Real-time Reconstruction of Symmetrical Image using Cellular Neural Network

978-1-4244-2287-6/08/$25.00 ©2008 IEEE

Real-time Reconstruction of Symmetrical Image

using Cellular Neural Network

Pham Duc Long

Faculty of Information Technology

Thai Nguyen University

Thai Nguyen, Viet Nam

E-mail: [email protected]

Pham Thuong Cat

Institute of Information Technology

Vietnam Academy of Science and Technology

Ha Noi, Viet Nam

E-mail: [email protected].

Abstract: A real-time algorithm to reconstruct a 2D vertically

symmetrical image using a Cellular Neural Network (CNN) is

proposed in this paper. The processing speed of the proposed

algorithm on a CNN machine is much faster in comparison with

that of algorithms running serially on a traditional digital

computer. The proposed algorithm serves as a basic routine in

CNN algorithms’ Library or can be used to reconstruct damaged

or partially known 2D symmetrical images in real-time

applications. The algorithm is tested on some images with good

results.

Keywords—Cellular Neural Network, Symmetrical Image

Reconstruction.

I. INTRODUCTION

A. Image processing of symmetrical objects in a serial

digital computer

Image processing of symmetrical objects plays an

important role in many fields such as object recognition,

image compression, encryption and transmission.

In recent years, research in symmetrical features of objects

and in reconstructing their images have attracted much

attention from researchers. Serial digital computers are usually

used for these tasks. Image reconstruction based on

symmetrical features is often applied on both 2D and 3D

images. Algorithms for finding symmetrical features of

images, and reconstructing the original images using these

features on a serial digital computer are presented in many

papers [10, 11, 12, 13, 14, 15, and 16]. Other papers

addressing related topics include: a recovery of 3D textured

models from images [17], an extension of the normalized-cut

(n-cut) segmentation algorithm to find symmetrical regions

[18], a photo edition algorithm based on symmetrical images

[19], a parametric reconstruction of generalized cylinders from

limb edges [20]. These methods are usually difficult to

implement in real-time with serial processing computers like a

personal computer (PC).

B. Image processing on CNN Universal Machine

Cellular Neural Networks [1, 2] are lattices of cells

that are locally connected analogical processors. CNNs are

implemented in VLSI technology and perfectly suitable for

analog image processing. The operation of a cell at location

(i,j) is described by the following dimensionless equations:

x A y B u z

dt

dx

i j i j i j

i j = − , + ⊗ , + ⊗ , + ,

ij (1)

(| 1 | | 1|) 2

1 ( ) yi, j x = xi, j + − xi, j − . (2)

where ⊗ denotes a two-dimensional discrete spatial

convolution such that k l i k j l

k l N i j

i j A y A y − −

∈

⊗ = ∑ , ,

, ( , )

, for k and l in

the neighborhood N(i,j) of cell (i,j). When r = 1, the number of

neighboring cells is 8. Matrices A and B are respectively the

so-called feedback and feed forward weighting matrices, and zij

is the cell bias. ui,j, xi,j, yi,j are the input, internal state and

output of a cell (i,j), respectively. The same set of parameters

A, B and z, also known as the cloning template, is repeated

periodically for each cell over the whole network, which

implies a reduced set of at most 19 control parameters, but

nevertheless a large number of possible processing operations.

The template sets the state of a CNN circuit after a transient

process. When an array is loaded into the input of CNN, we

obtain an output array after approximately a few microseconds.

The outcome of output array depends solely on the templates,

the input array u, and the initial state of the internal array x.

These templates are designed by methodes in [3. 4, 5, 6]

The typical architecture of CNN-UM is composed of

CNN programmable arrays, sensor arrays and DSP devices.

CNN-UM is a focal plan machine where an image sensor is

integrated with a CNN array. DSP devices are reserved for

arithmetic operations. The combination CNN-DSPs make not

only performing algorithms more flexible, exploiting strong

points parallel processing of CNNs, but also reduce template

design and construction of algorithms. The future CNN-UMs

will have also similar heritable properties. Nowadays, a typical

CNN-UM Bi-I V2 has an architecture as shown in Figure 1.