GARLIC: GAussian Representation LearnIng for spaCe partitioning

We introduce GARLIC (GAussian Representation LearnIng for spaCe partitioning), a novel indexing structure based on \(N\)-dimensional Gaussians for efficiently learning high-dimensional vector spaces. Our approach is inspired from Gaussian splatting techniques, typically used in 3D rendering, which we adapt for high-dimensional search and classification. We optimize Gaussian parameters using information-theoretic objectives that balance coverage, assignment confidence, and structural and semantic consistency. A key contribution is to progressively refine the representation through split and clone operations, handling hundreds of dimensions, thus handling varying data densities. GARLIC offers the fast building times of traditional space partitioning methods (e.g., under \(\sim5\) min build time for SIFT1M) while achieving \(\sim50\%\) Recall10@10 in low-candidate regimes. Experimental results on standard benchmarks demonstrate our method's consistency in (a) \(k\)-NN retrieval, outperforming methods, such as Faiss-IVF, in fast-recall by using about half their probes for the same Recall10@10 in Fashion-MNIST, and (b) in classification tasks, beating by \(\sim15\%\) accuracy other majority voting methods. Further, we show strong generalization capabilities, maintaining high accuracy even with downsampled training data: using just \(1\%\) of the training data returns \(\sim 45\%\) Recall@1, thus making GARLIC quite powerful for applications requiring both speed and accuracy.

Are Minimal Radial Distortion Solvers Really 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 two simple-to-implement approaches that do not use minimal radial distortion solvers: The first approach combines an efficient pinhole solver with sampled radial undistortion parameters, where the sampled parameters are used for undistortion prior to applying the pinhole solver. The second approach uses a state-of-the-art neural network to estimate the distortion parameters rather than sampling them from a set of potential values. Extensive experiments on multiple datasets, and different camera setups, show that complex minimal radial distortion solvers are not necessary in practice. We discuss under which conditions a simple sampling of radial undistortion parameters is preferable over calibrating cameras using a learning-based prior approach. Code and newly created benchmark for relative pose estimation under radial distortion are available at https://github.com/kocurvik/rdnet.

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.

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.