In this tutorial, we will continue the discussion, started in the tutorial 4, about the derivation of the fundamental solutions. In the former tutorial, we presented techniques for setting up the fundamental solution for simple and compound operators. Herein, we will discuss the use of operator decoupling technique to breakdown matrix operators to simple or compound scalar ones. This method is ...

The estimation of the fundamental matrix from a set of corresponding points is a relevant topic in epipolar stereo geometry [2]. Due to the high amount of outliers between the matches, RANSAC-based approaches [1] have been used to obtain the fundamental matrix. We introduce a new normalized epipolar error measure which takes into account the shape of the features used as matches [3] and does no...

A method for finding correspondences between widely separated views is presented. The proposed solution consists in estimating the local perspective distortion between the neighborhoods of junctions. To this end, a formulation is proposed, based on a constrained minimization involving an estimated fundamental matrix. An application is also proposed to fundamental matrix recovery using crude cam...

The purpose of this note is to give a specific form for Kruppa’s equations in terms of the Fundamental matrix. Kruppa’s equations can be written explicitly in terms of the singular value decomposition (SVD) of the

This paper deals with the problem of characterizing and parametrizing the manifold of trifocal tensors that describe the geometry of three views like the fundamental matrix characterizes the geometry of two. The paper contains two new results. First a new, simpler, set of algebraic constraints that characterizes the set of trifocal tensors is presented. Second, we give a new parametrization of ...

In this paper, we consider structure and motion recovery for scenes consisting of static and dynamic features. More particularly, we consider a single moving uncalibrated camera observing a scene consisting of points moving along straight lines converging to a unique point and lying on a motion plane. This scenario may describe a roadway observed by a moving camera whose motion is unknown. We s...

We propose, in maximum likelihood sense, an optimal method for the affine fundamental matrix estimation in the presence of both Gaussian noise and outliers. It is based on weighting the squared residuals by the iteratively computed, residual posterior probabilities to be relevant. The proposed principle is also used for the covariance matrix estimation of the affine F-matrix where the novelty i...

The goal of this work is to create several functions for processing of two input images of one object to uncover a geometry of the scene. There are well-known techniques how to compute a fundamental matrix and reconstruct 3D coordinates. Several techniques were tested to find the method that is fast and rather precise. The functions are implemented in the environment of Borland C++ Builder. Cal...