Search results for "fundamental matrix"
showing 10 items of 11 documents
Approximated overlap error for the evaluation of feature descriptors on 3D scenes
2013
This paper presents a new framework to evaluate feature descriptors on 3D datasets. The proposed method employs the approximated overlap error in order to conform with the reference planar evaluation case of the Oxford dataset based on the overlap error. The method takes into account not only the keypoint centre but also the feature shape and it does not require complex data setups, depth maps or an accurate camera calibration. Only a ground-truth fundamental matrix should be computed, so that the dataset can be freely extended by adding further images. The proposed approach is robust to false positives occurring in the evaluation process, which do not introduce any relevant changes in the …
noRANSAC for fundamental matrix estimation
2011
The estimation of the fundamental matrix from a set of corresponding points is a relevant topic in epipolar stereo geometry [10]. Due to the high amount of outliers between the matches, RANSAC-based approaches [7, 13, 29] have been used to obtain the fundamental matrix. In this paper two new contributes are presented: a new normalized epipolar error measure which takes into account the shape of the features used as matches [17] and a new strategy to compare fundamental matrices. The proposed error measure gives good results and it does not depend on the image scale. Moreover, the new evaluation strategy describes a valid tool to compare diffe rent RANSAC-based methods because it does not re…
Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations
2014
Nowadays the Lyapunov exponents and Lyapunov dimension have become so widespread and common that they are often used without references to the rigorous definitions or pioneering works. It may lead to a confusion since there are at least two well-known definitions, which are used in computations: the upper bounds of the exponential growth rate of the norms of linearized system solutions (Lyapunov characteristic exponents, LCEs) and the upper bounds of the exponential growth rate of the singular values of the fundamental matrix of linearized system (Lyapunov exponents, LEs). In this work the relation between Lyapunov exponents and Lyapunov characteristic exponents is discussed. The invariance…
An Integrated Neural and Algorithmic System for Optical Flow Computation
1997
Motion detection plays a central role in several visual environments: knowledge of object velocities and trajectories is fundamental in scene interpretation and segmentation. This task appears a simple problem, but detecting moving objects is very difficult, in fact this is a problem that cannot be considered completely solved today [1] [2] [3].
Quadratic ${\mathcal P}{\mathcal T}$-symmetric operators with real spectrum and similarity to self-adjoint operators
2012
It is established that a -symmetric elliptic quadratic differential operator with real spectrum is similar to a self-adjoint operator precisely when the associated fundamental matrix has no Jordan blocks.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
3-D shape reconstruction in an active stereo vision system using genetic algorithms
2003
Abstract The recovery of 3-D shape information (depth) using stereo vision analysis is one of the major areas in computer vision and has given rise to a great deal of literature in the recent past. The widely known stereo vision methods are the passive stereo vision approaches that use two cameras. Obtaining 3-D information involves the identification of the corresponding 2-D points between left and right images. Most existing methods tackle this matching task from singular points, i.e. finding points in both image planes with more or less the same neighborhood characteristics. One key problem we have to solve is that we are on the first instance unable to know a priori whether a point in t…
AN APPROACH TO CORRECTING IMAGE DISTORTION BY SELF CALIBRATION STEREOSCOPIC SCENE FROM MULTIPLE VIEWS
2012
International audience; An important step in the analysis and interpretation of video scenes for recognizing scenario is the aberration corrections introduced during the image acquisition in order to provide and correct real image data. This paper presents an approach on distortion correction based on stereoscopic self calibration from images sequences by using a multi-camera system of vision (network cameras). This approach for correcting image distortion brings an elegant and robust technique with good accuracy. Without any knowledge of shooting conditions, the camera's parameters will be estimated. For this, the image key points of interest are extracted from different overlapping views …
Evolutionary-based 3D reconstruction using an uncalibrated stereovision system: application of building a panoramic object view
2010
In this paper, we propose an original evolutionary-based method for 3D panoramic reconstruction from an uncalibrated stereovision system (USS). The USS is composed of five cameras located on an arc of a circle around the object to be analyzed. The main originality of this work concerns the process of the calculation of the 3D information. Actually, with our method, 3D coordinates are directly obtained without any prior estimation of the fundamental matrix. The method operates in two steps. Firstly, points of interest are detected in pairs of images acquired by two consecutive cameras of the USS are matched. And secondly, using evolutionary algorithms, we jointly compute the transformed matr…
A Symplectic Kovacic's Algorithm in Dimension 4
2018
Let $L$ be a $4$th order differential operator with coefficients in $\mathbb{K}(z)$, with $\mathbb{K}$ a computable algebraically closed field. The operator $L$ is called symplectic when up to rational gauge transformation, the fundamental matrix of solutions $X$ satisfies $X^t J X=J$ where $J$ is the standard symplectic matrix. It is called projectively symplectic when it is projectively equivalent to a symplectic operator. We design an algorithm to test if $L$ is projectively symplectic. Furthermore, based on Kovacic's algorithm, we design an algorithm that computes Liouvillian solutions of projectively symplectic operators of order $4$. Moreover, using Klein's Theorem, algebraic solution…
A real-time auto calibration technique for stereo camera
2020
Calibration of the internal and external parameters of a stereo vision camera is a well-known research problem in the computer vision. Usually, to get accurate 3D results the camera should be manua...