NIF: Normal-Intersection Fields for Geometrically Consistent Oriented Box Refinement

Shaokai Zheng

cs.CVOct 29, 2026

NIF: Normal-Intersection Fields for Geometrically Consistent Oriented Box Refinement

Authors: Shaokai Zheng

Organizations: Shanghai Zhongchao Automation Engineering Co., Ltd.

Abstract

Accurate oriented detection requires a box to follow object boundaries, yet a standard regression head predicts its center, size, and angle from a pooled region representation. Small errors in these coupled parameters can displace long boundaries even when the object is correctly classified. We propose NIF, a refinement module that replaces an additional box regressor with normal-intersection fields. Given a coarse oriented box, the module observes local features at 20 boundary anchors and predicts signed distances along their outward normals. These observations admit an exact affine representation in five geometric variables. A differentiable, reliability-weighted least-squares fit projects the predicted field onto this representation and analytically recovers a refined rectangle. Tangential pooling preserves the normal position profile, while shared projection limits the added network to 0.132M parameters. On DOTA-v1.0, NIF reaches 78.00%, 79.11%, and 79.02% mAP with Oriented R-CNN, LSKNet-S, and Strip R-CNN, respectively, achieving the highest single-scale SOTA result in Table 1. It reaches 68.19% on DIOR-R, improves matched FAIR1M/DIOR-R baselines by 0.30/0.68%, and raises HRSC mean IoU from 0.867 to 0.888 while reducing field error by 24.5%. Across four different detector frameworks with the detectors frozen, relative AP75 improves by 1.57-4.18% and COCO-style mAP by 0.42-3.74%, without detector retraining. Code is available at https://github.com/zsk466991125-collab/Normal-Intersection-Fields.

Figures & tables

Figure 1: Overview of NIF. The carrier predicts coarse boxes $P$ and class scores $p$ . Shared projection reduces FPN features to 64 channels; twenty $3\!\times\!9$ strips predict normal observations and reliabilities. Weighted fitting and analytic decoding refine boxes before rotated NMS. The DOTA example shows raw intersections $\hat{\mathbf{q}}_{i}$ and compatible intersections $\mathbf{q}_{i}^{+}$ , with signed normal distances in pixels. GT supplies supervision and visualization. Here, $J_{P}=J(P)$ , $N=4m=20$ , and $\bar{r}$ is mean observation reliability. $\mathcal{L}_{\mathrm{obs}}^{w}$ denotes the weighted loss in Eq. 11 . In the decoder tuple, $w^{+}=2a^{+}$ and $h^{+}=2b^{+}$ are full refined box dimensions.

Figure 2: Geometry of the normal-intersection field. (a) Anchors and outward normals are attached to the coarse rectangle. (b) The signed displacement ends at a corresponding target supporting line, including intersections beyond finite edges. (c) Translation, scale, and rotation induce different, coordinated constant and slope patterns. These patterns motivate an exact five-dimensional compatible field. Intersection labels

\mathbf{q}_{i}

denote target points

\mathbf{q}_{i}^{*}

;

\mathbf{c},\mathbf{u},\mathbf{v}

define the coarse-box frame.

Figure 3: Local observation network. Tensor sizes are per observation. T-pool averages along the tangent while preserving nine normal positions; C concatenates visual and geometric descriptors. The shared predictor outputs 20 field values and reliabilities per box. WLS fits five geometric variables for analytic rectangle decoding.

Method	PL	BD	BR	GTF	SV	LV	SH	TC	BC	ST	SBF	RA	HA	SP	HC	mAP
R. Faster R-CNN [ 40 ]	89.40	81.81	47.28	67.44	73.96	73.12	85.03	90.90	85.15	84.90	56.60	64.77	64.70	70.28	62.22	73.17
R 3 Det [ 51 ]	89.50	81.20	50.50	66.10	70.90	78.70	78.20	90.80	85.30	84.20	61.80	63.80	68.20	69.80	67.20	73.70
R 3 Det-GWD [ 53 ]	88.82	82.94	55.63	72.75	78.52	83.10	87.46	90.21	86.36	85.44	64.70	61.41	73.46	76.94	57.38	76.34
R 3 Det-KLD [ 56 ]	88.90	84.17	55.80	69.35	78.72	84.08	87.00	89.75	84.32	85.73	64.74	61.80	76.62	78.49	70.89	77.36
S 2 A-Net [ 16 ]	89.11	82.84	48.37	71.11	78.11	78.39	87.25	90.83	84.90	85.64	60.36	62.60	65.26	69.13	57.94	74.12
RoI Transformer [ 9 ]	89.01	77.48	51.64	72.07	74.43	77.55	87.76	90.81	79.71	85.27	58.36	64.11	76.50	71.99	54.06	74.05

Table 1: Comparisons with SOTA methods on the DOTA-v1.0 dataset (AP in percent). PL, BD, BR, GTF, SV, LV, SH, TC, BC, ST, SBF, RA, HA, SP, and HC follow the standard DOTA category abbreviations.

Method	Params (M)	GFLOPs	AP 50	AP 75	mAP
PASCAL VOC 2007
O-RCNN [ 47 ]	41.37	211.43	90.40	88.60	70.66
O-RCNN + NIF	41.50	220.48	90.50	89.70	74.33
LSKNet-S [ 28 ]	30.98	173.68	90.50	88.20	69.80
LSKNet-S + NIF	31.11	182.72	90.30	89.40	74.55
PKINet-v2-S [ 2 ]	30.73	173.68	90.30	88.40	69.53

Table 2: Comparisons with SOTA methods on the HRSC2016 dataset (AP in %). All models are trained locally on trainval and evaluated on test with the final 36-epoch checkpoint. Complexity uses

1024\!\times\!1024

reference inputs and the common mean NIF cost described in the text. AP uses VOC 2007/2012 interpolation; mAP follows the COCO-style metric.

Method	G. V. * [ 49 ]	RetinaNet * [ 30 ]	C-RCNN * [ 3 ]	F-RCNN * [ 40 ]	RoI Trans. * [ 9 ]	O-RCNN [ 47 ]	LSKNet-S [ 28 ]	Strip R-CNN [ 62 ]	O-RCNN + NIF	LSKNet-S + NIF	Strip R-CNN + NIF
mAP (%)	29.92	30.67	31.18	32.12	35.29	45.60	47.87	47.92	46.36	48.13	48.22

Table 3: Comparisons with SOTA methods on the FAIR1M-v1.0 dataset . *: Results are referenced from the FAIR1M paper [ 42 ] .

Method	Params (M)	GFLOPs	mAP (%)
RetinaNet-O [ 30 ]	–	–	57.55
Faster R-CNN-O [ 40 ]	41.10	198.00	59.54
TIOE-Det [ 36 ]	41.10	198.00	61.98
O-RCNN [ 47 ]	41.37	211.43	64.30
ARS-DETR [ 63 ]	41.10	198.00	66.12
O-RepPoints [ 26 ]	36.60	–	66.71

Table 4: Comparisons with SOTA methods on the DIOR-R dataset . Literature complexity follows Strip R-CNN [ 62 ] where reported. O-RCNN, LSKNet-S, Strip R-CNN, and their NIF counterparts use the standardized estimates in Table 2 :

1024\!\times\!1024

input, 1,000 baseline proposals, and the common mean NIF cost.

	Frozen carrier		Carrier + NIF
Carrier	AP 75	mAP	AP 75	mAP
YOLO26-L OBB [ 24 ]	59.19	54.18	60.12	54.41
O2-RTDETR [ 13 ]	54.28	51.09	56.05	52.10
LSKNet-S + FAA [ 28 , 15 ]	51.88	48.35	54.05	50.16
PKINet-v2-S [ 2 ]	54.58	50.83	56.17	52.07

Table 5: Cross-framework transfer on DOTA-v1.0 . Each carrier is initialized from its official single-scale checkpoint, with all detector parameters frozen and only NIF optimized. AP 75 is evaluated at IoU

0.75

; mAP is the COCO-style mean AP averaged over IoU thresholds from

0.50

0.95

. “LSKNet-S + FAA” denotes the FAA Head carrier.

Figure 4: Geometric refinement evidence on HRSC2016. (a) Normal observations, box refinement, and Grad-CAM for the final update. (b) Normal-field error. (c) Paired IoU gain by coarse IoU.

Class	Strip R-CNN	O-RCNN+NIF	LSKNet-S+NIF	Strip R-CNN+NIF
Airplane	71.90	71.59	80.84	71.88
Airport	35.66	40.80	44.48	41.55
Baseball field	80.23	72.00	80.24	79.95
Basketball court	88.69	89.29	89.62	89.57
Bridge	44.89	43.43	45.18	45.19
Chimney	78.23	77.41	78.30	78.73

Table 6: DIOR-R per-class AP (%). Native DIORDataset evaluation at rotated IoU

0.5

with VOC2007 eleven-point AP.

Figure 5: Qualitative DIOR-R test-set refinements from LSKNet-S+NIF (epoch 12). White dashed, orange dashed, and green solid outlines represent the matched ground truth, the coarse detector box, and the NIF-refined box. Each panel reports the rotated IoU before and after refinement for the same candidate.

Coarse	Fine class	GV ∗	Retina ∗	Cascade ∗	Faster ∗	ROI Trans. ∗	O-RCNN	LSKNet-T	LSKNet-S	Strip R-CNN	O-RCNN+NIF	LSKNet-S+NIF	Strip R-CNN+NIF
Airplane	Boeing737	35.43	38.46	40.42	36.43	39.58	42.84	45.12	39.84	40.08	44.58	40.96	43.75
	Boeing747	47.88	55.36	52.86	50.68	73.56	87.61	84.97	86.63	85.82	85.94	85.58	86.29
	Boeing777	15.67	24.75	29.07	22.50	18.32	18.83	20.16	24.21	18.73	19.57	22.18	22.80
	Boeing787	48.32	51.81	52.47	51.86	56.43	62.92	56.00	56.48	54.97	60.36	54.70	61.51
	C919	0.01	0.81	0.00	0.01	0.00	22.17	25.77	24.17	23.12	20.99	28.07	27.32
	A220	40.11	40.50	44.37	47.81	47.67	47.87	50.05	52.20	49.04	48.59	51.16	50.62

Table 7: FAIR1M-v1.0 fine-grained AP (%).

Figure 6: Qualitative FAIR1M-v1.0 test-set predictions from LSKNet-S+NIF (epoch 12).

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RiO-DETRv2: Geometry-Aware Uncertainty Modeling Meets Real-Time Oriented Object Detection Transformer

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Open paper AskPDF arXiv

RiO-DETR is the first real-time end-to-end transformer for oriented object detection, yet further localization gains require a more expressive box representation. Although distributional regression has succeeded in horizontal DETRs, extending it to oriented detection introduces geometry-misaligned boundary modeling and topology-inconsistent orientation refinement. We present RiO-DETRv2, a geometry-aware uncertainty modeling framework for real-time oriented object detection. To resolve the geometry mismatch, Object-Aligned Boundary Distribution Refinement represents box boundaries as probability distributions in an object-aligned coordinate system and progressively refines them across decoder layers. For better orientation topology consistency, we introduce Circular-to-Local Angular Residual Refinement that transitions from global periodic search to local fine-grained estimation. Unified OBB Quality-Aligned Learning further aligns classification, boundary and angular refinement with complete-OBB localization quality. Together, these designs improve localization without compromising efficiency, achieving a better balance between speed and accuracy. Specifically, RiO-DETRv2-l/x achieves 53.7/54.1 mAP50-95 on DOTA, outperforming RiO-DETR-l/x by 1.2/1.5 points with nearly unchanged computational cost. Code is available at https://github.com/RicePasteM/RiO-DETRv2.

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