2,810 research outputs found
Beyond Gr\"obner Bases: Basis Selection for Minimal Solvers
Many computer vision applications require robust estimation of the underlying
geometry, in terms of camera motion and 3D structure of the scene. These robust
methods often rely on running minimal solvers in a RANSAC framework. In this
paper we show how we can make polynomial solvers based on the action matrix
method faster, by careful selection of the monomial bases. These monomial bases
have traditionally been based on a Gr\"obner basis for the polynomial ideal.
Here we describe how we can enumerate all such bases in an efficient way. We
also show that going beyond Gr\"obner bases leads to more efficient solvers in
many cases. We present a novel basis sampling scheme that we evaluate on a
number of problems
A sparse resultant based method for efficient minimal solvers
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 Gr\"obner bases 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 Gr\"obner 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 Gr\"obner 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 Gr\"obner basis methods for minimal
problems in computer vision
Computational Methods for Computer Vision : Minimal Solvers and Convex Relaxations
Robust fitting of geometric models is a core problem in computer vision. The most common approach is to use a hypothesize-and-test framework, such as RANSAC. In these frameworks the model is estimated from as few measurements as possible, which minimizes the risk of selecting corrupted measurements. These estimation problems are called minimal problems, and they can often be formulated as systems of polynomial equations. In this thesis we present new methods for building so-called minimal solvers or polynomial solvers, which are specialized code for solving such systems. On several minimal problems we improve on the state-of-the-art both with respect to numerical stability and execution time.In many computer vision problems low rank matrices naturally occur. The rank can serve as a measure of model complexity and typically a low rank is desired. Optimization problems containing rank penalties or constraints are in general difficult. Recently convex relaxations, such as the nuclear norm, have been used to make these problems tractable. In this thesis we present new convex relaxations for rank-based optimization which avoid drawbacks of previous approaches and provide tighter relaxations. We evaluate our methods on a number of real and synthetic datasets and show state-of-the-art results
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
Infrastructure-based Multi-Camera Calibration using Radial Projections
Multi-camera systems are an important sensor platform for intelligent systems
such as self-driving cars. Pattern-based calibration techniques can be used to
calibrate the intrinsics of the cameras individually. However, extrinsic
calibration of systems with little to no visual overlap between the cameras is
a challenge. Given the camera intrinsics, infrastucture-based calibration
techniques are able to estimate the extrinsics using 3D maps pre-built via SLAM
or Structure-from-Motion. In this paper, we propose to fully calibrate a
multi-camera system from scratch using an infrastructure-based approach.
Assuming that the distortion is mainly radial, we introduce a two-stage
approach. We first estimate the camera-rig extrinsics up to a single unknown
translation component per camera. Next, we solve for both the intrinsic
parameters and the missing translation components. Extensive experiments on
multiple indoor and outdoor scenes with multiple multi-camera systems show that
our calibration method achieves high accuracy and robustness. In particular,
our approach is more robust than the naive approach of first estimating
intrinsic parameters and pose per camera before refining the extrinsic
parameters of the system. The implementation is available at
https://github.com/youkely/InfrasCal.Comment: ECCV 202
Robust Estimation of Motion Parameters and Scene Geometry : Minimal Solvers and Convexification of Regularisers for Low-Rank Approximation
In the dawning age of autonomous driving, accurate and robust tracking of vehicles is a quintessential part. This is inextricably linked with the problem of Simultaneous Localisation and Mapping (SLAM), in which one tries to determine the position of a vehicle relative to its surroundings without prior knowledge of them. The more you know about the object you wish to track—through sensors or mechanical construction—the more likely you are to get good positioning estimates. In the first part of this thesis, we explore new ways of improving positioning for vehicles travelling on a planar surface. This is done in several different ways: first, we generalise the work done for monocular vision to include two cameras, we propose ways of speeding up the estimation time with polynomial solvers, and we develop an auto-calibration method to cope with radially distorted images, without enforcing pre-calibration procedures.We continue to investigate the case of constrained motion—this time using auxiliary data from inertial measurement units (IMUs) to improve positioning of unmanned aerial vehicles (UAVs). The proposed methods improve the state-of-the-art for partially calibrated cases (with unknown focal length) for indoor navigation. Furthermore, we propose the first-ever real-time compatible minimal solver for simultaneous estimation of radial distortion profile, focal length, and motion parameters while utilising the IMU data.In the third and final part of this thesis, we develop a bilinear framework for low-rank regularisation, with global optimality guarantees under certain conditions. We also show equivalence between the linear and the bilinear framework, in the sense that the objectives are equal. This enables users of alternating direction method of multipliers (ADMM)—or other subgradient or splitting methods—to transition to the new framework, while being able to enjoy the benefits of second order methods. Furthermore, we propose a novel regulariser fusing two popular methods. This way we are able to combine the best of two worlds by encouraging bias reduction while enforcing low-rank solutions
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