4,337 research outputs found
Radially-Distorted Conjugate Translations
This paper introduces the first minimal solvers that jointly solve for
affine-rectification and radial lens distortion from coplanar repeated
patterns. Even with imagery from moderately distorted lenses, plane
rectification using the pinhole camera model is inaccurate or invalid. The
proposed solvers incorporate lens distortion into the camera model and extend
accurate rectification to wide-angle imagery, which is now common from consumer
cameras. The solvers are derived from constraints induced by the conjugate
translations of an imaged scene plane, which are integrated with the division
model for radial lens distortion. The hidden-variable trick with ideal
saturation is used to reformulate the constraints so that the solvers generated
by the Grobner-basis method are stable, small and fast.
Rectification and lens distortion are recovered from either one conjugately
translated affine-covariant feature or two independently translated
similarity-covariant features. The proposed solvers are used in a \RANSAC-based
estimator, which gives accurate rectifications after few iterations. The
proposed solvers are evaluated against the state-of-the-art and demonstrate
significantly better rectifications on noisy measurements. Qualitative results
on diverse imagery demonstrate high-accuracy undistortions and rectifications.
The source code is publicly available at https://github.com/prittjam/repeats
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
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
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
3D Reconstruction with Low Resolution, Small Baseline and High Radial Distortion Stereo Images
In this paper we analyze and compare approaches for 3D reconstruction from
low-resolution (250x250), high radial distortion stereo images, which are
acquired with small baseline (approximately 1mm). These images are acquired
with the system NanEye Stereo manufactured by CMOSIS/AWAIBA. These stereo
cameras have also small apertures, which means that high levels of illumination
are required. The goal was to develop an approach yielding accurate
reconstructions, with a low computational cost, i.e., avoiding non-linear
numerical optimization algorithms. In particular we focused on the analysis and
comparison of radial distortion models. To perform the analysis and comparison,
we defined a baseline method based on available software and methods, such as
the Bouguet toolbox [2] or the Computer Vision Toolbox from Matlab. The
approaches tested were based on the use of the polynomial model of radial
distortion, and on the application of the division model. The issue of the
center of distortion was also addressed within the framework of the application
of the division model. We concluded that the division model with a single
radial distortion parameter has limitations
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
3D Reconstruction with Low Resolution, Small Baseline and High Radial Distortion Stereo Images
In this paper we analyze and compare approaches for 3D reconstruction from
low-resolution (250x250), high radial distortion stereo images, which are
acquired with small baseline (approximately 1mm). These images are acquired
with the system NanEye Stereo manufactured by CMOSIS/AWAIBA. These stereo
cameras have also small apertures, which means that high levels of illumination
are required. The goal was to develop an approach yielding accurate
reconstructions, with a low computational cost, i.e., avoiding non-linear
numerical optimization algorithms. In particular we focused on the analysis and
comparison of radial distortion models. To perform the analysis and comparison,
we defined a baseline method based on available software and methods, such as
the Bouguet toolbox [2] or the Computer Vision Toolbox from Matlab. The
approaches tested were based on the use of the polynomial model of radial
distortion, and on the application of the division model. The issue of the
center of distortion was also addressed within the framework of the application
of the division model. We concluded that the division model with a single
radial distortion parameter has limitations
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