Fredrik Kahl

CV
h-index27
51papers
1,152citations
Novelty53%
AI Score62

51 Papers

CVAug 30, 2023Code
Learning Structure-from-Motion with Graph Attention Networks

Lucas Brynte, José Pedro Iglesias, Carl Olsson et al.

In this paper we tackle the problem of learning Structure-from-Motion (SfM) through the use of graph attention networks. SfM is a classic computer vision problem that is solved though iterative minimization of reprojection errors, referred to as Bundle Adjustment (BA), starting from a good initialization. In order to obtain a good enough initialization to BA, conventional methods rely on a sequence of sub-problems (such as pairwise pose estimation, pose averaging or triangulation) which provide an initial solution that can then be refined using BA. In this work we replace these sub-problems by learning a model that takes as input the 2D keypoints detected across multiple views, and outputs the corresponding camera poses and 3D keypoint coordinates. Our model takes advantage of graph neural networks to learn SfM-specific primitives, and we show that it can be used for fast inference of the reconstruction for new and unseen sequences. The experimental results show that the proposed model outperforms competing learning-based methods, and challenges COLMAP while having lower runtime. Our code is available at https://github.com/lucasbrynte/gasfm/.

LGMay 11, 2022Code
DoubleMatch: Improving Semi-Supervised Learning with Self-Supervision

Erik Wallin, Lennart Svensson, Fredrik Kahl et al.

Following the success of supervised learning, semi-supervised learning (SSL) is now becoming increasingly popular. SSL is a family of methods, which in addition to a labeled training set, also use a sizable collection of unlabeled data for fitting a model. Most of the recent successful SSL methods are based on pseudo-labeling approaches: letting confident model predictions act as training labels. While these methods have shown impressive results on many benchmark datasets, a drawback of this approach is that not all unlabeled data are used during training. We propose a new SSL algorithm, DoubleMatch, which combines the pseudo-labeling technique with a self-supervised loss, enabling the model to utilize all unlabeled data in the training process. We show that this method achieves state-of-the-art accuracies on multiple benchmark datasets while also reducing training times compared to existing SSL methods. Code is available at https://github.com/walline/doublematch.

LGJan 24, 2023Code
Improving Open-Set Semi-Supervised Learning with Self-Supervision

Erik Wallin, Lennart Svensson, Fredrik Kahl et al.

Open-set semi-supervised learning (OSSL) embodies a practical scenario within semi-supervised learning, wherein the unlabeled training set encompasses classes absent from the labeled set. Many existing OSSL methods assume that these out-of-distribution data are harmful and put effort into excluding data belonging to unknown classes from the training objective. In contrast, we propose an OSSL framework that facilitates learning from all unlabeled data through self-supervision. Additionally, we utilize an energy-based score to accurately recognize data belonging to the known classes, making our method well-suited for handling uncurated data in deployment. We show through extensive experimental evaluations that our method yields state-of-the-art results on many of the evaluated benchmark problems in terms of closed-set accuracy and open-set recognition when compared with existing methods for OSSL. Our code is available at https://github.com/walline/ssl-tf2-sefoss.

70.2CVMay 28Code
SwInception -- Local Attention Meets Convolutions

David Hagerman, Roman Naeem, Jakob Lindqvist et al.

Sparse vision transformers have gained popularity as efficient encoders for medical volumetric segmentation, with Swin emerging as a prominent choice. Swin uses local attention to reduce complexity and yields excellent performance for many tasks but still tends to overfit on small datasets. To mitigate this weakness, we propose a novel architecture that further enhances Swin's inductive bias by introducing Inception blocks in the feed-forward layers. The introduction of these multi-branch convolutions enables more direct reasoning over local, multi-scale features within the transformer block. We have also modified the decoder layers in order to capture finer details using fewer parameters. We demonstrate a performance improvement on eleven different medical datasets through extensive experimentation. We specifically showcase advancements over the previous state-of-the-art backbones on benchmark challenges like the Medical Segmentation Decathlon and Beyond the Cranial Vault. By showing that the existing inductive bias in Swin can be further improved, our work presents a promising avenue for enhancing the capabilities of sparse vision transformers for both medical and natural image segmentation tasks. Code and pre-trained weights can be accessed at https://github.com/Eiphodos/SwInception.

59.9CVJun 3
GeM-NR: Geometry-Aware Multi-View Editing for Nonrigid Scene Changes

Josef Bengtson, Yaroslava Lochman, Fredrik Kahl

Recent developments in multi-view image editing with generative models have brought us a step closer toward general 3D content generation and customization. Most existing works focus on rigid or appearance-only edits by utilizing the geometry of the unedited scene. This naturally limits these methods to edits that preserve the underlying scene structure. Other approaches are trained for specific image editing tasks, such as object removal and addition. Despite this progress, general nonrigid edits, i.e., edits that substantially change the scene geometry, remain challenging for existing methods. We propose GeM-NR, a fast and flexible training-free approach for general multi-view consistent image editing, including edits that drastically change the geometry and appearance of the scene. Given an anchor image edited with a chosen backbone editor (such as FLUX, Qwen, BrushNet) and a query unedited image, GeM-NR edits the query image consistently with the anchor edit. The method incorporates multiple stages: (i) depth map estimation, where we propose a strategy to maximize the alignment between the 3D point clouds of the edited and unedited scenes, (ii) projection onto a query viewpoint, and (iii) refinement of the obtained image conditioned on the unedited query. The conditioning-based formulation scales well from two to many views of an object. We demonstrate the ability of our method to handle edits with significant changes in geometry and appearance, something that existing methods struggle with. We perform an extensive evaluation showing that our method improves consistency for a wide variety of edit tasks, including generating 3D representations of the edited scene. Both quantitative and qualitative results indicate the state-of-the-art performance of our method in terms of edit quality as well as geometric and photometric consistency across multiple views.

CVSep 17, 2024Code
Obfuscation Based Privacy Preserving Representations are Recoverable Using Neighborhood Information

Kunal Chelani, Assia Benbihi, Fredrik Kahl et al.

Rapid growth in the popularity of AR/VR/MR applications and cloud-based visual localization systems has given rise to an increased focus on the privacy of user content in the localization process. This privacy concern has been further escalated by the ability of deep neural networks to recover detailed images of a scene from a sparse set of 3D or 2D points and their descriptors - the so-called inversion attacks. Research on privacy-preserving localization has therefore focused on preventing these inversion attacks on both the query image keypoints and the 3D points of the scene map. To this end, several geometry obfuscation techniques that lift points to higher-dimensional spaces, i.e., lines or planes, or that swap coordinates between points % have been proposed. In this paper, we point to a common weakness of these obfuscations that allows to recover approximations of the original point positions under the assumption of known neighborhoods. We further show that these neighborhoods can be computed by learning to identify descriptors that co-occur in neighborhoods. Extensive experiments show that our approach for point recovery is practically applicable to all existing geometric obfuscation schemes. Our results show that these schemes should not be considered privacy-preserving, even though they are claimed to be privacy-preserving. Code will be available at https://github.com/kunalchelani/RecoverPointsNeighborhood.

LGJul 16, 2024Code
ProSub: Probabilistic Open-Set Semi-Supervised Learning with Subspace-Based Out-of-Distribution Detection

Erik Wallin, Lennart Svensson, Fredrik Kahl et al.

In open-set semi-supervised learning (OSSL), we consider unlabeled datasets that may contain unknown classes. Existing OSSL methods often use the softmax confidence for classifying data as in-distribution (ID) or out-of-distribution (OOD). Additionally, many works for OSSL rely on ad-hoc thresholds for ID/OOD classification, without considering the statistics of the problem. We propose a new score for ID/OOD classification based on angles in feature space between data and an ID subspace. Moreover, we propose an approach to estimate the conditional distributions of scores given ID or OOD data, enabling probabilistic predictions of data being ID or OOD. These components are put together in a framework for OSSL, termed ProSub, that is experimentally shown to reach SOTA performance on several benchmark problems. Our code is available at https://github.com/walline/prosub.

CVApr 21, 2022
A case for using rotation invariant features in state of the art feature matchers

Georg Bökman, Fredrik Kahl

The aim of this paper is to demonstrate that a state of the art feature matcher (LoFTR) can be made more robust to rotations by simply replacing the backbone CNN with a steerable CNN which is equivariant to translations and image rotations. It is experimentally shown that this boost is obtained without reducing performance on ordinary illumination and viewpoint matching sequences.

CVJan 23Code
Semi-Supervised Hierarchical Open-Set Classification

Erik Wallin, Fredrik Kahl, Lars Hammarstrand

Hierarchical open-set classification handles previously unseen classes by assigning them to the most appropriate high-level category in a class taxonomy. We extend this paradigm to the semi-supervised setting, enabling the use of large-scale, uncurated datasets containing a mixture of known and unknown classes to improve the hierarchical open-set performance. To this end, we propose a teacher-student framework based on pseudo-labeling. Two key components are introduced: 1) subtree pseudo-labels, which provide reliable supervision in the presence of unknown data, and 2) age-gating, a mechanism that mitigates overconfidence in pseudo-labels. Experiments show that our framework outperforms self-supervised pretraining followed by supervised adaptation, and even matches the fully supervised counterpart when using only 20 labeled samples per class on the iNaturalist19 benchmark. Our code is available at https://github.com/walline/semihoc.

CVAug 26, 2024Code
Affine steerers for structured keypoint description

Georg Bökman, Johan Edstedt, Michael Felsberg et al.

We propose a way to train deep learning based keypoint descriptors that makes them approximately equivariant for locally affine transformations of the image plane. The main idea is to use the representation theory of GL(2) to generalize the recently introduced concept of steerers from rotations to affine transformations. Affine steerers give high control over how keypoint descriptions transform under image transformations. We demonstrate the potential of using this control for image matching. Finally, we propose a way to finetune keypoint descriptors with a set of steerers on upright images and obtain state-of-the-art results on several standard benchmarks. Code will be published at github.com/georg-bn/affine-steerers.

73.1CVApr 13Code
Who Handles Orientation? Investigating Invariance in Feature Matching

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.

CVSep 19, 2024Code
EdgeGaussians -- 3D Edge Mapping via Gaussian Splatting

Kunal Chelani, Assia Benbihi, Torsten Sattler et al.

With their meaningful geometry and their omnipresence in the 3D world, edges are extremely useful primitives in computer vision. 3D edges comprise of lines and curves, and methods to reconstruct them use either multi-view images or point clouds as input. State-of-the-art image-based methods first learn a 3D edge point cloud then fit 3D edges to it. The edge point cloud is obtained by learning a 3D neural implicit edge field from which the 3D edge points are sampled on a specific level set (0 or 1). However, such methods present two important drawbacks: i) it is not realistic to sample points on exact level sets due to float imprecision and training inaccuracies. Instead, they are sampled within a range of levels so the points do not lie accurately on the 3D edges and require further processing. ii) Such implicit representations are computationally expensive and require long training times. In this paper, we address these two limitations and propose a 3D edge mapping that is simpler, more efficient, and preserves accuracy. Our method learns explicitly the 3D edge points and their edge direction hence bypassing the need for point sampling. It casts a 3D edge point as the center of a 3D Gaussian and the edge direction as the principal axis of the Gaussian. Such a representation has the advantage of being not only geometrically meaningful but also compatible with the efficient training optimization defined in Gaussian Splatting. Results show that the proposed method produces edges as accurate and complete as the state-of-the-art while being an order of magnitude faster. Code is released at https://github.com/kunalchelani/EdgeGaussians.

CVJun 2, 2023
Adjustable Visual Appearance for Generalizable Novel View Synthesis

Josef Bengtson, David Nilsson, Che-Tsung Lin et al.

We present a generalizable novel view synthesis method which enables modifying the visual appearance of an observed scene so rendered views match a target weather or lighting condition without any scene specific training or access to reference views at the target condition. Our method is based on a pretrained generalizable transformer architecture and is fine-tuned on synthetically generated scenes under different appearance conditions. This allows for rendering novel views in a consistent manner for 3D scenes that were not included in the training set, along with the ability to (i) modify their appearance to match the target condition and (ii) smoothly interpolate between different conditions. Experiments on real and synthetic scenes show that our method is able to generate 3D consistent renderings while making realistic appearance changes, including qualitative and quantitative comparisons. Please refer to our project page for video results: https://ava-nvs.github.io/

CVSep 29, 2022
In Search of Projectively Equivariant Networks

Georg Bökman, Axel Flinth, Fredrik Kahl

Equivariance of linear neural network layers is well studied. In this work, we relax the equivariance condition to only be true in a projective sense. We propose a way to construct a projectively equivariant neural network through building a standard equivariant network where the linear group representations acting on each intermediate feature space are "multiplicatively modified lifts" of projective group representations. By theoretically studying the relation of projectively and linearly equivariant linear layers, we show that our approach is the most general possible when building a network out of linear layers. The theory is showcased in two simple experiments.

CVDec 4, 2023Code
Steerers: A framework for rotation equivariant keypoint descriptors

Georg Bökman, Johan Edstedt, Michael Felsberg et al.

Image keypoint descriptions that are discriminative and matchable over large changes in viewpoint are vital for 3D reconstruction. However, descriptions output by learned descriptors are typically not robust to camera rotation. While they can be made more robust by, e.g., data augmentation, this degrades performance on upright images. Another approach is test-time augmentation, which incurs a significant increase in runtime. Instead, we learn a linear transform in description space that encodes rotations of the input image. We call this linear transform a steerer since it allows us to transform the descriptions as if the image was rotated. From representation theory, we know all possible steerers for the rotation group. Steerers can be optimized (A) given a fixed descriptor, (B) jointly with a descriptor or (C) we can optimize a descriptor given a fixed steerer. We perform experiments in these three settings and obtain state-of-the-art results on the rotation invariant image matching benchmarks AIMS and Roto-360. We publish code and model weights at https://github.com/georg-bn/rotation-steerers.

70.8CVApr 6Code
LoMa: Local Feature Matching Revisited

David Nordström, Johan Edstedt, Georg Bökman et al.

Local feature matching has long been a fundamental component of 3D vision systems such as Structure-from-Motion (SfM), yet progress has lagged behind the rapid advances of modern data-driven approaches. The newer approaches, such as feed-forward reconstruction models, have benefited extensively from scaling dataset sizes, whereas local feature matching models are still only trained on a few mid-sized datasets. In this paper, we revisit local feature matching from a data-driven perspective. In our approach, which we call LoMa, we combine large and diverse data mixtures, modern training recipes, scaled model capacity, and scaled compute, resulting in remarkable gains in performance. Since current standard benchmarks mainly rely on collecting sparse views from successful 3D reconstructions, the evaluation of progress in feature matching has been limited to relatively easy image pairs. To address the resulting saturation of benchmarks, we collect 1000 highly challenging image pairs from internet data into a new dataset called HardMatch. Ground truth correspondences for HardMatch are obtained via manual annotation by the authors. In our extensive benchmarking suite, we find that LoMa makes outstanding progress across the board, outperforming the state-of-the-art method ALIKED+LightGlue by +18.6 mAA on HardMatch, +29.5 mAA on WxBS, +21.4 (1m, 10$^\circ$) on InLoc, +24.2 AUC on RUBIK, and +12.4 mAA on IMC 2022. We release our code and models publicly at https://github.com/davnords/LoMa.

66.6CVMar 27
ARTA: Adaptive Mixed-Resolution Token Allocation for Efficient Dense Feature Extraction

David Hagerman, Roman Naeem, Erik Brorsson et al.

We present ARTA, a mixed-resolution coarse-to-fine vision transformer for efficient dense feature extraction. Unlike models that begin with dense high-resolution (fine) tokens, ARTA starts with low-resolution (coarse) tokens and uses a lightweight allocator to predict which regions require more fine tokens. The allocator iteratively predicts a semantic (class) boundary score and allocates additional tokens to patches above a low threshold, concentrating token density near boundaries while maintaining high sensitivity to weak boundary evidence. This targeted allocation encourages tokens to represent a single semantic class rather than a mixture of classes. Mixed-resolution attention enables interaction between coarse and fine tokens, focusing computation on semantically complex areas while avoiding redundant processing in homogeneous regions. Experiments demonstrate that ARTA achieves state-of-the-art results on ADE20K and COCO-Stuff with substantially fewer FLOPs, and delivers competitive performance on Cityscapes at markedly lower compute. For example, ARTA-Base attains 54.6 mIoU on ADE20K in the ~100M-parameter class while using fewer FLOPs and less memory than comparable backbones.

LGMar 27, 2025Code
ProHOC: Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks

Erik Wallin, Fredrik Kahl, Lars Hammarstrand

Out-of-distribution (OOD) detection in deep learning has traditionally been framed as a binary task, where samples are either classified as belonging to the known classes or marked as OOD, with little attention given to the semantic relationships between OOD samples and the in-distribution (ID) classes. We propose a framework for detecting and classifying OOD samples in a given class hierarchy. Specifically, we aim to predict OOD data to their correct internal nodes of the class hierarchy, whereas the known ID classes should be predicted as their corresponding leaf nodes. Our approach leverages the class hierarchy to create a probabilistic model and we implement this model by using networks trained for ID classification at multiple hierarchy depths. We conduct experiments on three datasets with predefined class hierarchies and show the effectiveness of our method. Our code is available at https://github.com/walline/prohoc.

CVNov 19, 2025Code
RoMa v2: Harder Better Faster Denser Feature Matching

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

CVJul 15, 2025Code
Trexplorer Super: Topologically Correct Centerline Tree Tracking of Tubular Objects in CT Volumes

Roman Naeem, David Hagerman, Jennifer Alvén et al.

Tubular tree structures, such as blood vessels and airways, are essential in human anatomy and accurately tracking them while preserving their topology is crucial for various downstream tasks. Trexplorer is a recurrent model designed for centerline tracking in 3D medical images but it struggles with predicting duplicate branches and terminating tracking prematurely. To address these issues, we present Trexplorer Super, an enhanced version that notably improves performance through novel advancements. However, evaluating centerline tracking models is challenging due to the lack of public datasets. To enable thorough evaluation, we develop three centerline datasets, one synthetic and two real, each with increasing difficulty. Using these datasets, we conduct a comprehensive evaluation of existing state-of-the-art (SOTA) models and compare them with our approach. Trexplorer Super outperforms previous SOTA models on every dataset. Our results also highlight that strong performance on synthetic data does not necessarily translate to real datasets. The code and datasets are available at https://github.com/RomStriker/Trexplorer-Super.

CVJun 5, 2024Code
Tiny models from tiny data: Textual and null-text inversion for few-shot distillation

Erik Landolsi, Fredrik Kahl

Few-shot learning deals with problems such as image classification using very few training examples. Recent vision foundation models show excellent few-shot transfer abilities, but are large and slow at inference. Using knowledge distillation, the capabilities of high-performing but slow models can be transferred to tiny, efficient models. However, common distillation methods require a large set of unlabeled data, which is not available in the few-shot setting. To overcome this lack of data, there has been a recent interest in using synthetic data. We expand on this line of research by presenting a novel diffusion model inversion technique (TINT) combining the diversity of textual inversion with the specificity of null-text inversion. Using this method in a few-shot distillation pipeline leads to state-of-the-art accuracy among small student models on popular benchmarks, while being significantly faster than prior work. Popular few-shot benchmarks involve evaluation over a large number of episodes, which is computationally cumbersome for methods involving synthetic data generation. We also present a theoretical analysis on how the accuracy estimator variance depends on the number of episodes and query examples, and use these results to lower the computational effort required for method evaluation. Finally, to further motivate the use of generative models in few-shot distillation, we demonstrate that our method outperforms training on real data mined from the dataset used in the original diffusion model training. Source code is available at https://github.com/pixwse/tiny2.

CVMar 16, 2021Code
Back to the Feature: Learning Robust Camera Localization from Pixels to Pose

Paul-Edouard Sarlin, Ajaykumar Unagar, Måns Larsson et al.

Camera pose estimation in known scenes is a 3D geometry task recently tackled by multiple learning algorithms. Many regress precise geometric quantities, like poses or 3D points, from an input image. This either fails to generalize to new viewpoints or ties the model parameters to a specific scene. In this paper, we go Back to the Feature: we argue that deep networks should focus on learning robust and invariant visual features, while the geometric estimation should be left to principled algorithms. We introduce PixLoc, a scene-agnostic neural network that estimates an accurate 6-DoF pose from an image and a 3D model. Our approach is based on the direct alignment of multiscale deep features, casting camera localization as metric learning. PixLoc learns strong data priors by end-to-end training from pixels to pose and exhibits exceptional generalization to new scenes by separating model parameters and scene geometry. The system can localize in large environments given coarse pose priors but also improve the accuracy of sparse feature matching by jointly refining keypoints and poses with little overhead. The code will be publicly available at https://github.com/cvg/pixloc.

CVMar 8, 2021Code
How Privacy-Preserving are Line Clouds? Recovering Scene Details from 3D Lines

Kunal Chelani, Fredrik Kahl, Torsten Sattler

Visual localization is the problem of estimating the camera pose of a given image with respect to a known scene. Visual localization algorithms are a fundamental building block in advanced computer vision applications, including Mixed and Virtual Reality systems. Many algorithms used in practice represent the scene through a Structure-from-Motion (SfM) point cloud and use 2D-3D matches between a query image and the 3D points for camera pose estimation. As recently shown, image details can be accurately recovered from SfM point clouds by translating renderings of the sparse point clouds to images. To address the resulting potential privacy risks for user-generated content, it was recently proposed to lift point clouds to line clouds by replacing 3D points by randomly oriented 3D lines passing through these points. The resulting representation is unintelligible to humans and effectively prevents point cloud-to-image translation. This paper shows that a significant amount of information about the 3D scene geometry is preserved in these line clouds, allowing us to (approximately) recover the 3D point positions and thus to (approximately) recover image content. Our approach is based on the observation that the closest points between lines can yield a good approximation to the original 3D points. Code is available at https://github.com/kunalchelani/Line2Point.

45.0CGMay 7
Scalable GPU Construction of 3D Voronoi and Power Diagrams

Bernardo Taveira, Carl Lindström, Maryam Fatemi et al.

Voronoi diagrams, and their more general weighted counterpart, power diagrams, are fundamental geometric constructs with wide-ranging applications. Recently, they have gained renewed attention in mesh-based neural rendering. Despite being extensively studied, the construction of 3D Voronoi diagrams for large-scale point sets remains computationally expensive, limiting their adoption in large-scale applications. Existing CPU-based approaches typically rely on computing its dual, the Delaunay tetrahedralization, but are prohibitively slow for large diagrams, while GPU-based methods either struggle to scale efficiently to large point sets or assume homogeneous point distributions. The weighted case, power diagrams, is even less explored in this context. Existing approaches are typically tailored to the application at hand, assuming homogeneous point distributions and small weight variations, making them unsuitable for general use in more complex heterogeneous data. In this paper, we present a highly parallelizable GPU algorithm for the fast construction of large-scale 3D Voronoi and power diagrams. Our approach constructs each convex cell from a weighted 3D point by progressively clipping an initial cell volume against bisecting planes induced by candidate neighboring points. To efficiently identify candidate neighbors under arbitrary spatial distributions, we introduce a culling criterion based on directional geometric bounds of the evolving cell, combined with a hierarchical best-first traversal of bounding volumes. We achieve performance on par with state-of-the-art Delaunay tetrahedralization methods on small and moderate problem sizes, while exhibiting robust scalability to large point sets and diverse spatial distributions. Moreover, our method naturally generalizes to power diagrams without additional assumptions. See https://research.zenseact.com/publications/paragram .

CVDec 22, 2023
TimePillars: Temporally-Recurrent 3D LiDAR Object Detection

Ernesto Lozano Calvo, Bernardo Taveira, Fredrik Kahl et al.

Object detection applied to LiDAR point clouds is a relevant task in robotics, and particularly in autonomous driving. Single frame methods, predominant in the field, exploit information from individual sensor scans. Recent approaches achieve good performance, at relatively low inference time. Nevertheless, given the inherent high sparsity of LiDAR data, these methods struggle in long-range detection (e.g. 200m) which we deem to be critical in achieving safe automation. Aggregating multiple scans not only leads to a denser point cloud representation, but it also brings time-awareness to the system, and provides information about how the environment is changing. Solutions of this kind, however, are often highly problem-specific, demand careful data processing, and tend not to fulfil runtime requirements. In this context we propose TimePillars, a temporally-recurrent object detection pipeline which leverages the pillar representation of LiDAR data across time, respecting hardware integration efficiency constraints, and exploiting the diversity and long-range information of the novel Zenseact Open Dataset (ZOD). Through experimentation, we prove the benefits of having recurrency, and show how basic building blocks are enough to achieve robust and efficient results.

CVJun 9, 2025
R3D2: Realistic 3D Asset Insertion via Diffusion for Autonomous Driving Simulation

William Ljungbergh, Bernardo Taveira, Wenzhao Zheng et al. · berkeley

Validating autonomous driving (AD) systems requires diverse and safety-critical testing, making photorealistic virtual environments essential. Traditional simulation platforms, while controllable, are resource-intensive to scale and often suffer from a domain gap with real-world data. In contrast, neural reconstruction methods like 3D Gaussian Splatting (3DGS) offer a scalable solution for creating photorealistic digital twins of real-world driving scenes. However, they struggle with dynamic object manipulation and reusability as their per-scene optimization-based methodology tends to result in incomplete object models with integrated illumination effects. This paper introduces R3D2, a lightweight, one-step diffusion model designed to overcome these limitations and enable realistic insertion of complete 3D assets into existing scenes by generating plausible rendering effects-such as shadows and consistent lighting-in real time. This is achieved by training R3D2 on a novel dataset: 3DGS object assets are generated from in-the-wild AD data using an image-conditioned 3D generative model, and then synthetically placed into neural rendering-based virtual environments, allowing R3D2 to learn realistic integration. Quantitative and qualitative evaluations demonstrate that R3D2 significantly enhances the realism of inserted assets, enabling use-cases like text-to-3D asset insertion and cross-scene/dataset object transfer, allowing for true scalability in AD validation. To promote further research in scalable and realistic AD simulation, we will release our dataset and code, see https://research.zenseact.com/publications/R3D2/.

CVFeb 7, 2025
Flopping for FLOPs: Leveraging equivariance for computational efficiency

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.

CVMar 11, 2025
A Framework for Reducing the Complexity of Geometric Vision Problems and its Application to Two-View Triangulation with Approximation Bounds

Felix Rydell, Georg Bökman, Fredrik Kahl et al.

In this paper, we present a new framework for reducing the computational complexity of geometric vision problems through targeted reweighting of the cost functions used to minimize reprojection errors. Triangulation - the task of estimating a 3D point from noisy 2D projections across multiple images - is a fundamental problem in multiview geometry and Structure-from-Motion (SfM) pipelines. We apply our framework to the two-view case and demonstrate that optimal triangulation, which requires solving a univariate polynomial of degree six, can be simplified through cost function reweighting reducing the polynomial degree to two. This reweighting yields a closed-form solution while preserving strong geometric accuracy. We derive optimal weighting strategies, establish theoretical bounds on the approximation error, and provide experimental results on real data demonstrating the effectiveness of the proposed approach compared to standard methods. Although this work focuses on two-view triangulation, the framework generalizes to other geometric vision problems.

35.6CVApr 9
Weakly-Supervised Lung Nodule Segmentation via Training-Free Guidance of 3D Rectified Flow

Richard Petersen, Fredrik Kahl, Jennifer Alvén

Dense annotations, such as segmentation masks, are expensive and time-consuming to obtain, especially for 3D medical images where expert voxel-wise labeling is required. Weakly supervised approaches aim to address this limitation, but often rely on attribution-based methods that struggle to accurately capture small structures such as lung nodules. In this paper, we propose a weakly-supervised segmentation method for lung nodules by combining pretrained state-of-the-art rectified flow and predictor models in a plug-and-play manner. Our approach uses training-free guidance of a 3D rectified flow model, requiring only fine-tuning of the predictor using image-level labels and no retraining of the generative model. The proposed method produces improved-quality segmentations for two separate predictors, consistently detecting lung nodules of varying size and shapes. Experiments on LUNA16 demonstrate improvements over baseline methods, highlighting the potential of generative foundation models as tools for weakly supervised 3D medical image segmentation.

QMFeb 19, 2025
Optimizing Gene-Based Testing for Antibiotic Resistance Prediction

David Hagerman, Anna Johnning, Roman Naeem et al.

Antibiotic Resistance (AR) is a critical global health challenge that necessitates the development of cost-effective, efficient, and accurate diagnostic tools. Given the genetic basis of AR, techniques such as Polymerase Chain Reaction (PCR) that target specific resistance genes offer a promising approach for predictive diagnostics using a limited set of key genes. This study introduces GenoARM, a novel framework that integrates reinforcement learning (RL) with transformer-based models to optimize the selection of PCR gene tests and improve AR predictions, leveraging observed metadata for improved accuracy. In our evaluation, we developed several high-performing baselines and compared them using publicly available datasets derived from real-world bacterial samples representing multiple clinically relevant pathogens. The results show that all evaluated methods achieve strong and reliable performance when metadata is not utilized. When metadata is introduced and the number of selected genes increases, GenoARM demonstrates superior performance due to its capacity to approximate rewards for unseen and sparse combinations. Overall, our framework represents a major advancement in optimizing diagnostic tools for AR in clinical settings.

CVNov 27, 2025
3D-Consistent Multi-View Editing by Diffusion Guidance

Josef Bengtson, David Nilsson, Dong In Lee et al.

Recent advancements in diffusion models have greatly improved text-based image editing, yet methods that edit images independently often produce geometrically and photometrically inconsistent results across different views of the same scene. Such inconsistencies are particularly problematic for editing of 3D representations such as NeRFs or Gaussian Splat models. We propose a training-free diffusion framework that enforces multi-view consistency during the image editing process. The key assumption is that corresponding points in the unedited images should undergo similar transformations after editing. To achieve this, we introduce a consistency loss that guides the diffusion sampling toward coherent edits. The framework is flexible and can be combined with widely varying image editing methods, supporting both dense and sparse multi-view editing setups. Experimental results show that our approach significantly improves 3D consistency compared to existing multi-view editing methods. We also show that this increased consistency enables high-quality Gaussian Splat editing with sharp details and strong fidelity to user-specified text prompts. Please refer to our project page for video results: https://3d-consistent-editing.github.io/

CVNov 25, 2025
RefTr: Recurrent Refinement of Confluent Trajectories for 3D Vascular Tree Centerline Graphs

Roman Naeem, David Hagerman, Jennifer Alvén et al.

Tubular trees, such as blood vessels and lung airways, are essential for material transport within the human body. Accurately detecting their centerlines with correct tree topology is critical for clinical tasks such as diagnosis, treatment planning, and surgical navigation. In these applications, maintaining high recall is crucial, as missing small branches can result in fatal mistakes caused by incomplete assessments or undetected abnormalities. We present RefTr, a 3D image-to-graph model for centerline generation of vascular trees via recurrent refinement of confluent trajectories. RefTr uses a Producer-Refiner architecture based on a Transformer decoder, where the Producer proposes a set of initial confluent trajectories that are recurrently refined by the Refiner to produce final trajectories, which forms the centerline graph. The confluent trajectory representation enables refinement of complete trajectories while explicitly enforcing a valid tree topology. The recurrent refinement scheme improves precision and reuses the same Refiner block across multiple steps, yielding a 2.4x reduction in decoder parameters compared to previous SOTA. We also introduce an efficient non-maximum suppression algorithm for spatial tree graphs to merge duplicate branches and boost precision. Across multiple public centerline datasets, RefTr achieves superior recall and comparable precision to previous SOTA, while offering faster inference and substantially fewer parameters, demonstrating its potential as a new state-of-the-art framework for vascular tree analysis in 3D medical imaging.

CVNov 21, 2025
MuM: Multi-View Masked Image Modeling for 3D Vision

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.

CVMay 21, 2025
Octic Vision Transformers: Quicker ViTs Through Equivariance

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.

CVMay 12, 2025
Addressing degeneracies in latent interpolation for diffusion models

Erik Landolsi, Fredrik Kahl

There is an increasing interest in using image-generating diffusion models for deep data augmentation and image morphing. In this context, it is useful to interpolate between latents produced by inverting a set of input images, in order to generate new images representing some mixture of the inputs. We observe that such interpolation can easily lead to degenerate results when the number of inputs is large. We analyze the cause of this effect theoretically and experimentally, and suggest a suitable remedy. The suggested approach is a relatively simple normalization scheme that is easy to use whenever interpolation between latents is needed. We measure image quality using FID and CLIP embedding distance and show experimentally that baseline interpolation methods lead to a drop in quality metrics long before the degeneration issue is clearly visible. In contrast, our method significantly reduces the degeneration effect and leads to improved quality metrics also in non-degenerate situations.

CVApr 11, 2025
Geometric Consistency Refinement for Single Image Novel View Synthesis via Test-Time Adaptation of Diffusion Models

Josef Bengtson, David Nilsson, Fredrik Kahl

Diffusion models for single image novel view synthesis (NVS) can generate highly realistic and plausible images, but they are limited in the geometric consistency to the given relative poses. The generated images often show significant errors with respect to the epipolar constraints that should be fulfilled, as given by the target pose. In this paper we address this issue by proposing a methodology to improve the geometric correctness of images generated by a diffusion model for single image NVS. We formulate a loss function based on image matching and epipolar constraints, and optimize the starting noise in a diffusion sampling process such that the generated image should both be a realistic image and fulfill geometric constraints derived from the given target pose. Our method does not require training data or fine-tuning of the diffusion models, and we show that we can apply it to multiple state-of-the-art models for single image NVS. The method is evaluated on the MegaScenes dataset and we show that geometric consistency is improved compared to the baseline models while retaining the quality of the generated images.

LGMay 26, 2023
Investigating how ReLU-networks encode symmetries

Georg Bökman, Fredrik Kahl

Many data symmetries can be described in terms of group equivariance and the most common way of encoding group equivariances in neural networks is by building linear layers that are group equivariant. In this work we investigate whether equivariance of a network implies that all layers are equivariant. On the theoretical side we find cases where equivariance implies layerwise equivariance, but also demonstrate that this is not the case generally. Nevertheless, we conjecture that CNNs that are trained to be equivariant will exhibit layerwise equivariance and explain how this conjecture is a weaker version of the recent permutation conjecture by Entezari et al. [2022]. We perform quantitative experiments with VGG-nets on CIFAR10 and qualitative experiments with ResNets on ImageNet to illustrate and support our theoretical findings. These experiments are not only of interest for understanding how group equivariance is encoded in ReLU-networks, but they also give a new perspective on Entezari et al.'s permutation conjecture as we find that it is typically easier to merge a network with a group-transformed version of itself than merging two different networks.

CVMay 8, 2023
Privacy-Preserving Representations are not Enough -- Recovering Scene Content from Camera Poses

Kunal Chelani, Torsten Sattler, Fredrik Kahl et al.

Visual localization is the task of estimating the camera pose from which a given image was taken and is central to several 3D computer vision applications. With the rapid growth in the popularity of AR/VR/MR devices and cloud-based applications, privacy issues are becoming a very important aspect of the localization process. Existing work on privacy-preserving localization aims to defend against an attacker who has access to a cloud-based service. In this paper, we show that an attacker can learn about details of a scene without any access by simply querying a localization service. The attack is based on the observation that modern visual localization algorithms are robust to variations in appearance and geometry. While this is in general a desired property, it also leads to algorithms localizing objects that are similar enough to those present in a scene. An attacker can thus query a server with a large enough set of images of objects, \eg, obtained from the Internet, and some of them will be localized. The attacker can thus learn about object placements from the camera poses returned by the service (which is the minimal information returned by such a service). In this paper, we develop a proof-of-concept version of this attack and demonstrate its practical feasibility. The attack does not place any requirements on the localization algorithm used, and thus also applies to privacy-preserving representations. Current work on privacy-preserving representations alone is thus insufficient.

CVJan 31, 2022
Rigidity Preserving Image Transformations and Equivariance in Perspective

Lucas Brynte, Georg Bökman, Axel Flinth et al.

We characterize the class of image plane transformations which realize rigid camera motions and call these transformations `rigidity preserving'. In particular, 2D translations of pinhole images are not rigidity preserving. Hence, when using CNNs for 3D inference tasks, it can be beneficial to modify the inductive bias from equivariance towards translations to equivariance towards rigidity preserving transformations. We investigate how equivariance with respect to rigidity preserving transformations can be approximated in CNNs, and test our ideas on both 6D object pose estimation and visual localization. Experimentally, we improve on several competitive baselines.

CVNov 30, 2021
ZZ-Net: A Universal Rotation Equivariant Architecture for 2D Point Clouds

Georg Bökman, Fredrik Kahl, Axel Flinth

In this paper, we are concerned with rotation equivariance on 2D point cloud data. We describe a particular set of functions able to approximate any continuous rotation equivariant and permutation invariant function. Based on this result, we propose a novel neural network architecture for processing 2D point clouds and we prove its universality for approximating functions exhibiting these symmetries. We also show how to extend the architecture to accept a set of 2D-2D correspondences as indata, while maintaining similar equivariance properties. Experiments are presented on the estimation of essential matrices in stereo vision.

CVSep 9, 2021
CrowdDriven: A New Challenging Dataset for Outdoor Visual Localization

Ara Jafarzadeh, Manuel Lopez Antequera, Pau Gargallo et al.

Visual localization is the problem of estimating the position and orientation from which a given image (or a sequence of images) is taken in a known scene. It is an important part of a wide range of computer vision and robotics applications, from self-driving cars to augmented/virtual reality systems. Visual localization techniques should work reliably and robustly under a wide range of conditions, including seasonal, weather, illumination and man-made changes. Recent benchmarking efforts model this by providing images under different conditions, and the community has made rapid progress on these datasets since their inception. However, they are limited to a few geographical regions and often recorded with a single device. We propose a new benchmark for visual localization in outdoor scenes, using crowd-sourced data to cover a wide range of geographical regions and camera devices with a focus on the failure cases of current algorithms. Experiments with state-of-the-art localization approaches show that our dataset is very challenging, with all evaluated methods failing on its hardest parts. As part of the dataset release, we provide the tooling used to generate it, enabling efficient and effective 2D correspondence annotation to obtain reference poses.

CVJan 6, 2021
On the Tightness of Semidefinite Relaxations for Rotation Estimation

Lucas Brynte, Viktor Larsson, José Pedro Iglesias et al.

Why is it that semidefinite relaxations have been so successful in numerous applications in computer vision and robotics for solving non-convex optimization problems involving rotations? In studying the empirical performance we note that there are few failure cases reported in the literature, in particular for estimation problems with a single rotation, motivating us to gain further theoretical understanding. A general framework based on tools from algebraic geometry is introduced for analyzing the power of semidefinite relaxations of problems with quadratic objective functions and rotational constraints. Applications include registration, hand-eye calibration and rotation averaging. We characterize the extreme points, and show that there exist failure cases for which the relaxation is not tight, even in the case of a single rotation. We also show that some problem classes are always tight given an appropriate parametrization. Our theoretical findings are accompanied with numerical simulations, providing further evidence and understanding of the results.

CVAug 21, 2020
Single-Image Depth Prediction Makes Feature Matching Easier

Carl Toft, Daniyar Turmukhambetov, Torsten Sattler et al.

Good local features improve the robustness of many 3D re-localization and multi-view reconstruction pipelines. The problem is that viewing angle and distance severely impact the recognizability of a local feature. Attempts to improve appearance invariance by choosing better local feature points or by leveraging outside information, have come with pre-requisites that made some of them impractical. In this paper, we propose a surprisingly effective enhancement to local feature extraction, which improves matching. We show that CNN-based depths inferred from single RGB images are quite helpful, despite their flaws. They allow us to pre-warp images and rectify perspective distortions, to significantly enhance SIFT and BRISK features, enabling more good matches, even when cameras are looking at the same scene but in opposite directions.

CVMay 13, 2020
Pose Proposal Critic: Robust Pose Refinement by Learning Reprojection Errors

Lucas Brynte, Fredrik Kahl

In recent years, considerable progress has been made for the task of rigid object pose estimation from a single RGB-image, but achieving robustness to partial occlusions remains a challenging problem. Pose refinement via rendering has shown promise in order to achieve improved results, in particular, when data is scarce. In this paper we focus our attention on pose refinement, and show how to push the state-of-the-art further in the case of partial occlusions. The proposed pose refinement method leverages on a simplified learning task, where a CNN is trained to estimate the reprojection error between an observed and a rendered image. We experiment by training on purely synthetic data as well as a mixture of synthetic and real data. Current state-of-the-art results are outperformed for two out of three metrics on the Occlusion LINEMOD benchmark, while performing on-par for the final metric.

CVAug 18, 2019
Fine-Grained Segmentation Networks: Self-Supervised Segmentation for Improved Long-Term Visual Localization

Måns Larsson, Erik Stenborg, Carl Toft et al.

Long-term visual localization is the problem of estimating the camera pose of a given query image in a scene whose appearance changes over time. It is an important problem in practice, for example, encountered in autonomous driving. In order to gain robustness to such changes, long-term localization approaches often use segmantic segmentations as an invariant scene representation, as the semantic meaning of each scene part should not be affected by seasonal and other changes. However, these representations are typically not very discriminative due to the limited number of available classes. In this paper, we propose a new neural network, the Fine-Grained Segmentation Network (FGSN), that can be used to provide image segmentations with a larger number of labels and can be trained in a self-supervised fashion. In addition, we show how FGSNs can be trained to output consistent labels across seasonal changes. We demonstrate through extensive experiments that integrating the fine-grained segmentations produced by our FGSNs into existing localization algorithms leads to substantial improvements in localization performance.

CVJun 19, 2019
Monocular 3D Object Detection and Box Fitting Trained End-to-End Using Intersection-over-Union Loss

Eskil Jörgensen, Christopher Zach, Fredrik Kahl

Three-dimensional object detection from a single view is a challenging task which, if performed with good accuracy, is an important enabler of low-cost mobile robot perception. Previous approaches to this problem suffer either from an overly complex inference engine or from an insufficient detection accuracy. To deal with these issues, we present SS3D, a single-stage monocular 3D object detector. The framework consists of (i) a CNN, which outputs a redundant representation of each relevant object in the image with corresponding uncertainty estimates, and (ii) a 3D bounding box optimizer. We show how modeling heteroscedastic uncertainty improves performance upon our baseline, and furthermore, how back-propagation can be done through the optimizer in order to train the pipeline end-to-end for additional accuracy. Our method achieves SOTA accuracy on monocular 3D object detection, while running at 20 fps in a straightforward implementation. We argue that the SS3D architecture provides a solid framework upon which high performing detection systems can be built, with autonomous driving being the main application in mind.

CVMar 16, 2019
A Cross-Season Correspondence Dataset for Robust Semantic Segmentation

Måns Larsson, Erik Stenborg, Lars Hammarstrand et al.

In this paper, we present a method to utilize 2D-2D point matches between images taken during different image conditions to train a convolutional neural network for semantic segmentation. Enforcing label consistency across the matches makes the final segmentation algorithm robust to seasonal changes. We describe how these 2D-2D matches can be generated with little human interaction by geometrically matching points from 3D models built from images. Two cross-season correspondence datasets are created providing 2D-2D matches across seasonal changes as well as from day to night. The datasets are made publicly available to facilitate further research. We show that adding the correspondences as extra supervision during training improves the segmentation performance of the convolutional neural network, making it more robust to seasonal changes and weather conditions.

CVJul 28, 2017
Benchmarking 6DOF Outdoor Visual Localization in Changing Conditions

Torsten Sattler, Will Maddern, Carl Toft et al.

Visual localization enables autonomous vehicles to navigate in their surroundings and augmented reality applications to link virtual to real worlds. Practical visual localization approaches need to be robust to a wide variety of viewing condition, including day-night changes, as well as weather and seasonal variations, while providing highly accurate 6 degree-of-freedom (6DOF) camera pose estimates. In this paper, we introduce the first benchmark datasets specifically designed for analyzing the impact of such factors on visual localization. Using carefully created ground truth poses for query images taken under a wide variety of conditions, we evaluate the impact of various factors on 6DOF camera pose estimation accuracy through extensive experiments with state-of-the-art localization approaches. Based on our results, we draw conclusions about the difficulty of different conditions, showing that long-term localization is far from solved, and propose promising avenues for future work, including sequence-based localization approaches and the need for better local features. Our benchmark is available at visuallocalization.net.

CVMay 3, 2017
Rotation Averaging and Strong Duality

Anders Eriksson, Carl Olsson, Fredrik Kahl et al.

In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization over multiple rotation constraints. As these constraints are non-convex, this problem is generally considered challenging to solve globally. We show how to circumvent this difficulty through the use of Lagrangian duality. While such an approach is well-known it is normally not guaranteed to provide a tight relaxation. Based on spectral graph theory, we analytically prove that in many cases there is no duality gap unless the noise levels are severe. This allows us to obtain certifiably global solutions to a class of important non-convex problems in polynomial time. We also propose an efficient, scalable algorithm that out-performs general purpose numerical solvers and is able to handle the large problem instances commonly occurring in structure from motion settings. The potential of this proposed method is demonstrated on a number of different problems, consisting of both synthetic and real-world data.

CVJan 24, 2017
A Projected Gradient Descent Method for CRF Inference allowing End-To-End Training of Arbitrary Pairwise Potentials

Måns Larsson, Anurag Arnab, Fredrik Kahl et al.

Are we using the right potential functions in the Conditional Random Field models that are popular in the Vision community? Semantic segmentation and other pixel-level labelling tasks have made significant progress recently due to the deep learning paradigm. However, most state-of-the-art structured prediction methods also include a random field model with a hand-crafted Gaussian potential to model spatial priors, label consistencies and feature-based image conditioning. In this paper, we challenge this view by developing a new inference and learning framework which can learn pairwise CRF potentials restricted only by their dependence on the image pixel values and the size of the support. Both standard spatial and high-dimensional bilateral kernels are considered. Our framework is based on the observation that CRF inference can be achieved via projected gradient descent and consequently, can easily be integrated in deep neural networks to allow for end-to-end training. It is empirically demonstrated that such learned potentials can improve segmentation accuracy and that certain label class interactions are indeed better modelled by a non-Gaussian potential. In addition, we compare our inference method to the commonly used mean-field algorithm. Our framework is evaluated on several public benchmarks for semantic segmentation with improved performance compared to previous state-of-the-art CNN+CRF models.