David Nordström

David Nordström, Johan Edstedt, Fredrik Kahl et al.

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.

Johan Edstedt, David Nordström, Yushan Zhang et al.

Dense feature matching aims to estimate all correspondences between two images of a 3D scene and has recently been established as the gold-standard due to its high accuracy and robustness. However, existing dense matchers still fail or perform poorly for many hard real-world scenarios, and high-precision models are often slow, limiting their applicability. In this paper, we attack these weaknesses on a wide front through a series of systematic improvements that together yield a significantly better model. In particular, we construct a novel matching architecture and loss, which, combined with a curated diverse training distribution, enables our model to solve many complex matching tasks. We further make training faster through a decoupled two-stage matching-then-refinement pipeline, and at the same time, significantly reduce refinement memory usage through a custom CUDA kernel. Finally, we leverage the recent DINOv3 foundation model along with multiple other insights to make the model more robust and unbiased. In our extensive set of experiments we show that the resulting novel matcher sets a new state-of-the-art, being significantly more accurate than its predecessors. Code is available at https://github.com/Parskatt/romav2

Georg Bökman, David Nordström, Fredrik Kahl

Incorporating geometric invariance into neural networks enhances parameter efficiency but typically increases computational costs. This paper introduces new equivariant neural networks that preserve symmetry while maintaining a comparable number of floating-point operations (FLOPs) per parameter to standard non-equivariant networks. We focus on horizontal mirroring (flopping) invariance, common in many computer vision tasks. The main idea is to parametrize the feature spaces in terms of mirror-symmetric and mirror-antisymmetric features, i.e., irreps of the flopping group. This decomposes the linear layers to be block-diagonal, requiring half the number of FLOPs. Our approach reduces both FLOPs and wall-clock time, providing a practical solution for efficient, scalable symmetry-aware architectures.

David Nordström, Johan Edstedt, Fredrik Kahl et al.

Self-supervised learning on images seeks to extract meaningful visual representations from unlabeled data. When scaled to large datasets, this paradigm has achieved state-of-the-art performance and the resulting trained models such as DINOv3 have seen widespread adoption. However, most prior efforts are optimized for semantic understanding rather than geometric reasoning. One important exception is Cross-View Completion, CroCo, which is a form of masked autoencoding (MAE) tailored for 3D understanding. In this work, we continue on the path proposed by CroCo and focus on learning features tailored for 3D vision. In a nutshell, we extend MAE to arbitrarily many views of the same scene. By uniformly masking all views and employing a lightweight decoder with inter-frame attention, our approach is inherently simpler and more scalable than CroCo. We evaluate the resulting model, MuM, extensively on downstream tasks including feedforward reconstruction, dense image matching and relative pose estimation, finding that it outperforms the state-of-the-art visual encoders DINOv3 and CroCo v2.

David Nordström, Johan Edstedt, Fredrik Kahl et al.

Why are state-of-the-art Vision Transformers (ViTs) not designed to exploit natural geometric symmetries such as 90-degree rotations and reflections? In this paper, we argue that there is no fundamental reason, and what has been missing is an efficient implementation. To this end, we introduce Octic Vision Transformers (octic ViTs) which rely on octic group equivariance to capture these symmetries. In contrast to prior equivariant models that increase computational cost, our octic linear layers achieve 5.33x reductions in FLOPs and up to 8x reductions in memory compared to ordinary linear layers. In full octic ViT blocks the computational reductions approach the reductions in the linear layers with increased embedding dimension. We study two new families of ViTs, built from octic blocks, that are either fully octic equivariant or break equivariance in the last part of the network. Training octic ViTs supervised (DeiT-III) and unsupervised (DINOv2) on ImageNet-1K, we find that they match baseline accuracy while at the same time providing substantial efficiency gains.