Feature matching is a challenging computer vision task that involves finding correspondences between two images of a 3D scene. In this paper we consider the dense approach instead of the more common sparse paradigm, thus striving to find all correspondences. Perhaps counter-intuitively, dense methods have previously shown inferior performance to their sparse and semi-sparse counterparts for estimation of two-view geometry. This changes with our novel dense method, which outperforms both dense and sparse methods on geometry estimation. The novelty is threefold: First, we propose a kernel regression global matcher. Secondly, we propose warp refinement through stacked feature maps and depthwise convolution kernels. Thirdly, we propose learning dense confidence through consistent depth and a balanced sampling approach for dense confidence maps. Through extensive experiments we confirm that our proposed dense method, Dense Kernelized Feature Matching, sets a new state-of-the-art on multiple geometry estimation benchmarks. In particular, we achieve an improvement on MegaDepth-1500 of +4.9 and +8.9 AUC@5° compared to the best previous sparse method and dense method respectively. Our code is provided at the following repository: https://github.com/Parskatt/DKM.

Emerging from low-level vision theory, steerable filters found their counterpart in prior work on steerable convolutional neural networks equivariant to rigid transformations. In our work, we propose a steerable feed-forward learning-based approach that consists of neurons with spherical decision surfaces and operates on point clouds. Such spherical neurons are obtained by conformal embedding of Euclidean space and have recently been revisited in the context of learning representations of point sets. Focusing on 3D geometry, we exploit the isometry property of spherical neurons and derive a 3D steerability constraint. After training spherical neurons to classify point clouds in a canonical orientation, we use a tetrahedron basis to quadruplicate the neurons and construct rotation-equivariant spherical filter banks. We then apply the derived constraint to interpolate the filter bank outputs and, thus, obtain a rotation-invariant network. Finally, we use a synthetic point set and real-world 3D skeleton data to verify our theoretical findings. The code is available at https://github.com/pavlo-melnyk/steerable-3d-neurons.

In this paper, we argue that modern pre-integration methods for inertial measurement units (IMUs) are accurate enough to ignore the drift for short time intervals. This allows us to consider a simplified camera model, which in turn admits further intrinsic calibration. We develop the first-ever solver to jointly solve the relative pose problem with unknown and equal focal length and radial distortion profile while utilizing the IMU data. Furthermore, we show significant speed-up compared to state-of-the-art algorithms, with small or negligible loss in accuracy for partially calibrated setups.The proposed algorithms are tested on both synthetic and real data, where the latter is focused on navigation using unmanned aerial vehicles (UAVs). We evaluate the proposed solvers on different commercially available low-cost UAVs, and demonstrate that the novel assumption on IMU drift is feasible in real-life applications. The extended intrinsic auto-calibration enables us to use distorted input images, making tedious calibration processes obsolete, compared to current state-of-the-art methods. Code available at: https://github.com/marcusvaltonen/DronePoseLib.

In this paper we present a novel algorithm for onboard radial distortion correction for unmanned aerial vehicles (UAVs) equipped with an inertial measurement unit (IMU), that runs in real-time. This approach makes calibration procedures redundant, thus allowing for exchange of optics extemporaneously. By utilizing the IMU data, the cameras can be aligned with the gravity direction. This allows us to work with fewer degrees of freedom, and opens up for further intrinsic calibration. We propose a fast and robust minimal solver for simultaneously estimating the focal length, radial distortion profile and motion parameters from homographies. The proposed solver is tested on both synthetic and real data, and perform better or on par with state-of-the-art methods relying on pre-calibration procedures. Code available at: https://github.com/marcusvaltonen/HomLib. 1

Solving geometric tasks involving point clouds by using machine learning is a challenging problem. Standard feed-forward neural networks combine linear or, if the bias parameter is included, affine layers and activation functions. Their geometric modeling is limited, which motivated the prior work introducing the multilayer hypersphere perceptron (MLHP). Its constituent part, i.e., the hypersphere neuron, is obtained by applying a conformal embedding of Euclidean space. By virtue of Clifford algebra, it can be implemented as the Cartesian dot product of inputs and weights. If the embedding is applied in a manner consistent with the dimensionality of the input space geometry, the decision surfaces of the model units become combinations of hyperspheres and make the decision-making process geometrically interpretable for humans. Our extension of the MLHP model, the multilayer geometric perceptron (MLGP), and its respective layer units, i.e., geometric neurons, are consistent with the 3D geometry and provide a geometric handle of the learned coefficients. In particular, the geometric neuron activations are isometric in 3D, which is necessary for rotation and translation equivariance. When classifying the 3D Tetris shapes, we quantitatively show that our model requires no activation function in the hidden layers other than the embedding to outperform the vanilla multilayer perceptron. In the presence of noise in the data, our model is also superior to the MLHP.

In this paper we consider a collection of relative pose problems which arise naturally in applications for visual indoor navigation using unmanned aerial vehicles (UAVs). We focus on cases where additional information from an onboard IMU is available and thus provides a partial extrinsic calibration through the gravitational vector. The solvers are designed for a partially calibrated camera, for a variety of realistic indoor scenarios, which makes it possible to navigate using images of the ground floor. Current state-of-the-art solvers use more general assumptions, such as using arbitrary planar structures; however, these solvers do not yield adequate reconstructions for real scenes, nor do they perform fast enough to be incorporated in real-time systems. We show that the proposed solvers enjoy better numerical stability, are faster, and require fewer point correspondences, compared to state-of-the-art approaches. These properties are vital components for robust navigation in real-time systems, and we demonstrate on both synthetic and real data that our method outperforms other solvers, and yields superior motion estimation(1).

In many computer vision applications, one acquires images of planar surfaces from two different vantage points. One can use a projective transformation to map pixel coordinates associated with a particular planar surface from one image to another. The transformation, called a homography, can be represented by a unique, to within a scale factor, 3 × 3 matrix. One requires a different homography matrix, scale differences apart, for each planar surface whose two images one wants to relate. However, a collection of homography matrices forms a valid set only if the matrices satisfy consistency constraints implied by the rigidity of the motion and the scene. We explore what it means for a set of homography matrices to be compatible and show that two seemingly disparate definitions are in fact equivalent. Our insight lays the theoretical foundations upon which the derivation of various sets of homography consistency constraints can proceed.