Determination of cellular neural networks parameters for feature detection of two-dimensional images

2002 ◽  
Author(s):  
K. Slot
Keyword(s):  
Neural Networks ◽  
Feature Detection ◽  
Cellular Neural Networks ◽  
Two Dimensional ◽  
Two Dimensional Images

scholarly journals Determination of hard X-ray polarization from two-dimensional images

2020 ◽  
Vol 53 (6) ◽  
pp. 1559-1561
Author(s):  
Robert B. Von Dreele ◽  
Wenqian Xu
Keyword(s):  
Incident Beam ◽  
Beam Polarization ◽  
Two Dimensional ◽  
One Dimensional ◽  
X Ray ◽  
Dimensional Image ◽  
Two Dimensional Image ◽  
The Difference ◽  
Two Dimensional Images

An estimate of synchrotron hard X-ray incident beam polarization is obtained by partial two-dimensional image masking followed by integration. With the correct polarization applied to each pixel in the image, the resulting one-dimensional pattern shows no discontinuities arising from the application of the mask. Minimization of the difference between the sums of the masked and unmasked powder patterns allows estimation of the polarization to ±0.001.

PIECEWISE TWO-DIMENSIONAL MAPS AND APPLICATIONS TO CELLULAR NEURAL NETWORKS

2004 ◽  
Vol 14 (07) ◽  
pp. 2223-2228 ◽  
Author(s):  
HSIN-MEI CHANG ◽  
JONG JUANG
Keyword(s):  
Neural Networks ◽  
Cellular Neural Networks ◽  
Two Dimensional ◽  
Smale Horseshoe ◽  
Linear Map ◽  
One Dimensional ◽  
Spatial Chaos

Of concern is a two-dimensional map T of the form T(x,y)=(y,F(y)-bx). Here F is a three-piece linear map. In this paper, we first prove a theorem which states that a semiconjugate condition for T implies the existence of Smale horseshoe. Second, the theorem is applied to show the spatial chaos of one-dimensional Cellular Neural Networks. We improve a result of Hsu [2000].

ON THE TEMPLATES CORRESPONDING TO CYCLE-SYMMETRIC CONNECTIVITY IN CELLULAR NEURAL NETWORKS

2002 ◽  
Vol 12 (12) ◽  
pp. 2957-2966 ◽  
Author(s):  
CHIH-WEN SHIH ◽  
CHIH-WEN WENG
Keyword(s):  
Neural Networks ◽  
Dimensional Space ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Necessary And Sufficient Conditions ◽  
Local Interaction ◽  
Two Dimensional ◽  
Linear Coupling ◽  
Symmetric Connectivity ◽  
Necessary And Sufficient

In the architecture of cellular neural networks (CNN), connections among cells are built on linear coupling laws. These laws are characterized by the so-called templates which express the local interaction weights among cells. Recently, the complete stability for CNN has been extended from symmetric connections to cycle-symmetric connections. In this presentation, we investigate a class of two-dimensional space-invariant templates. We find necessary and sufficient conditions for the class of templates to have cycle-symmetric connections. Complete stability for CNN with several interesting templates is thus concluded.

COMPLETE STABILITY FOR STANDARD CELLULAR NEURAL NETWORKS

1999 ◽  
Vol 09 (05) ◽  
pp. 909-918 ◽  
Author(s):  
SONG-SUN LIN ◽  
CHIH-WEN SHIH
Keyword(s):  
Neural Networks ◽  
Boundary Condition ◽  
Symmetric Space ◽  
Dirichlet Boundary Condition ◽  
Periodic Boundary ◽  
Dirichlet Boundary ◽  
Periodic Boundary Conditions ◽  
Cellular Neural Networks ◽  
Two Dimensional ◽  
Space Variant

We consider cellular neural networks with symmetric space-variant feedback template. The complete stability is proved via detailed analysis on the energy function. The proof is presented for the two-dimensional case with Dirichlet boundary condition. It can be extended to other dimensions with minor adjustments. Modifications to the cases of Neumann and periodic boundary conditions are also mentioned.

SMALE HORSESHOE OF CELLULAR NEURAL NETWORKS

2000 ◽  
Vol 10 (09) ◽  
pp. 2119-2127 ◽  
Author(s):  
CHENG-HSIUNG HSU
Keyword(s):  
Neural Networks ◽  
Cellular Neural Networks ◽  
Two Dimensional ◽  
Smale Horseshoe ◽  
One Dimensional

The paper shows the spatial disorder of one-dimensional Cellular Neural Networks (CNN) using the iteration map method. Under certain parameters, the map is two-dimensional and the Smale horseshoe is constructed. Moreover, we also illustrate the variant of CNN, closely related to Henón-type and Belykh maps, and discrete Allen–Cahn equations.

ON THE SPATIAL ENTROPY AND PATTERNS OF TWO-DIMENSIONAL CELLULAR NEURAL NETWORKS

2002 ◽  
Vol 12 (01) ◽  
pp. 115-128 ◽  
Author(s):  
SONG-SUN LIN ◽  
TZI-SHENG YANG
Keyword(s):  
Neural Networks ◽  
Growth Rate ◽  
Lower Bound ◽  
Finite Lattice ◽  
Cellular Neural Networks ◽  
Exponential Growth Rate ◽  
Two Dimensional ◽  
Spatial Entropy ◽  
Global Patterns ◽  
Pattern Formations

This work investigates binary pattern formations of two-dimensional standard cellular neural networks (CNN) as well as the complexity of the binary patterns. The complexity is measured by the exponential growth rate in which the patterns grow as the size of the lattice increases, i.e. spatial entropy. We propose an algorithm to generate the patterns in the finite lattice for general two-dimensional CNN. For the simplest two-dimensional template, the parameter space is split up into finitely many regions which give rise to different binary patterns. Qualitatively, the global patterns are classified for each region. Quantitatively, the upper bound of the spatial entropy is estimated by computing the number of patterns in the finite lattice, and the lower bound is given by observing a maximal set of patterns of a suitable size which can be adjacent to each other.

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