Motion Estimation by Direct Minimisation of the Energy Function of the Hopfield Neural Network

1996 ◽  
pp. 443-446
Author(s):  
Leszek Ciepliński ◽  
Czesław Jcedrzejek
Keyword(s):  
Neural Network ◽  
Motion Estimation ◽  
Energy Function ◽  
Hopfield Neural Network

scholarly journals BOUNDARY DEPTH INFORMATION USING HOPFIELD NEURAL NETWORK

2016 ◽  
Vol XLI-B5 ◽  
pp. 139-146
Author(s):  
Sheng Xu ◽  
Ruisheng Wang
Keyword(s):  
Neural Network ◽  
Energy Function ◽  
Stereo Matching ◽  
Boundary Energy ◽  
Region Of Interest ◽  
Hopfield Neural Network ◽  
Depth Information ◽  
Matching Methods ◽  
The Difference ◽  
Smoothness Term

Depth information is widely used for representation, reconstruction and modeling of 3D scene. Generally two kinds of methods can obtain the depth information. One is to use the distance cues from the depth camera, but the results heavily depend on the device, and the accuracy is degraded greatly when the distance from the object is increased. The other one uses the binocular cues from the matching to obtain the depth information. It is more and more mature and convenient to collect the depth information of different scenes by stereo matching methods. In the objective function, the data term is to ensure that the difference between the matched pixels is small, and the smoothness term is to smooth the neighbors with different disparities. Nonetheless, the smoothness term blurs the boundary depth information of the object which becomes the bottleneck of the stereo matching. This paper proposes a novel energy function for the boundary to keep the discontinuities and uses the Hopfield neural network to solve the optimization. We first extract the region of interest areas which are the boundary pixels in original images. Then, we develop the boundary energy function to calculate the matching cost. At last, we solve the optimization globally by the Hopfield neural network. The Middlebury stereo benchmark is used to test the proposed method, and results show that our boundary depth information is more accurate than other state-of-the-art methods and can be used to optimize the results of other stereo matching methods.

Hopfield Neural Network for Motion Estimation and Interpretation

ICANN ’94 ◽  
1994 ◽  
pp. 78-81 ◽  
Author(s):  
G. Convertino ◽  
M. Brattoli ◽  
A. Distante
Keyword(s):  
Neural Network ◽  
Motion Estimation ◽  
Hopfield Neural Network

Study of Reconfiguration Algorithm in Distribution System Based on Hopfield Network

2012 ◽  
Vol 241-244 ◽  
pp. 1900-1903
Author(s):  
Na Wei ◽  
Zhe Cheng ◽  
Xiao Meng Wu
Keyword(s):  
Neural Network ◽  
Energy Function ◽  
Distribution System ◽  
Distribution Network ◽  
Hopfield Neural Network ◽  
Hopfield Network ◽  
Network Reconfiguration ◽  
Power Sources ◽  
Distribution Network Reconfiguration ◽  
The Neural Network

In accordance with the characteristic of radial running an algorithm for distribution network reconfiguration based on Hopfield neural network is put forward. The in-degree of each node is determined by Hopfield neural network, it is determined whether the lines run according to the in-degree of the nodes, and the state of each loop switch is determined according to whether the lines run, and thus the distribution network reconfiguration scheme is determined finally. The energy function of the neural network and its solution method are presented. In the energy function are considered the radial running of distribution network, the lowest distribution network loss and no loop switch in some lines. The IEEE distribution network structure with three power sources obtained by the algorithm is basically consistent to that obtained by genetic algorithm, but the time spent using the former is shorter than that the latter.

scholarly journals BOUNDARY DEPTH INFORMATION USING HOPFIELD NEURAL NETWORK

2016 ◽  
Vol XLI-B5 ◽  
pp. 139-146
Author(s):  
Sheng Xu ◽  
Ruisheng Wang
Keyword(s):  
Neural Network ◽  
Energy Function ◽  
Stereo Matching ◽  
Boundary Energy ◽  
Region Of Interest ◽  
Hopfield Neural Network ◽  
Depth Information ◽  
Matching Methods ◽  
The Difference ◽  
Smoothness Term

Depth information is widely used for representation, reconstruction and modeling of 3D scene. Generally two kinds of methods can obtain the depth information. One is to use the distance cues from the depth camera, but the results heavily depend on the device, and the accuracy is degraded greatly when the distance from the object is increased. The other one uses the binocular cues from the matching to obtain the depth information. It is more and more mature and convenient to collect the depth information of different scenes by stereo matching methods. In the objective function, the data term is to ensure that the difference between the matched pixels is small, and the smoothness term is to smooth the neighbors with different disparities. Nonetheless, the smoothness term blurs the boundary depth information of the object which becomes the bottleneck of the stereo matching. This paper proposes a novel energy function for the boundary to keep the discontinuities and uses the Hopfield neural network to solve the optimization. We first extract the region of interest areas which are the boundary pixels in original images. Then, we develop the boundary energy function to calculate the matching cost. At last, we solve the optimization globally by the Hopfield neural network. The Middlebury stereo benchmark is used to test the proposed method, and results show that our boundary depth information is more accurate than other state-of-the-art methods and can be used to optimize the results of other stereo matching methods.

A GENERAL UPDATING RULE FOR DISCRETE HOPFIELD-TYPE NEURAL NETWORK WITH TIME-DELAY AND THE CORRESPONDING SEARCH ALGORITHM

2001 ◽  
Vol 01 (04) ◽  
pp. 399-412 ◽  
Author(s):  
DANIEL S. YEUNG ◽  
SHENSHAN QIU ◽  
ERIC C. C. TSANG ◽  
XIZHAO WANG
Keyword(s):  
Neural Network ◽  
Convergence Rate ◽  
Energy Function ◽  
Optimization Problems ◽  
Local Maximum ◽  
Hopfield Neural Network ◽  
Connection Matrix ◽  
High Convergence Rate ◽  
Updating Rule ◽  
Step Algorithm

In this paper, the Hopfield neural network with delay (HNND) is studied from the standpoint of regarding it as an optimizing computational model. Two general updating rules for networks with delay (GURD) are given based on Hopfield-type neural networks with delay for optimization problems and characterized by dynamic thresholds. It is proved that in any sequence of updating rule modes, the GURD monotonously converges to a stable state of the network. The diagonal elements of the connection matrix are shown to have an important influence on the convergence process, and they represent the relationship of the local maximum value of the energy function to the stable states of the networks. All the ordinary discrete Hopfield neural network (DHNN) algorithms are instances of the GURD. It can be shown that the convergence conditions of the GURD may be relaxed in the context of applications, for instance, the condition of nonnegative diagonal elements of the connection matrix can be removed from the original convergence theorem. A new updating rule mode and restrictive conditions can guarantee the network to achieve a local maximum of the energy function with a step-by-step algorithm. The convergence rate improves evidently when compared with other methods. For a delay item considered as a noise disturbance item, the step-by-step algorithm demonstrates its efficiency and a high convergence rate. Experimental results support our proposed algorithm.

ASSOCIATIVE MEMORY IN QUATERNIONIC HOPFIELD NEURAL NETWORK

2008 ◽  
Vol 18 (02) ◽  
pp. 135-145 ◽  
Author(s):  
TEIJIRO ISOKAWA ◽  
HARUHIKO NISHIMURA ◽  
NAOTAKE KAMIURA ◽  
NOBUYUKI MATSUI
Keyword(s):  
Neural Network ◽  
Associative Memory ◽  
Energy Function ◽  
Hopfield Neural Network ◽  
Input Output ◽  
Stable States ◽  
Hypercomplex Number ◽  
Number Systems

Associative memory networks based on quaternionic Hopfield neural network are investigated in this paper. These networks are composed of quaternionic neurons, and input, output, threshold, and connection weights are represented in quaternions, which is a class of hypercomplex number systems. The energy function of the network and the Hebbian rule for embedding patterns are introduced. The stable states and their basins are explored for the networks with three neurons and four neurons. It is clarified that there exist at most 16 stable states, called multiplet components, as the degenerated stored patterns, and each of these states has its basin in the quaternionic networks.

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