Affine steerers for structured keypoint description

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.

From 2D to 3D: AISG-SLA Visual Localization Challenge

Research in 3D mapping is crucial for smart city applications, yet the cost of acquiring 3D data often hinders progress. Visual localization, particularly monocular camera position estimation, offers a solution by determining the camera's pose solely through visual cues. However, this task is challenging due to limited data from a single camera. To tackle these challenges, we organized the AISG-SLA Visual Localization Challenge (VLC) at IJCAI 2023 to explore how AI can accurately extract camera pose data from 2D images in 3D space. The challenge attracted over 300 participants worldwide, forming 50+ teams. Winning teams achieved high accuracy in pose estimation using images from a car-mounted camera with low frame rates. The VLC dataset is available for research purposes upon request via vlc-dataset@aisingapore.org.

DeDoDe v2: Analyzing and Improving the DeDoDe Keypoint Detector

In this paper, we analyze and improve into the recently proposed DeDoDe keypoint detector. We focus our analysis on some key issues. First, we find that DeDoDe keypoints tend to cluster together, which we fix by performing non-max suppression on the target distribution of the detector during training. Second, we address issues related to data augmentation. In particular, the DeDoDe detector is sensitive to large rotations. We fix this by including 90-degree rotations as well as horizontal flips. Finally, the decoupled nature of the DeDoDe detector makes evaluation of downstream usefulness problematic. We fix this by matching the keypoints with a pretrained dense matcher (RoMa) and evaluating two-view pose estimates. We find that the original long training is detrimental to performance, and therefore propose a much shorter training schedule. We integrate all these improvements into our proposed detector DeDoDe v2 and evaluate it with the original DeDoDe descriptor on the MegaDepth-1500 and IMC2022 benchmarks. Our proposed detector significantly increases pose estimation results, notably from 75.9 to 78.3 mAA on the IMC2022 challenge. Code and weights are available at https://github.com/Parskatt/DeDoDe

Steerers: A framework for rotation equivariant keypoint descriptors

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. We instead 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 all of 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 github.com/georg-bn/rotation-steerers.

Leveraging Cutting Edge Deep Learning Based Image Matching for Reconstructing a Large Scene from Sparse Images

We present the top ranked solution for the AISG-SLA Visual Localisation Challenge benchmark (IJCAI 2023), where the task is to estimate relative motion between images taken in sequence by a camera mounted on a car driving through an urban scene. For matching images we use our recent deep learning based matcher RoMa. Matching image pairs sequentially and estimating relative motion from point correspondences sampled by RoMa already gives very competitive results -- third rank on the challenge benchmark. To improve the estimations we extract keypoints in the images, match them using RoMa, and perform structure from motion reconstruction using COLMAP. We choose our recent DeDoDe keypoints for their high repeatability. Further, we address time jumps in the image sequence by matching specific non-consecutive image pairs based on image retrieval with DINOv2. These improvements yield a solution beating all competitors. We further present a loose upper bound on the accuracy obtainable by the image retrieval approach by also matching hand-picked non-consecutive pairs.

ICML 2023 Topological Deep Learning Challenge : Design and Results

This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competition asked participants to provide open-source implementations of topological neural networks from the literature by contributing to the python packages TopoNetX (data processing) and TopoModelX (deep learning). The challenge attracted twenty-eight qualifying submissions in its two-month duration. This paper describes the design of the challenge and summarizes its main findings.

DeDoDe: Detect, Don't Describe -- Describe, Don't Detect for Local Feature Matching

Keypoint detection is a pivotal step in 3D reconstruction, whereby sets of (up to) K points are detected in each view of a scene. Crucially, the detected points need to be consistent between views, i.e., correspond to the same 3D point in the scene. One of the main challenges with keypoint detection is the formulation of the learning objective. Previous learning-based methods typically jointly learn descriptors with keypoints, and treat the keypoint detection as a binary classification task on mutual nearest neighbours. However, basing keypoint detection on descriptor nearest neighbours is a proxy task, which is not guaranteed to produce 3D-consistent keypoints. Furthermore, this ties the keypoints to a specific descriptor, complicating downstream usage. In this work, we instead learn keypoints directly from 3D consistency. To this end, we train the detector to detect tracks from large-scale SfM. As these points are often overly sparse, we derive a semi-supervised two-view detection objective to expand this set to a desired number of detections. To train a descriptor, we maximize the mutual nearest neighbour objective over the keypoints with a separate network. Results show that our approach, DeDoDe, achieves significant gains on multiple geometry benchmarks. Code is provided at https://github.com/Parskatt/DeDoDe

Investigating how ReLU-networks encode symmetries

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.

RoMa: Revisiting Robust Losses for Dense Feature Matching

Dense feature matching is an important computer vision task that involves estimating all correspondences between two images of a 3D scene. In this paper, we revisit robust losses for matching from a Markov chain perspective, yielding theoretical insights and large gains in performance. We begin by constructing a unifying formulation of matching as a Markov chain, based on which we identify two key stages which we argue should be decoupled for matching. The first is the coarse stage, where the estimated result needs to be globally consistent. The second is the refinement stage, where the model needs precise localization capabilities. Inspired by the insight that these stages concern distinct issues, we propose a coarse matcher following the regression-by-classification paradigm that provides excellent globally consistent, albeit not exactly localized, matches. This is followed by a local feature refinement stage using well-motivated robust regression losses, yielding extremely precise matches. Our proposed approach, which we call RoMa, achieves significant improvements compared to the state-of-the-art. Code is available at https://github.com/Parskatt/RoMa

In Search of Projectively Equivariant Neural Networks

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. In particular, we study the relation of projective and ordinary equivariance and show that for important examples, the problems are in fact equivalent. The rotation group in 3D acts projectively on the projective plane. We experimentally study the practical importance of rotation equivariance when designing networks for filtering 2D-2D correspondences. Fully equivariant models perform poorly, and while a simple addition of invariant features to a strong baseline yields improvements, this seems to not be due to improved equivariance.