1,411 research outputs found
Projective rectification from the fundamental matrix
This paper describes a direct, self-contained method for planar image rectification of stereo pairs. The method is based solely on an examination of the Fundamental matrix, where an improved method is given for the derivation of two projective transformations that horizontally align all the epipolar projections. A novel approach is proposed to uniquely optimise each transform in order to minimise perspective distortions. This ensures the rectified images resemble the original images as closely as possible. Detailed results show that the rectification precision exactly matches the estimation error of the Fundamental matrix. In tests the remaining perspective distortion offers on average less than one percent viewpoint distortion. Both these factors offer superior robustness and performance compared with existing techniques
SuperPoint: Self-Supervised Interest Point Detection and Description
This paper presents a self-supervised framework for training interest point
detectors and descriptors suitable for a large number of multiple-view geometry
problems in computer vision. As opposed to patch-based neural networks, our
fully-convolutional model operates on full-sized images and jointly computes
pixel-level interest point locations and associated descriptors in one forward
pass. We introduce Homographic Adaptation, a multi-scale, multi-homography
approach for boosting interest point detection repeatability and performing
cross-domain adaptation (e.g., synthetic-to-real). Our model, when trained on
the MS-COCO generic image dataset using Homographic Adaptation, is able to
repeatedly detect a much richer set of interest points than the initial
pre-adapted deep model and any other traditional corner detector. The final
system gives rise to state-of-the-art homography estimation results on HPatches
when compared to LIFT, SIFT and ORB.Comment: Camera-ready version for CVPR 2018 Deep Learning for Visual SLAM
Workshop (DL4VSLAM2018
Seafloor Video Mapping: Modeling, Algorithms, Apparatus
This paper discusses a technique used for construction of high-resolution image mosaic from a videosequence and the synchronously logged camera attitude information. It allows one to infer geometric characteristics of the imaged terrain and hence improve the mosaic quality and reduce the computational burden. The technique is demonstrated using numerical modeling and is applied to videodata collected on Rainsford Island, Mass. Calculation of the transformation relating consecutive image frames is an essential operation affecting reliability of the whole mosaicing process. Improvements to the algorithm are suggested, which significantly decrease the possibility of convergence to an inappropriate solution
Homography-based ground plane detection using a single on-board camera
This study presents a robust method for ground plane detection in vision-based systems with a non-stationary camera. The proposed method is based on the reliable estimation of the homography between ground planes in successive images. This homography is computed using a feature matching approach, which in contrast to classical approaches to on-board motion estimation does not require explicit ego-motion calculation. As opposed to it, a novel homography calculation method based on a linear estimation framework is presented. This framework provides predictions of the ground plane transformation matrix that are dynamically updated with new measurements. The method is specially suited for challenging environments, in particular traffic scenarios, in which the information is scarce and the homography computed from the images is usually inaccurate or erroneous. The proposed estimation framework is able to remove erroneous measurements and to correct those that are inaccurate, hence producing a reliable homography estimate at each instant. It is based on the evaluation of the difference between the predicted and the observed transformations, measured according to the spectral norm of the associated matrix of differences. Moreover, an example is provided on how to use the information extracted from ground plane estimation to achieve object detection and tracking. The method has been successfully demonstrated for the detection of moving vehicles in traffic environments
Solving the "Isomorphism of Polynomials with Two Secrets" Problem for all Pairs of Quadratic Forms
We study the Isomorphism of Polynomial (IP2S) problem with m=2 homogeneous
quadratic polynomials of n variables over a finite field of odd characteristic:
given two quadratic polynomials (a, b) on n variables, we find two bijective
linear maps (s,t) such that b=t . a . s. We give an algorithm computing s and t
in time complexity O~(n^4) for all instances, and O~(n^3) in a dominant set of
instances.
The IP2S problem was introduced in cryptography by Patarin back in 1996. The
special case of this problem when t is the identity is called the isomorphism
with one secret (IP1S) problem. Generic algebraic equation solvers (for example
using Gr\"obner bases) solve quite well random instances of the IP1S problem.
For the particular cyclic instances of IP1S, a cubic-time algorithm was later
given and explained in terms of pencils of quadratic forms over all finite
fields; in particular, the cyclic IP1S problem in odd characteristic reduces to
the computation of the square root of a matrix.
We give here an algorithm solving all cases of the IP1S problem in odd
characteristic using two new tools, the Kronecker form for a singular quadratic
pencil, and the reduction of bilinear forms over a non-commutative algebra.
Finally, we show that the second secret in the IP2S problem may be recovered in
cubic time
P-symbols, Heun Identities, and 3F2 Identities
The usefulness of Riemann P-symbols in deriving identities involving the
parametrized special function Hl is explored. Hl is the analytic local solution
of the Heun equation, the canonical second-order differential equation on the
Riemann sphere with four regular singular points. The identities discussed
include ones coming from Moebius automorphisms and F-homotopies, and also
quadratic and biquadratic transformations. The case when Hl is identical to a
generalized hypergeometric function of 3F2 type is examined, and Pfaff and
Euler transformations of 3F2(a1,a2,e+1;b1,e;x) are derived. They extend several
3F2 identities of Bailey and Slater.Comment: 20 page
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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