3D-DIoU Feature Matching for GPR Pipeline Detection

• 3D-DIoU is a geometric metric that integrates volumetric Intersection-over-Union with a center-distance penalty to enhance multi-view matching.
• It lifts 2D detections from B-scan, C-scan, and D-scan views into coherent 3D cuboids, ensuring consistent spatial alignment.
• The algorithm achieves state-of-the-art performance with over 90% true match retention and efficient real-time processing in noisy environments.

The 3D-DIoU spatial feature matching algorithm is a geometric and metric-based multi-view association technique designed to automate the correspondence of pipeline detections across B-scan, C-scan, and D-scan views in ground-penetrating radar (GPR) based subsurface pipeline localization. It combines three-dimensional Intersection-over-Union (3D-IoU) with a center-distance penalty, providing a robust, noise-tolerant method for fusing annotations into consistent 3D objects. The algorithm is a core component of a lightweight 3D pipeline detection framework utilizing cross-view information and advanced object detection strategies, achieving state-of-the-art accuracy and recall in complex underground settings (Lv et al., 24 Dec 2025).

1. Mathematical Definition of the 3D-DIoU Metric

3D-DIoU extends the 2D DIoU loss to axis-aligned cuboids in 3D Euclidean space. For any two cuboids $A$ and $B$:

• A cuboid $A$ is parameterized by $$(x_A^{\min}, x_A^{\max}, y_A^{\min}, y_A^{\max}, z_A^{\min}, z_A^{\max})$$.
• The volume is:

$$V(A) = (x_A^{\max} - x_A^{\min})(y_A^{\max} - y_A^{\min})(z_A^{\max} - z_A^{\min})$$

• The intersection volume is calculated as

$$V(A \cap B) = \max(0, \Delta x) \cdot \max(0, \Delta y) \cdot \max(0, \Delta z)$$

where, for example, $$\Delta x = \min(x_A^{\max}, x_B^{\max}) - \max(x_A^{\min}, x_B^{\min})$$.

• The union volume is $V(A \cup B) = V(A) + V(B) - V(A \cap B)$.
• 3D-IoU is given by

$$\mathrm{3D\text{-}IoU}(A,B) = \frac{V(A \cap B)}{V(A \cup B)}\quad\in[0,1]$$

• The center-distance penalty uses the cuboid centers,

$$d(A,B) = \lVert \mathbf{c}_A - \mathbf{c}_B \rVert_2 = \sqrt{ (c_{A,x} - c_{B,x})^2 + (c_{A,y} - c_{B,y})^2 + (c_{A,z} - c_{B,z})^2 }$$

• The diameter (diagonal) $c$ of the smallest enclosing cuboid is computed as the $\ell_2$ norm across corresponding axes.

The 3D-DIoU metric is then

$$\mathrm{3D\text{-}DIoU}(A,B) = \mathrm{3D\text{-}IoU}(A,B) - \frac{d(A,B)^2}{c^2}$$

The implementation in (Lv et al., 24 Dec 2025) uses $\lambda=1$ as the penalty weight.

2. Lifting 2D Detections to Constrained 3D Cuboids

Each GPR view inherently lacks information about one spatial axis:

• B-scan yields $(x, z)$ bounding boxes,
• C-scan yields $(x, y)$ bounding boxes,
• D-scan yields $(y, z)$ bounding boxes.

Matching requires synthesizing complete 3D cuboids from partial 2D observations:

• For B-scan: $$(x_b^{\min}, x_b^{\max}, y_c^{\min}, y_c^{\max}, z_b^{\min}, z_b^{\max})$$
• For C-scan: $$(x_c^{\min}, x_c^{\max}, y_c^{\min}, y_c^{\max}, z_d^{\min}, z_d^{\max})$$
• For D-scan: $$(x_b^{\min}, x_b^{\max}, y_d^{\min}, y_d^{\max}, z_d^{\min}, z_d^{\max})$$

Here, normalization maps all axes to a common 3D coordinate system using linear mappings inferred from the acquisition geometry described as “main_view” offsets. This dimensional completion enforces geometric consistency across scans.

3. Matching Algorithmic Pipeline

The pipeline automates association of multi-view detections into physical pipeline hypotheses:

function MATCH_MULTI_VIEW(B_boxes, C_boxes, D_boxes, T_conf=0.5, T_DIoU=0.4): # Filter boxes by confidence B_filt = [b for b in B_boxes if b.confidence >= T_conf] C_filt = [c for c in C_boxes if c.confidence >= T_conf] D_filt = [d for d in D_boxes if d.confidence >= T_conf] B3 = {b: LIFT_TO_3D(b, view='B') for b in B_filt} C3 = {c: LIFT_TO_3D(c, view='C') for c in C_filt} D3 = {d: LIFT_TO_3D(d, view='D') for d in D_filt} matches = [] for b in B_filt: for c in C_filt: if COMPUTE_3D_DIoU(B3[b], C3[c]) < T_DIoU: continue for d in D_filt: if COMPUTE_3D_DIoU(B3[b], D3[d]) < T_DIoU: continue if COMPUTE_3D_DIoU(C3[c], D3[d]) < T_DIoU: continue matches.append((b, c, d)) return matches

Each candidate triplet corresponds to a hypothesized pipeline. The approach leverages early filtering and confidence scoring, enhancing both precision and real-time capability.

4. Thresholding, Hyperparameters, and Robustness

The algorithm’s main hyperparameters are:

Hyperparameter	Default Value	Significance
Detection confidence $T_\mathrm{conf}$	0.5	Limits to high-confidence proposals
3D-DIoU threshold $T_\mathrm{DIoU}$	0.4	Governs spatial matching for association
NMS IoU for detector	0.7	(In detection) Non-maximum suppression granularity
DIoU penalty weight $\lambda$	1	(Typically fixed) Balances overlap vs. distance

A threshold $T_{\mathrm{DIoU}}=0.4$ was chosen by inspecting the empirical score distributions: 100% of B–C pairings and 91.8% of B–D pairings of true matches exceeded this value; robustness remains above 92% under moderate Gaussian noise ($\sigma=0.1$). Lower thresholds increase false positives; higher thresholds decrease recall (Lv et al., 24 Dec 2025).

5. Computational Complexity and Practical Considerations

Key computational aspects:

• Dimensional lifting and 3D-DIoU computation are both $O(1)$ per box or per pair, respectively.
• The naïve cost for $|B|\times|C|\times|D|$ triplet matching is negligible in typical applications (few boxes per view).
• Early filtering by DIoU accelerates execution, and spatial binning can further avoid unnecessary pairwise tests.
• The memory footprint remains minimal, with no dense 3D arrays required; only box metadata are stored.

This efficiency allows real-time multi-view matching even in complex environments.

6. Empirical Validation and Performance

Distribution analysis of DIoU, as reported in (Lv et al., 24 Dec 2025), demonstrates that a threshold of 0.4 retains over 90% of true matches even under synthetic noise up to $\sigma=0.2$. The overall system, combining DCO-YOLO object detection and 3D-DIoU geometric matching, achieves 96.2% accuracy, 93.3% recall, and 96.7% mean average precision on urban pipeline data—outperforming baseline strategies by up to 2% in recall. The high robustness under noise and sharp decrease in false matches below threshold underpin the metric’s discriminative power. No explicit ablation isolating DIoU is reported, but the improvements are directly attributed to this geometric consistency.

7. Illustrative Example: Metric Calculation and Filtering

For two boxes (B-scan and C-scan lifts):

• B3: $x \in [1.2, 1.8]$, $y \in [2.5, 2.8]$, $z \in [0.35, 0.45]$
• C3: $x \in [1.3, 1.7]$, $y \in [2.4, 2.9]$, $z \in [0.30, 0.50]$
• Overlap: $\Delta x = 0.4$, $\Delta y = 0.3$, $\Delta z = 0.10$
• $V_{\cap} = 0.012$, $V(A) = 0.018$, $V(B) = 0.040$, $V_{\cup} = 0.046$, $\mathrm{3D\text{-}IoU} \approx 0.26$
• With $d = 0.1$ and $c = 1.0$, $\mathrm{3D\text{-}DIoU} = 0.25\ (<0.4)$, thus rejected as a match

This demonstrates how the algorithm rejects weakly overlapping or spatially misaligned pairs, enforcing strict geometric correspondence.

Summary

The 3D-DIoU spatial feature matching algorithm delivers robust, interpretable, and computationally efficient 3D object association by integrating volumetric intersection metrics with spatial penalty terms. Its design, emphasizing pairwise geometric consistency across multi-view GPR scans, obviates the need for heuristic spatial rules, achieves high empirical performance, and is suitable for real-time deployments in noisy, ambiguous pipeline localization contexts (Lv et al., 24 Dec 2025).