Self-calibration of hybrid central catadioptric and perspective cameras

Hybrid central catadioptric and perspective cameras are desired in practice, because the hybrid camera system can capture large field of view as well as high-resolution images. However, the calibration of the system is challenging due to heavy distortions in catadioptric cameras. In addition, previous calibration methods are only suitable for the camera system consisting of perspective cameras and catadioptric cameras with only parabolic mirrors, in which priors about the intrinsic parameters of perspective cameras are required. In this work, we provide a new approach to handle the problems. We show that if the hybrid camera system consists of at least two central catadioptric and one perspective cameras, both the intrinsic and extrinsic parameters of the system can be calibrated linearly without priors about intrinsic parameters of the perspective cameras, and the supported central catadioptric cameras of our method can be more generic. In this work, an approximated polynomial model is derived and used for rectification of catadioptric image. Firstly, with the epipolar geometry between the perspective and rectified catadioptric images, the distortion parameters of the polynomial model can be estimated linearly. Then a new method is proposed to estimate the intrinsic parameters of a central catadioptric camera with the parameters in the polynomial model, and hence the catadioptric cameras can be calibrated. Finally, a linear self-calibration method for the hybrid system is given with the calibrated catadioptric cameras. The main advantage of our method is that it cannot only calibrate both the intrinsic and extrinsic parameters of the hybrid camera system, but also simplify a traditional nonlinear self-calibration of perspective cameras to a linear process. Experiments show that our proposed method is robust and reliable.     

Calibrating effective focal length for central catadioptric cameras using one space line

In camera calibration, focal length is the most important parameter to be estimated, while other parameters can be obtained by prior information about scene or system configuration. In this paper, we present a polynomial constraint on the effective focal length with the condition that all the other parameters are known. The polynomial degree is 4 for paracatadioptric cameras and 16 for other catadioptric cameras. However, if the skew is 0 or the ratio between the skew and effective focal length is known, the constraint becomes a linear one or a polynomial one with degree 4 on the effective focal length square for paracatadioptric cameras and other catadioptric cameras, respectively. Based on this constraint, we propose a simple method for estimation of the effective focal length of central catadioptric cameras. Unlike many approaches using lines in literature, the proposed method needs no conic fitting of line images, which is error-prone and highly affects the calibration accuracy. It is easy to implement, and only a single view of one space line is enough with no other space information needed. Experiments on simulated and real data show this method is robust and effective.     

A new algorithm for linear system identification

This correspondence considers the on-line parameter identification of a forced linear discrete-time dynamic system from a sequence of white-noise-corrupted output measurements. In contrast to other approaches, the proposed stochastic approximation algorithm does not require knowledge of the noise statistics and converges to the true value of the parameters in the mean-square sense. If the input measurements are also corrupted with white noise, an additional term depending on the variance of the noise is required.     

A new linear algorithm for triangulating monotone polygons

Let P = (p₁, p₂,…,p_n) be a monotone polygon whose vertices are specified in terms of cartesian coordinates in order. A new simple two-step procedure is presented for triangulating P, without the addition of new vertices, in O(n) time. Unlike the previous algorithm no specialized code is needed since the new approach uses well-known existing algorithms for first decomposing P into edge-visible polygons and subsequently triangulating these.     

On calibrating computer controlled cameras for perceiving 3-D scenes

A problem that arises is getting computers to perceive 3-D scenes is relating information from several different viewpoints. In particular, if the computer moves its sensor, it has to be able to predict changes in images of objects it has seen without having to completely re-recognize them. A solution to this problem has been implemented at Stanford using a calibrated camera model which expresses the relation between object space and image space as a function of the computer's control variables. The modelling problem is relatively well understood. Calibration techniques, however, are not. This article deals with these.     

A new algorithm for state estimation of stochastic linear discretesystems

A novel algorithm is proposed for state estimation of linear discrete-time systems. The procedure performs explicit minimization of the innovation variance and is based upon the principle of pseudo linear regression (PLR) method. Sufficient conditions for algorithm convergence are also derived     

A new algorithm for solving nearly penta-diagonal Toeplitz linear systems

A new numerical algorithm for solving nearly penta-diagonal Toeplitz linear systems is presented. The algorithm is suited for implementation using Computer Algebra Systems (CASs) such as MATLAB, MACSYMA and MAPLE. Numerical examples are given in order to illustrate the efficiency of our algorithm.     

A new robust adaptive control algorithm for linear time-varying plants

Robustness is an important property of a control system. Robust adaptive control has been an active research area for more than a decade. Since it was shown that un-modelled dynamics or even a small bounded disturbance can cause most adaptive control algorithms to go unstable, various modifications of the adaptive control algorithms have been developed to counteract instability and improve robustness with respect to unmodelled dynamics and bounded disturbances. However, we know that most of the modified approaches to achieve robustness require knowledge of either the parameter of bounding function on the unmodelled dynamics, or the upper bound on the disturbances, or the bound on the norm of unknown matching controller/plant parameters, and such knowledge can hardly be obtained in practice. A new indirect adaptive control algorithm for linear time-varying plants is proposed to achieve robustness to a class of unmodelled dynamics, bounded disturbances and plant parameter time variations. A modified relative dead zone technique is used, so that knowledge of the parameters of the upper bounding function on the unmodelled dynamics and the disturbances is not required. The stability analysis and the robust performance of adoptively controlled time-varying systems are provided for the new scheme. A simulation example is given to show the effectiveness of the proposed algorithm.     

A pole-assignment algorithm for linear state feedback

A new algorithm for the pole-assignment problem of a controllable time-invariant linear multivariable system with linear state feedback is presented. The resulting feedback matrix is a least-squares solution and is robust in a loose sense. The method is based on the controllability canonical (staircase) form and amounts to a new proof for the existence of a solution of the pole-assignment problem. Illustrative examples are given.     

A fast algorithm for clusterwise linear regression

A fast implementation of a formerly [5] published algorithm is given.     

无重叠视域多摄像机的数据关联算法

大范围的监控通常会用到多个没有重叠视域的摄像机,目标的出现在时间和空间上都是离散的,摄像机间的目标关联是实现大范围的目标跟踪的关键问题.提出一种基于权重二部图的关联策略,以目标为节点,结合时间约束和空间约束构造边,目标的相似度为边的权重,通过求取二部图的最大权匹配得到最优关联结果.针对刚体目标提出一种LICS特征用于计算目标间的相似度,该特征对光照和目标姿态变化都不敏感.采用真实视频和仿真方法对算法进行实验,实验结果表明有好的关联效果.     

一种应用于煤矿井下线型WSN的时间同步算法

针对煤矿井下线型网络结构的特殊性及传统TPSN算法存在线型网络末端节点同步误差比较大的问题,提出了基于分簇结构的线型WSN时间同步算法。该算法以传统分簇算法为基础,运用时钟漂移补偿、异常数据过滤技术,降低了网络的时间同步误差,同时平衡了整个网络的能量损耗。仿真结果证明了该算法的正确性。     

A hybrid direction algorithm for solving linear programs

In this paper we suggest a new ascent direction for the adaptive method developed by Gabasov et al. (A method of solving general linear programming problems, Doklady AN BSSR 23(3) (1979), pp. 197–200 (in Russian)) for solving linear programs with bounded variables. A quantity called optimality estimate is defined, necessary and sufficient conditions of optimality based on this estimate are derived. An algorithm called the adaptive method with hybrid direction (AMHD) is suggested and a numerical example is given for illustration purpose. In order to compare the suggested algorithm with the classical primal simplex algorithm employing Dantzig's rule (PSA), we have developed a numerical implementation under the MATLAB programming language. The experimental study involves the CPU time and the iterations number of the two algorithms applied to solve randomly generated test problems of different dimensions. It has been shown that when the problem dimension increases, the superiority of AMHD over primal simplex algorithm increases.     

A simple linear algorithm for intersecting convex polygons

LetP andQ be two convex polygons withm andn vertices, respectively, which are specified by their cartesian coordinates in order. A simpleO(m+n) algorithm is presented for computing the intersection ofP andQ. Unlike previous algorithms, the new algorithm consists of a two-step combination of two simple algorithms for finding convex hulls and triangulations of polygons.     

A simple linear hidden-line algorithm for star-shaped polygons

A very simple, linear-running-time algorithm is presented for solving the hidden-line problem for star-shaped polygons. The algorithm first decomposes the visibility regions into edge-visible polygons and then solves the hidden-line problem for these simpler polygons. In addition to simplicity the algorithm possesses the virtue of affording a very easy proof of correctness. Some applications where this problem arises are mentioned.     

A simple linear algorithm for intersecting convex polygons

LetP andQ be two convex polygons withm andn vertices, respectively, which are specified by their cartesian coordinates in order. A simpleO(m+n) algorithm is presented for computing the intersection ofP andQ. Unlike previous algorithms, the new algorithm consists of a two-step combination of two simple algorithms for finding convex hulls and triangulations of polygons.     

A linear space algorithm for the LCS problem

Summary The LCS problem is to determine the longest common subsequence (LCS) of two strings. A new linear-space algorithm to solve the LCS problem is presented. The only other algorithm with linear-space complexity is by Hirschberg and has runtime complexity O(mn). Our algorithm, based on the divide and conquer technique, has runtime complexity O(n(m-p)), where p is the length of the LCS.     

A monotonic projective algorithm for fractional linear programming

We demonstrate that Karmarkar's projective algorithm is fundamentally an algorithm for fractional linear programming on the simplex. Convergence for the latter problem is established assuming only an initial lower bound on the optimal objective value. We also show that the algorithm can be easily modified so as to assure monotonicity of the true objective values, while retaining all global convergence properties. Finally, we show how the monotonic algorithm can be used to obtain an initial lower bound when none is otherwise available.     

A systolic algorithm for solving dense linear systems

For an arbitrary n × n matrix A and an n × 1 column vector b, we present a systolic algorithm to solve the dense linear equations Ax = b. An important consideration is that the pivot row can be changed during the execution of our systolic algorithm. The computational model consists of n linear systolic arrays. For 1 ≤ i ≤ n, the i^th linear array is responsible to eliminate the i^th unknown variable x_i of x. This algorithm requires 4n time steps to solve the linear system. The elapsed time unit within a time step is independent of the problem size n. Since the structure of a PE is simple and the same type PE executes the identical instructions, it is very suitable for VLSI implementation. The design process and correctness proof are considered in detail. Moreover, this algorithm can detect whether A is singular or not.