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...

This paper deals with the problem of analysing sequences of images taken by uncalibrated cameras. It is assumed that the correspondences between the points in the different images are known. This paper introduces a new framework for this problem. The situation of two cameras is described by the reduced fundamental matrix. Another new concept, the reduced fundamental tensor, describes the situat...

When the camera viewing an action is moving, the motion observed in the video not only contains the motion of the actor but also the motion of the camera. At each time instant, in addition to the camera motion, a different view of the action is observed. In this paper, we propose a novel method to perform action recognition in presence of camera motion. Proposed method is based on the epipolar ...

We study the rank and geometry of the multibody fundamental matrix, a geometric entity characterizing the two-view geometry of dynamic scenes consisting of multiple rigidbody motions. We derive an upper bound on the rank of the multibody fundamental matrix that depends on the number of independent translations. We also derive an algebraic characterization of the SVD of a multibody fundamental m...

We use conference matrices to define an action of the complex numbers on the real Euclidean vector space R. In certain cases, the lattice D n becomes a module over a ring of quadratic integers. We can then obtain new unimodular lattices, essentially by multiplying the lattice D n by a non-principal ideal in this ring. We show that lattices constructed via quadratic residue codes, including the ...