Homography from two orientation- and scale-covariant features

This paper proposes a geometric interpretation of the angles and scales which the orientation- and scale-covariant feature detectors, e.g. SIFT, provide. Two new general constraints are derived on the scales and rotations which can be used in any geometric model estimation tasks. Using these formulas, two new constraints on homography estimation are introduced. Exploiting the derived equations, a solver for estimating the homography from the minimal number of two correspondences is proposed. Also, it is shown how the normalization of the point correspondences affects the rotation and scale parameters, thus achieving numerically stable results. Due to requiring merely two feature pairs, robust estimators, e.g. RANSAC, do significantly fewer iterations than by using the four-point algorithm. When using covariant features, e.g. SIFT, the information about the scale and orientation is given at no cost. The proposed homography estimation method is tested in a synthetic environment and on publicly available real-world datasets

Rectification from Radially-Distorted Scales

This paper introduces the first minimal solvers that jointly estimate lens distortion and affine rectification from repetitions of rigidly transformed coplanar local features. The proposed solvers incorporate lens distortion into the camera model and extend accurate rectification to wide-angle images that contain nearly any type of coplanar repeated content. We demonstrate a principled approach to generating stable minimal solvers by the Grobner basis method, which is accomplished by sampling feasible monomial bases to maximize numerical stability. Synthetic and real-image experiments confirm that the solvers give accurate rectifications from noisy measurements when used in a RANSAC-based estimator. The proposed solvers demonstrate superior robustness to noise compared to the state-of-the-art. The solvers work on scenes without straight lines and, in general, relax the strong assumptions on scene content made by the state-of-the-art. Accurate rectifications on imagery that was taken with narrow focal length to near fish-eye lenses demonstrate the wide applicability of the proposed method. The method is fully automated, and the code is publicly available at https://github.com/prittjam/repeats.Comment: pre-prin

Globally Optimal Relative Pose Estimation with Gravity Prior

Smartphones, tablets and camera systems used, e.g., in cars and UAVs, are typically equipped with IMUs (inertial measurement units) that can measure the gravity vector accurately. Using this additional information, the $y$-axes of the cameras can be aligned, reducing their relative orientation to a single degree-of-freedom. With this assumption, we propose a novel globally optimal solver, minimizing the algebraic error in the least-squares sense, to estimate the relative pose in the over-determined case. Based on the epipolar constraint, we convert the optimization problem into solving two polynomials with only two unknowns. Also, a fast solver is proposed using the first-order approximation of the rotation. The proposed solvers are compared with the state-of-the-art ones on four real-world datasets with approx. 50000 image pairs in total. Moreover, we collected a dataset, by a smartphone, consisting of 10933 image pairs, gravity directions, and ground truth 3D reconstructions

Hybrid Focal Stereo Networks for Pattern Analysis in Homogeneous Scenes

In this paper we address the problem of multiple camera calibration in the presence of a homogeneous scene, and without the possibility of employing calibration object based methods. The proposed solution exploits salient features present in a larger field of view, but instead of employing active vision we replace the cameras with stereo rigs featuring a long focal analysis camera, as well as a short focal registration camera. Thus, we are able to propose an accurate solution which does not require intrinsic variation models as in the case of zooming cameras. Moreover, the availability of the two views simultaneously in each rig allows for pose re-estimation between rigs as often as necessary. The algorithm has been successfully validated in an indoor setting, as well as on a difficult scene featuring a highly dense pilgrim crowd in Makkah.Comment: 13 pages, 6 figures, submitted to Machine Vision and Application

Relative Pose from Deep Learned Depth and a Single Affine Correspondence

We propose a new approach for combining deep-learned non-metric monocular depth with affine correspondences (ACs) to estimate the relative pose of two calibrated cameras from a single correspondence. Considering the depth information and affine features, two new constraints on the camera pose are derived. The proposed solver is usable within 1-point RANSAC approaches. Thus, the processing time of the robust estimation is linear in the number of correspondences and, therefore, orders of magnitude faster than by using traditional approaches. The proposed 1AC+D solver is tested both on synthetic data and on 110395 publicly available real image pairs where we used an off-the-shelf monocular depth network to provide up-to-scale depth per pixel. The proposed 1AC+D leads to similar accuracy as traditional approaches while being significantly faster. When solving large-scale problems, e.g., pose-graph initialization for Structure-from-Motion (SfM) pipelines, the overhead of obtaining ACs and monocular depth is negligible compared to the speed-up gained in the pairwise geometric verification, i.e., relative pose estimation. This is demonstrated on scenes from the 1DSfM dataset using a state-of-the-art global SfM algorithm. Source code: https://github.com/eivan/one-ac-pos

Unknown Radial Distortion Centers in Multiple View Geometry Problems

The radial undistortion model proposed by Fitzgibbon and the radial fundamental matrix were early steps to extend classical epipolar geometry to distorted cameras. Later minimal solvers have been proposed to find relative pose and radial distortion, given point correspondences between images. However, a big drawback of all these approaches is that they require the distortion center to be exactly known. In this paper we show how the distortion center can be absorbed into a new radial fundamental matrix. This new formulation is much more practical in reality as it allows also digital zoom, cropped images and camera-lens systems where the distortion center does not exactly coincide with the image center. In particular we start from the setting where only one of the two images contains radial distortion, analyze the structure of the particular radial fundamental matrix and show that the technique also generalizes to other linear multi-view relationships like trifocal tensor and homography. For the new radial fundamental matrix we propose different estimation algorithms from 9,10 and 11 points. We show how to extract the epipoles and prove the practical applicability on several epipolar geometry image pairs with strong distortion that - to the best of our knowledge - no other existing algorithm can handle properly

A sparse resultant based method for efficient minimal solvers

Abstract Many computer vision applications require robust and efficient estimation of camera geometry. The robust estimation is usually based on solving camera geometry problems from a minimal number of input data measurements, i.e. solving minimal problems in a RANSAC framework. Minimal problems often result in complex systems of polynomial equations. Many state-of-the-art efficient polynomial solvers to these problems are based on Gröbner basis and the action-matrix method that has been automatized and highly optimized in recent years. In this paper we study an alternative algebraic method for solving systems of polynomial equations, i.e., the sparse resultant-based method and propose a novel approach to convert the resultant constraint to an eigenvalue problem. This technique can significantly improve the efficiency and stability of existing resultant-based solvers. We applied our new resultant-based method to a large variety of computer vision problems and show that for most of the considered problems, the new method leads to solvers that are the same size as the the best available Gröbner basis solvers and of similar accuracy. For some problems the new sparse-resultant based method leads to even smaller and more stable solvers than the state-of-the-art Gröbner basis solvers. Our new method can be fully automatized and incorporated into existing tools for automatic generation of efficient polynomial solvers and as such it represents a competitive alternative to popular Gröbner basis methods for minimal problems in computer vision