Hopfield network for stereo vision correspondence

An optimization approach is used to solve the correspondence problem for a set of features extracted from a pair of stereo images. A cost function is defined to represent the constraints on the solution, which is then mapped onto a two-dimensional Hopfield neural network for minimization. Each neuron in the network represents a possible match between a feature in the left image and one in the right image. Correspondence is achieved by initializing (exciting) each neuron that represents a possible match and then allowing the network to settle down into a stable state. The network uses the initial inputs and the compatibility measures between the matched points to find a stable state.     

Liver stereoscopic visualisation by using Hopfield neural nets

Three dimensional visualisation techniques have been used as a powerful tool in surgical and therapeutic applications. Due to large medical data, huge computations are necessary on 3D visualisation, especially for a real-time system. Many existing methods are sequential, which are too slow to be practical in real applications. In our previous work, we showed boundary detection and feature points extraction by using Hopfield networks. In this paper, a new feature points matching method for 3D surfaces using a Hopfield neural network is proposed. Taking advantage of parallel and energy convergence capabilities in the Hopfield networks, this method is faster and more stable for feature points matching. Stereoscopic visualisation is the display result of our system. With stereoscopic visualisation, the 3D liver used in the experiment can leap out of the screen in true 3D stereoscopic depth. This increases a doctor's ability to analyse complex graphics.     

Line segment matching for 3D computer vision using a new iteration scheme

A new iteration scheme is proposed to solve the line segment matching problem in stereo vision analysis. A match function which directly reflects the requirements of the epipolar and disparity constraints is proposed for line segment matching. The information contained in the match function is used to determine line segment correspondences indirectly. After a match network is established according to the match function values, a new iteration algorithm is employed to tune the strengths of the match links in the match network so that the match network can converge to a stable state. No explicit compatibility coefficient need be defined for computing the support function values in the iterations, resulting in a faster computation speed than those of conventional relaxation matching techniques. The inherent anti-symmetric characteristic of relaxation matching for the image correspondence problem is also avoided naturally. The experimental results show that the proposed iteration scheme is effective and suitable for matching line segments even when images are complicated.     

Development of neurofuzzy architecture for solving the N-Queens problem

Neural networks are dynamic systems consisting of highly interconnected and parallel nonlinear processing elements that are shown to be extremely effective in computation. This paper presents an architecture of recurrent neural networks for solving the N-Queens problem. More specifically, a modified Hopfield network is developed and its internal parameters are explicitly computed using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points, which represent a solution of the considered problem. The network is shown to be completely stable and globally convergent to the solutions of the N-Queens problem. A fuzzy logic controller is also incorporated in the network to minimize convergence time. Simulation results are presented to validate the proposed approach.     

Fuzzy Cognitive Maps for stereovision matching

This paper outlines a method for solving the stereovision matching problem using edge segments as the primitives. In stereovision matching the following constraints are commonly used: epipolar, similarity, smoothness, ordering and uniqueness. We propose a new matching strategy under a fuzzy context in which such constraints are mapped. The fuzzy context integrates both Fuzzy Clustering and Fuzzy Cognitive Maps. With such purpose a network of concepts (nodes) is designed, each concept represents a pair of primitives to be matched. Each concept has associated a fuzzy value which determines the degree of the correspondence. The goal is to achieve high performance in terms of correct matches. The main findings of this paper are reflected in the use of the fuzzy context that allows building the network of concepts where the matching constraints are mapped. Initially, each concept value is loaded via the Fuzzy Clustering and then updated by the Fuzzy Cognitive Maps framework. This updating is achieved through the influence of the remainder neighboring concepts until a good global matching solution is achieved. Under this fuzzy approach we gain quantitative and qualitative matching correspondences. This method works as a relaxation matching approach and its performance is illustrated by comparative analysis against some existing global matching methods.     

The Hopfield neural network applied to the Quadratic Assignment Problem

The Hopfield neural network is proposed as a method for solving the Quadratic Assignment Problem. The study involves determining the relevant parameter constraints, and provides a comparison of the performance of the Hopfield model with that of a conventional approach.     

On the complexity of distributed stable matching with small messages

We consider the distributed complexity of the stable matching problem (a.k.a. “stable marriage”). In this problem, the communication graph is undirected and bipartite, and each node ranks its neighbors. Given a matching of the nodes, a pair of unmatched nodes is called blocking if they prefer each other to their assigned match. A matching is called stable if it does not induce any blocking pair. In the distributed model, nodes exchange messages in each round over the communication links, until they find a stable matching. We show that if messages may contain at most B bits each, then any distributed algorithm that solves the stable matching problem requires ${\Omega(\sqrt{n/B\log n})}We consider the distributed complexity of the stable matching problem (a.k.a. “stable marriage”). In this problem, the communication graph is undirected and bipartite, and each node ranks its neighbors. Given a matching of the nodes, a pair of unmatched nodes is called blocking if they prefer each other to their assigned match. A matching is called stable if it does not induce any blocking pair. In the distributed model, nodes exchange messages in each round over the communication links, until they find a stable matching. We show that if messages may contain at most B bits each, then any distributed algorithm that solves the stable matching problem requires W(?{n/Blogn}){\Omega(\sqrt{n/B\log n})} communication rounds in the worst case, even for graphs of diameter O(log n), where n is the number of nodes in the graph. Furthermore, the lower bound holds even if we allow the output to contain O(?n){O(\sqrt n)} blocking pairs, and if a pair is considered blocking only if they like each other much more then their assigned match.     

Parallel stereocorrelation on a reconfigurable multi-ring network

A reconfigurable network termed as the reconfigurable multi-ring network (RMRN) is described. The RMRN is shown to be a truly scalable network in that each node in the network has a fixed degree of connectivity and the reconfiguration mechanism ensures a network diameter of O(log₂ N) for anN-processor network. Algorithms for the two-dimensional mesh and the SIMD or SPMD n-cube are shown to map very elegantly onto the RMRN. Basic message passing and reconfiguration primitives for the SIMD/SPMD RMRN are designed for use as building blocks for more complex parallel algorithms. The RMRN is shown to be a viable architecture for image processing and computer vision problems using the parallel computation of the stereocorrelation imaging operation as an example. Stereocorrelation is one of the most computationally intensive imaging tasks. It is used as a visualization tool in many applications, including remote sensing, geographic information systems and robot vision.An earlier version of this paper was presented at the 1995 International Conference on Parallel and Distributed Processing Techniques and Applications.     

离散时间Hopfield网络的动力系统分析

离散时间的Hopfield网络模型是一个非线性动力系统．对网络的状态变量引入新的能量函数，利用凸函数次梯度性质可以得到网络状态能量单调减少的条件．对于神经元的连接权值且激活函数单调非减(不一定严格单调增加)的Hopfield网络，若神经元激活函数的增益大于权值矩阵的最小特征值，则全并行时渐进收敛；而当网络串行时，只要网络中每个神经元激活函数的增益与该神经元的自反馈连接权值的和大于零即可．同时，若神经元激活函数单调，网络连接权值对称，利用凸函数次梯度的性质，证明了离散时间的Hopfield网络模型全并行时收敛到周期不大于2的极限环．     

A higher order Hopfield network for vector quantisation

A higher order version of the Hopfield neural network is presented which will perform a simple vector quantisation or clustering function. This model requires no penalty terms to impose constraints in the Hopfield energy, in contrast to the usual one where the energy involves only terms quadratic in the state vector. The energy function is shown to have no local minima within the unit hypercube of the state vector so the network only converges to valid final states. Optimisation trials show that the network can consistently find optimal clusterings for small, trial problems and near optimal ones for a large data set consisting of the intensity values from a digitised, grey- level image.     

H2 norm accumulation and its impact on synchronisation of complex dynamical networks

This article addresses the H ₂ norm accumulation problem of linearly coupled dynamical networks. An interesting outer-coupling relationship is constructed, under which the H ₂ norm of the newly constructed network with column-input and row-output matrices increases exponentially fast in terms of the node number N: it increases generally much faster than 2 ^N when N is large while the H ₂ norm of each node is 1. However, the H ₂ norm of the network with a diffusive coupling is equal to γ₂ N, i.e. increasing only linearly, when the network is stable, where γ₂ is the H ₂ norm of a single node. And the H ₂ norm of the network with antisymmetrical coupling also increases, but rather slowly, with respect to the node number N. Other networks with block-diagonal-input and block-diagonal-output matrices behave similarly. It demonstrates that the changes of H ₂ norms in different networks are very complicated, despite the fact that the network structures are linear. Finally, the influence of the H ₂ norm of the locally linearised network on the output of a network with Lur'e node dynamics is discussed, demonstrating a significant effect of the H ₂ norm on the network output synchronisation behaviours.     

用神经网络求解机器人动态调度中的近似指派问题

本文利用HOPFIELD神经网络，对机器人动态调度中的近似指派问题提出了合理的神经网络表示方法，给出了网络的能量函数表示法及神经元状态方程，从而得出了机器人动态调度中近似指派问题的快速求解策略，满足了动态调度的实时性要求．本文从理论上论证了所提算法的收敛性．软件仿真结果表明，本文提出的近似指派问题网络求解方法是有效的，计算结果是满意的．     

A 3.4 dB NF k‐band LNA with a tapped capacitor matching network in 65 nm CMOS technology

This article proposes a tapped capacitor network for low‐noise amplifier (LNA) input matching which can provide much broader bandwidth than traditional ones. According to the design, the implemented LNA can realize noise match and power match simultaneously, which will broaden LNA's bandwidth without introducing larger noise than traditional ones. In addition, input pad parasitic capacitance can be absorbed by the network. Then a k‐band LNA with the matching network designed in 65 nm CMOS technology is shown to demonstrate the performance of the matching network. The tested results show that frequency band of S₁₁ less than ?10 dB is about 17 GHz and minimum NF is about 3.4 dB. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:146–153, 2015.     

A Maximum Likelihood Stereo Algorithm

A stereo algorithm is presented that optimizes a maximum likelihood cost function. The maximum likelihood cost function assumes that corresponding features in the left and right images are normally distributed about a common true value and consists of a weighted squared error term if two features are matched or a (fixed) cost if a feature is determined to be occluded. The stereo algorithm finds the set of correspondences that maximize the cost function subject to ordering and uniqueness constraints. The stereo algorithm is independent of the matching primitives. However, for the experiments described in this paper, matching is performed on the $cf4$individual pixel intensities.$cf3$ Contrary to popular belief, the pixel-based stereo appears to be robust for a variety of images. It also has the advantages of (i) providing adensedisparity map, (ii) requiringnofeature extraction, and (iii)avoidingthe adaptive windowing problem of area-based correlation methods. Because feature extraction and windowing are unnecessary, a very fast implementation is possible. Experimental results reveal that good stereo correspondences can be found using only ordering and uniqueness constraints, i.e., withoutlocalsmoothness constraints. However, it is shown that the original maximum likelihood stereo algorithm exhibits multiple global minima. The dynamic programming algorithm is guaranteed to find one, but not necessarily the same one for each epipolar scanline, causing erroneous correspondences which are visible as small local differences between neighboring scanlines. Traditionally, regularization, which modifies the original cost function, has been applied to the problem of multiple global minima. We developed several variants of the algorithm that avoid classical regularization while imposing several global cohesiveness constraints. We believe this is a novel approach that has the advantage of guaranteeing that solutions minimize the original cost function and preserve discontinuities. The constraints are based on minimizing the total number of horizontal and/or vertical discontinuities along and/or between adjacent epipolar lines, and local smoothing is avoided. Experiments reveal that minimizing the sum of the horizontal and vertical discontinuities provides the most accurate results. A high percentage of correct matches and very little smearing of depth discontinuities are obtained. An alternative to imposing cohesiveness constraints to reduce the correspondence ambiguities is to use more than two cameras. We therefore extend the two camera maximum likelihood toNcameras. TheN-camera stereo algorithm determines the “best” set of correspondences between a given pair of cameras, referred to as the principal cameras. Knowledge of the relative positions of the cameras allows the 3D point hypothesized by an assumed correspondence of two features in the principal pair to be projected onto the image plane of the remainingN− 2 cameras. TheseN− 2 points are then used to verify proposed matches. Not only does the algorithm explicitly model occlusion between features of the principal pair, but the possibility of occlusions in theN− 2 additional views is also modeled. Previous work did not model this occlusion process, the benefits and importance of which are experimentally verified. Like other multiframe stereo algorithms, the computational and memory costs of this approach increase linearly with each additional view. Experimental results are shown for two outdoor scenes. It is clearly demonstrated that the number of correspondence errors is significantly reduced as the number of views/cameras is increased.     

Right,left characteristic sequences and column,row minimal indices of a singular pencil

For a general singular pencil sF — G?? ^m×n [s] the right, left characteristic sequences _r(F, G), _l(F, G) are defined and they are shown to be of the piecewise arithmetic progression type. The sets of column, row minimal indices ?_c(F, G), ?_r(F, G) are defined by a singular points analysis of _r(F, G), ?_l(F, G) respectively. Thus, ?_c(F, G), ?_r(F, G) emerge as numerical invariants of the ordered pair (F, G) and they may be computed by rank tests on Toeplitz matrices defined on (F, G).     

Understanding the Generalized Median Stable Matchings

Let I be a stable matching instance with N stable matchings. For each man m, order his (not necessarily distinct) N partners from his most preferred to his least preferred. Denote the ith woman in his sorted list as p _i (m). Let α _i consist of the man-woman pairs where each man m is matched to p _i (m). Teo and Sethuraman proved this surprising result: for i=1 to N, not only is α _i a matching, it is also stable. The α _i ’s are called the generalized median stable matchings of I. Determining if these stable matchings can be computed efficiently is an open problem.     

用改进的差分式Hopfield网络实现线性二次型最优控制

为解决差分式Hopfield网络能量函数的局部极小问题,本文对之改进得到一种具有迭代学习功能的线性差分式Hopfield网络.理论分析表明,该网络具有稳定性,且稳定状态使其能量函数达到唯一极小值.基于线性差分式Hopfield网络稳定性与其能量函数收敛特性的关系,本文将该网络用于求解多变量时变系统的线性二次型最优控制问题.网络的理论设计方法表明,网络的稳态输出就是欲求的最优控制向量.数字仿真取得了与理论分析一致的实验结果.     

Optimal horizons for a one-parameter family of unbiased FIR filters

In this paper, we find the optimal horizons and sampling intervals, both in the sense of the minimum mean square error (MSE), for a one-parameter family of the discrete-time unbiased finite impulse response (FIR) filters. On a horizon of N_l points in the nearest past, the FIR and the model k-state are represented with the l-degree and m-degree polynomials, respectively. The noise-free state space model is observed in the presence of zero-mean noise of an arbitrary distribution and covariance. The approach is based on the following. The FIR filter produces an unbiased estimate if lm. In order to reduce the noise, N_l needs to be increased. The model fits the increased horizon with a higher degree polynomial, m>l. Minimization of the mean square error for m>l gives the optimal horizon and sampling interval. Justification is provided for the global positioning system (GPS)-based measurements of the first state of a local crystal clock provided in the presence of uniformly distributed sawtooth noise induced by the GPS timing receiver.     

Associative Memory Design via Path Embedding into a Graph

A graph theoretical procedure for storing a set of n-dimensional binary vectors as asymptotically stable equilibrium points of a discrete Hopfield neural network is presented. The method gives an auto-associative memory which stores an arbitrary memory set completely. Spurious memories might occur only in a small neighborhood of the original memory vectors, so cause small errors.     

Hopfield network with constraint parameter adaptation foroverlapped shape recognition

We propose an energy formulation for homomorphic graph matching by the Hopfield network and a Lyapunov indirect method-based learning approach to adaptively learn the constraint parameter in the energy function. The adaptation scheme eliminates the need to specify the constraint parameter empirically and generates valid and better quality mappings than the analog Hopfield network with a fixed constraint parameter. The proposed Hopfield network with constraint parameter adaptation is applied to match silhouette images of keys and results are presented.