Are Minimal Radial Distortion Solvers Necessary for Relative Pose Estimation?

Estimating the relative pose between two cameras is a fundamental step in many applications such as Structure-from-Motion. The common approach to relative pose estimation is to apply a minimal solver inside a RANSAC loop. Highly efficient solvers exist for pinhole cameras. Yet, (nearly) all cameras exhibit radial distortion. Not modeling radial distortion leads to (significantly) worse results. However, minimal radial distortion solvers are significantly more complex than pinhole solvers, both in terms of run-time and implementation efforts. This paper compares radial distortion solvers with a simple-to-implement approach that combines an efficient pinhole solver with sampled radial distortion parameters. Extensive experiments on multiple datasets and RANSAC variants show that this simple approach performs similarly or better than the most accurate minimal distortion solvers at faster run-times while being significantly more accurate than faster non-minimal solvers. We clearly show that complex radial distortion solvers are not necessary in practice. Code and benchmark are available at https://github.com/kocurvik/rd.

Combining Absolute and Semi-Generalized Relative Poses for Visual Localization

Visual localization is the problem of estimating the camera pose of a given query image within a known scene. Most state-of-the-art localization approaches follow the structure-based paradigm and use 2D-3D matches between pixels in a query image and 3D points in the scene for pose estimation. These approaches assume an accurate 3D model of the scene, which might not always be available, especially if only a few images are available to compute the scene representation. In contrast, structure-less methods rely on 2D-2D matches and do not require any 3D scene model. However, they are also less accurate than structure-based methods. Although one prior work proposed to combine structure-based and structure-less pose estimation strategies, its practical relevance has not been shown. We analyze combining structure-based and structure-less strategies while exploring how to select between poses obtained from 2D-2D and 2D-3D matches, respectively. We show that combining both strategies improves localization performance in multiple practically relevant scenarios.

Obfuscation Based Privacy Preserving Representations are Recoverable Using Neighborhood Information

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 \url{https://github.com/kunalchelani/RecoverPointsNeighborhood}.

WildGaussians: 3D Gaussian Splatting in the Wild

While the field of 3D scene reconstruction is dominated by NeRFs due to their photorealistic quality, 3D Gaussian Splatting (3DGS) has recently emerged, offering similar quality with real-time rendering speeds. However, both methods primarily excel with well-controlled 3D scenes, while in-the-wild data - characterized by occlusions, dynamic objects, and varying illumination - remains challenging. NeRFs can adapt to such conditions easily through per-image embedding vectors, but 3DGS struggles due to its explicit representation and lack of shared parameters. To address this, we introduce WildGaussians, a novel approach to handle occlusions and appearance changes with 3DGS. By leveraging robust DINO features and integrating an appearance modeling module within 3DGS, our method achieves state-of-the-art results. We demonstrate that WildGaussians matches the real-time rendering speed of 3DGS while surpassing both 3DGS and NeRF baselines in handling in-the-wild data, all within a simple architectural framework.

Privacy-Preserving Representations are not Enough -- Recovering Scene Content from Camera Poses

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.

Visual Localization using Imperfect 3D Models from the Internet

Visual localization is a core component in many applications, including augmented reality (AR). Localization algorithms compute the camera pose of a query image w.r.t. a scene representation, which is typically built from images. This often requires capturing and storing large amounts of data, followed by running Structure-from-Motion (SfM) algorithms. An interesting, and underexplored, source of data for building scene representations are 3D models that are readily available on the Internet, e.g., hand-drawn CAD models, 3D models generated from building footprints, or from aerial images. These models allow to perform visual localization right away without the time-consuming scene capturing and model building steps. Yet, it also comes with challenges as the available 3D models are often imperfect reflections of reality. E.g., the models might only have generic or no textures at all, might only provide a simple approximation of the scene geometry, or might be stretched. This paper studies how the imperfections of these models affect localization accuracy. We create a new benchmark for this task and provide a detailed experimental evaluation based on multiple 3D models per scene. We show that 3D models from the Internet show promise as an easy-to-obtain scene representation. At the same time, there is significant room for improvement for visual localization pipelines. To foster research on this interesting and challenging task, we release our benchmark at v-pnk.github.io/cadloc.

Efficient solutions to the relative pose of three calibrated cameras from four points using virtual correspondences

We study the challenging problem of estimating the relative pose of three calibrated cameras. We propose two novel solutions to the notoriously difficult configuration of four points in three views, known as the 4p3v problem. Our solutions are based on the simple idea of generating one additional virtual point correspondence in two views by using the information from the locations of the four input correspondences in the three views. For the first solver, we train a network to predict this point correspondence. The second solver uses a much simpler and more efficient strategy based on the mean points of three corresponding input points. The new solvers are efficient and easy to implement since they are based on the existing efficient minimal solvers, i.e., the well-known 5-point relative pose and the P3P solvers. The solvers achieve state-of-the-art results on real data. The idea of solving minimal problems using virtual correspondences is general and can be applied to other problems, e.g., the 5-point relative pose problem. In this way, minimal problems can be solved using simpler non-minimal solvers or even using sub-minimal samples inside RANSAC. In addition, we compare different variants of 4p3v solvers with the baseline solver for the minimal configuration consisting of three triplets of points and two points visible in two views. We discuss which configuration of points is potentially the most practical in real applications.

Sparse resultant based minimal solvers in computer vision and their connection with the action matrix

Many computer vision applications require robust and efficient estimation of camera geometry from a minimal number of input data measurements, ie, solving minimal problems in a RANSAC framework. Minimal problems are usually formulated as complex systems of polynomial equations. Many state-of-the-art efficient polynomial solvers are based on the action matrix method that has been automated and highly optimised in recent years. In this paper we explore the theory of sparse resultants for generating minimal solvers and propose a novel approach based on a using an extra polynomial with a special form. We show that for some camera geometry problems our extra polynomial-based method leads to smaller and more stable solvers than the state-of-the-art Gr\"obner basis-based solvers. The proposed method can be fully automated and incorporated into existing tools for automatic generation of efficient polynomial solvers. It provides a competitive alternative to popular Gr\"obner basis-based methods for minimal problems in computer vision. Additionally, we study the conditions under which the minimal solvers generated by the state-of-the-art action matrix-based methods and the proposed extra polynomial resultant-based method, are equivalent. Specifically we consider a step-by-step comparison between the approaches based on the action matrix and the sparse resultant, followed by a set of substitutions, which would lead to equivalent minimal solvers.

Partially calibrated semi-generalized pose from hybrid point correspondences

In this paper we study the problem of estimating the semi-generalized pose of a partially calibrated camera, i.e., the pose of a perspective camera with unknown focal length w.r.t. a generalized camera, from a hybrid set of 2D-2D and 2D-3D point correspondences. We study all possible camera configurations within the generalized camera system. To derive practical solvers to previously unsolved challenging configurations, we test different parameterizations as well as different solving strategies based on the state-of-the-art methods for generating efficient polynomial solvers. We evaluate the three most promising solvers, i.e., the H51f solver with five 2D-2D correspondences and one 2D-3D correspondence viewed by the same camera inside generalized camera, the H32f solver with three 2D-2D and two 2D-3D correspondences, and the H13f solver with one 2D-2D and three 2D-3D correspondences, on synthetic and real data. We show that in the presence of noise in the 3D points these solvers provide better estimates than the corresponding absolute pose solvers.

MeshLoc: Mesh-Based Visual Localization

Visual localization, i.e., the problem of camera pose estimation, is a central component of applications such as autonomous robots and augmented reality systems. A dominant approach in the literature, shown to scale to large scenes and to handle complex illumination and seasonal changes, is based on local features extracted from images. The scene representation is a sparse Structure-from-Motion point cloud that is tied to a specific local feature. Switching to another feature type requires an expensive feature matching step between the database images used to construct the point cloud. In this work, we thus explore a more flexible alternative based on dense 3D meshes that does not require features matching between database images to build the scene representation. We show that this approach can achieve state-of-the-art results. We further show that surprisingly competitive results can be obtained when extracting features on renderings of these meshes, without any neural rendering stage, and even when rendering raw scene geometry without color or texture. Our results show that dense 3D model-based representations are a promising alternative to existing representations and point to interesting and challenging directions for future research.