Fast estimation of fundamental matrix based on stripe constraints

In order to improve the performance of estimating the fundamental matrix, a key problem arising in stereo vision, a novel method based on stripe constraints is presented. In contrast to traditional methods based on algebraic least-square algorithms, the proposed approach aims to minimize a cost function that is derived from the minimum radius of the Hough transform. In a structured-light system with a particular stripe code pattern, there are linear constraints that the points with the same code are on the same surface. Using the Hough transform, the pixels with the same code map to the Hough space, and the radius of the intersections can be defined as the evaluation function in the optimization progress. The global optimum solution of the fundamental matrix can be estimated using a Levenberg- Marquardt optimization iterative process based on the Hough transform radius. Results illustrate the validity of this algorithm, and prove that this method can obtain good performance with high efficiency.

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.

Strong stability of an optimal control hybrid system in fed-batch fermentation

In this paper, we consider a nonlinear hybrid dynamic （NHD） system to describe fedbatch culture where there is no analytical solutions and no equilibrium points. Our goal is to prove the strong stability with respect to initial state for the NHD system. To this end, we construct corresponding linear variational system （LVS） for the solution of the NHD system, also prove the boundedness of fundamental matrix solutions for the LVS. On this basis, the strong stability is proved by such boundedness.