Feature matching based on geometric constraints in weakly calibrated stereo views of curved scenes

The identification of the correspondences of points of views is an important task. A new feature matching algorithm for weakly calibrated stereo images of curved scenes is proposed, based on mere geometric constraints. After initial correspondences are built via the epipolar constraint, many point-to-point image mappings called homographies are set up to predict the matching position for feature points. To refine the predictions and reject false correspondences, four schemes are proposed. Extensive experiments on simulated data as well as on real images of scenes of variant depths show that the proposed method is effective and robust.

A Note on Exact Solutions to Linear Differential Equations by the Matrix Exponential

It is known that the solution to a Cauchy problem of linear differential equations:x'(t)=A(t)x(t),with x(t0)=x0,can be presented by the matrix exponential as exp(∫_(t0)^(t)A(s)ds)x0,if the commutativity condition for the coefficient matrix A(t)holds:[∫_(t0)^(t)A(s)ds,A(t)]=0.A natural question is whether this is true without the commutativity condition.To give a definite answer to this question,we present two classes of illustrative examples of coefficient matrices,which satisfy the chain rule d/dt exp(∫_(t0)^(t)A(s)ds)=A(t)exp(∫_(t0)^(t)A(s)ds),but do not possess the commutativity condition.The presented matrices consist of finite-times continuously differentiable entries or smooth entries.

Degeneracy from Twisted Cubic Under Two Views

Fundamental matrix,drawing geometric relationship between two images,plays an important role in 3- dimensional computer vision.Degenerate configurations of the space points and the two camera optical centers affect stability of computation for fundamental matrix.In order to robustly estimate fundamental matrix,it is necessary to study these degenerate configurations.We analyze all the possible degenerate configurations caused by twisted cubic and give the corresponding degenerate rank for each case.Relationships with general degeneracies,the previous ruled quadric degeneracy and the homography degeneracy,are also reported.

Necessary exponential stability conditions for linear discrete time-delay systems and application

Necessary conditions for the exponential stability of the linear discrete time-delay systems are presented by employing the so-called Lyapunov–Krasovskii functional approach.These conditions not only provide a new tool for stability analysis of the linear discrete timedelay system by characterising instability domains,but also extend the existing results of the linear discrete time-delay system.Simultaneously,we investigate several crucial properties that connect the Lyapunov matrix and the fundamental matrix of the system.Finally,the robust stability analysis of the linear discrete time-delay systems with norm-bounded uncertainties is presented.Numerical examples illustrate the validity of the obtained results.