Who Handles Orientation? Investigating Invariance in Feature Matching

David Nordström; Johan Edstedt; Fredrik Kahl; Georg Bökman

cs.CVApr 13, 2026

Who Handles Orientation? Investigating Invariance in Feature Matching

Authors: David Nordström, Johan Edstedt, Fredrik Kahl, Georg Bökman

Organizations: Chalmers University of Technology · Linköping University · University of Amsterdam

Abstract

Finding matching keypoints between images is a core problem in 3D computer vision. However, modern matchers struggle with large in-plane rotations. A straightforward mitigation is to learn rotation invariance via data augmentation. However, it remains unclear at which stage rotation invariance should be incorporated. In this paper, we study this in the context of a modern sparse matching pipeline. We perform extensive experiments by training on a large collection of 3D vision datasets and evaluating on popular image matching benchmarks. Surprisingly, we find that incorporating rotation invariance already in the descriptor yields similar performance to handling it in the matcher. However, rotation invariance is achieved earlier in the matcher when it is learned in the descriptor, allowing for a faster rotation-invariant matcher. Further, we find that enforcing rotation invariance does not hurt upright performance when trained at scale. Finally, we study the emergence of rotation invariance through scale and find that increasing the training data size substantially improves generalization to rotated images. We release two matchers robust to in-plane rotations that achieve state-of-the-art performance on e.g. multi-modal (WxBS), extreme (HardMatch), and satellite image matching (SatAst). Code is available at https://github.com/davnords/loma.

Figures & tables

Panel of Figure 1 — Figure 1: Who Handles the Orientation? We compare incorporating rotation invariance in (a) the matcher and (b) both the matcher and descriptor, by reporting the AUC@20 on MegaDepth-1500 [ 27 , 41 ] (rotated and upright) for different stopping layers using $N=2048$ keypoints. We average over 5 runs and include a 95% confidence interval.

Figure 2: Experimental setup. We train descriptors and matchers with and without rotation augmentation, resulting in the three different models used for our main experiments. NoRot corresponds to the LoMa-B baseline.

Figure 3: Training batch. Illustration of a training batch with rotation augmentation.

Datasets	Type / GT Source	Weight
ScanNet++ v2 [ 52 ]	Indoor / Mesh	1
BlendedMVS [ 51 ]	Aerial / Mesh	1
Map-Free [ 2 ]	Object-centric / MVS	1
Hypersim [ 37 ]	Indoor / Graphics	1
MegaScenes [ 44 ]	Outdoor / MVS	1
MegaDepth [ 27 ]	Outdoor / MVS	1

Table 1: Training data . For the main experiments we use a large collection of 3D datasets for training.

Rotated evaluation
Method	MegaDepth			ScanNet
AUC $@$ $\rightarrow$	$5^{\circ}$	$10^{\circ}$	$20^{\circ}$	$5^{\circ}$	$10^{\circ}$	$20^{\circ}$
SP+SG	13.3	19.1	23.8	4.6	9.6	15.0
SP+LG	13.2	19.0	23.9	3.7	7.8	12.3
ALIKED+LG	11.2	15.4	18.8	3.4	6.9	10.6
NoRot	52.4	68.8	81.2	16.8	31.2	44.3

Table 2: Relative pose estimation on MegaDepth-1500 [ 27 , 41 ] and ScanNet-1500 [ 12 , 39 ] . We evaluate both with and without random rotations.

Figure 4: ScanNet-1500 performance. We plot the AUC@20 for our different models.

Method	WxBS		SatAst
	Non-rotated	Rotated
SP+SG	45.6	7.3	19.8
SP+LG	46.0	10.9	12.8
ALIKED+LG	43.9	8.0	12.1
NoRot	68.7	50.0	18.8
RotMatch	71.2	62.8	42.4

Table 3: Challenging matching on WxBS [ 32 ] (mAA@10px) and SatAst [ 19 ] (AUC@10 ∘ ). SatAst includes arbitrary rotations by default.

Method	Rotated		Non-rotated
mAA@ $\rightarrow$	5px	10px	5px	10px
SP+SG	7.7	10.9	26.3	36.0
SP+LG	9.8	14.3	24.8	34.8
ALIKED+LG	6.5	9.3	26.4	35.7
NoRot	29.1	39.2	37.7	50.6
RotMatch	36.0	48.6	37.9	51.1

Table 4: Taking matching to the next level on HardMatch [ 34 ] (mAA@10px).

Figure 5: HardMatch group breakdown. We report mAA@10px for different subgroups of the non-rotated version of HardMatch. We find that our rotation-invariant models achieve significant gains on celestial matching.

Figure 6: Qualitative HardMatch pair. Rotation invariance significantly improves robustness to image pairs that lack a canonical orientation, such as star constellations. NoRot fails to find any matches above the threshold

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Training Data	Non-Rotated			Rotated
AUC $@$ $\rightarrow$	$5^{\circ}$	$10^{\circ}$	$20^{\circ}$	$5^{\circ}$	$10^{\circ}$	$20^{\circ}$
Only MegaDepth	53.2	69.5	82.0	16.1	22.9	29.1
All Data	55.0	71.3	83.2	52.2	68.7	81.0

Table 5: Effect of increased data. Relative pose estimation on MegaDepth-1500 [ 27 , 41 ] .

Panel of Figure 7 — Figure 7: Qualitative impact of rotation invariance. Descriptor features (a) trained with rotation augmentation and (b) without, for an image and its $180^{\circ}$ rotation. We visualize the features using SVD, mapping the top three components to RGB.

Method	Non-Rotated			Rotated
AUC $@$ $\rightarrow$	$5^{\circ}$	$10^{\circ}$	$20^{\circ}$	$5^{\circ}$	$10^{\circ}$	$20^{\circ}$
Joint Rot. Desc.	54.9	71.3	83.3	54.7	71.1	83.2
RotMatch	55.3	71.5	83.4	54.5	70.9	82.9
RotDesc&Match	55.0	71.1	83.2	54.2	70.6	82.8

Table 6: Effect of joint rotations. Relative pose estimation on MegaDepth-1500 [ 27 , 41 ] . We compare a descriptor with joint rotations and a matcher with independent rotations with our other models (trained with independent rotations).

Figure 8: Performance for arbitrary rotations. We report AUC@20 on MegaDepth-1500 at different rotation angles. We average over 5 runs and include a 95% confidence interval.

Figure 9: Visualizing an arbitrary rotation. Qualitative matches using circular cropping with $\alpha^{\mathcal{A}}=0^{\circ}$ and $\alpha^{\mathcal{B}}=210^{\circ}$ .

Image Matching

Image matching finds corresponding points, regions, or objects across images despite changes in viewpoint, scale, lighting, or sensor.

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Vision Foundation Models (VFMs) have significantly advanced dense feature matching, yet severe in-plane rotation remains a critical challenge. Existing solutions face a fundamental dilemma: data-driven methods require inefficient parameter scaling to implicitly learn rotations, whereas strictly equivariant networks lack the semantic capacity of modern VFMs. Consequently, current frameworks typically freeze VFMs and shift the entire burden of rotation generalization to the downstream decoder. To break this architectural bottleneck, we propose REDI-Match, an efficient framework driven by a novel Rotation-Equivariant Distillation (REDI) paradigm. Instead of relying on rotation data augmentation to establish rotational correspondences, REDI distills the non-equivariant semantic representations of a VFM into a lightweight, strictly rotation-equivariant encoder, leveraging an equivariant geometric architecture to constrain robust high-dimensional semantics. To fully exploit these features, we equip the decoder with an entropy-driven spatial alignment module. By evaluating discrete rotation hypotheses, this mechanism explicitly locks onto the canonical coordinate system, eliminating global ambiguity before continuous refinement. Extensive experiments demonstrate that REDI-Match establishes a new state-of-the-art (SOTA) across multiple benchmarks. Notably, it achieves a 13.89% absolute pose accuracy improvement on the highly challenging SatAst dataset while operating 1.9x faster than the current SOTA (RoMa v2), enabling real-time inference (~41 FPS) on a single RTX 4090 GPU. Code: https://github.com/YinjiGe/REDI-Match.

Abstract

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