 px	30.4

5.3 Results: Absolute Depth Error (%) #

• 0.5m – 3.0m: Insight 9 maintains <2% error, comparable to D455.
• 3.0m – 6.0m: Insight 9 maintains <4% error, significantly outperforming the D435 (which drifts to >8%).
• 6.0m – 10.0m: Insight 9 stays within 8% error.
  • Comparison: At 10 meters, the D435 error exceeds 18%, rendering it unusable for mapping. The Insight 9 remains functional for obstacle detection and loop closure.

Conclusion: The 100mm baseline of the Insight 9 provides superior geometric constraints, allowing for reliable depth sensing at distances where compact sensors fail.

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6. Recommended Operating Range #

Based on geometric constraints and experimental data:

• Min Range (0.19m): Limited by max disparity search range and stereo overlap.
• Max Effective Range (8.0m): Beyond 8 meters, disparity drops below 4 pixels. Depth estimation becomes dominated by sub-pixel noise. While detection is possible up to 30m, metric accuracy degrades.

Insight 9 Ideal Engineering Range: 0.2m – 8.0m