7 research outputs found
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
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
Monocular Vision based Crowdsourced 3D Traffic Sign Positioning with Unknown Camera Intrinsics and Distortion Coefficients
Autonomous vehicles and driver assistance systems utilize maps of 3D semantic
landmarks for improved decision making. However, scaling the mapping process as
well as regularly updating such maps come with a huge cost. Crowdsourced
mapping of these landmarks such as traffic sign positions provides an appealing
alternative. The state-of-the-art approaches to crowdsourced mapping use ground
truth camera parameters, which may not always be known or may change over time.
In this work, we demonstrate an approach to computing 3D traffic sign positions
without knowing the camera focal lengths, principal point, and distortion
coefficients a priori. We validate our proposed approach on a public dataset of
traffic signs in KITTI. Using only a monocular color camera and GPS, we achieve
an average single journey relative and absolute positioning accuracy of 0.26 m
and 1.38 m, respectively.Comment: Accepted at 2020 IEEE 23rd International Conference on Intelligent
Transportation Systems (ITSC
The bottleneck degree of algebraic varieties
A bottleneck of a smooth algebraic variety is a pair
of distinct points such that the Euclidean normal spaces at
and contain the line spanned by and . The narrowness of bottlenecks
is a fundamental complexity measure in the algebraic geometry of data. In this
paper we study the number of bottlenecks of affine and projective varieties,
which we call the bottleneck degree. The bottleneck degree is a measure of the
complexity of computing all bottlenecks of an algebraic variety, using for
example numerical homotopy methods. We show that the bottleneck degree is a
function of classical invariants such as Chern classes and polar classes. We
give the formula explicitly in low dimension and provide an algorithm to
compute it in the general case.Comment: Major revision. New introduction. Added some new illustrative lemmas
and figures. Added pseudocode for the algorithm to compute bottleneck degree.
Fixed some typo
Exhaustive linearization for robust camera pose and focal length estimation
We propose a novel approach for the estimation of the pose and focal length of a camera from a set of 3D-to-2D point correspondences. Our method compares favorably to competing approaches in that it is both more accurate than existing closed form solutions, as well as faster and also more accurate than iterative ones. Our approach is inspired on the EPnP algorithm, a recent O(n) solution for the calibrated case. Yet we show that considering the focal length as an additional unknown renders the linearization and relinearization techniques of the original approach no longer valid, especially with large amounts of noise. We present new methodologies to circumvent this limitation termed exhaustive linearization and exhaustive relinearization which perform a systematic exploration of the solution space in closed form. The method is evaluated on both real and synthetic data, and our results show that besides producing precise focal length estimation, the retrieved camera pose is almost as accurate as the one computed using the EPnP, which assumes a calibrated camera.Peer ReviewedPostprint (author’s final draft
Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion
A number of minimal problems of structure from motion for cameras with radial distortion have recently been studied and solved in some cases. These problems are known to be numerically very challenging and in several cases there were no practical algorithms yielding solutions in floating point arithmetic. We make some crucial observations concerning the floating point implementation of Gröbner basis computations and use these new insights to formulate fast and stable algorithms for two minimal problems with radial distortion previously solved in exact rational arithmetic only: (i) simultaneous estimation of essential matrix and a common radial distortion parameter for two partially calibrated views and six image point correspondences and (ii) estimation of fundamental matrix and two different radial distortion parameters for two uncalibrated views and nine image point correspondences. We demonstrate that these two problems can be efficiently solved in floating point arithmetic in simulated and real experiments. For comparison we have also invented a new non-minimal algorithm for estimating fundamental matrix and two different radial distortion parameters for two uncalibrated views and twelve image point correspondences based on a generalized eigenvalue problem