Cellular neural networks and active contours: a tool for image segmentation

We describe a novel cellular connectionist neural network model for the implementation of clustering-based Bayesian image segmentation with Gibbs random-field spatial constraints. The success of this algorithm is largely due to the neighborhood constraints modeled by the Gibbs random field. However, the iterative enforcement of the neighborhood constraints involved in the Bayesian estimation would generally require tremendous computational power. Such computational requirement hinders the real-time application of the Bayesian image segmentation algorithms. The cellular connectionist model proposed aims at implementing the Bayesian image segmentation with real-time processing potentials. With a cellular neural network architecture mapped onto the image spatial domain, the powerful Gibbs spatial constraints are realized through the interactions among neurons connected through their spatial cellular layout. This network model is structurally similar to the conventional cellular network. However, in this new cellular model, the processing elements designed within the connectionist network are functionally more versatile to meet the challenging needs of Bayesian image segmentation based on the Gibbs random field. We prove that this cellular neural network does converge to the desired steady state with a properly designed update scheme. Examples of CT volumetric medical image segmentation are presented to demonstrate the potential of this cellular neural network for a specific image segmentation application.

The problem of segmentation of a given image using the active contour technique is considered. An abstract calculus to find appropriate speed functions for active contour models in image segmentation or related problems based on variational principles is presented. The speed method from shape sensitivity analysis is used to derive speed functions which correspond to gradient or Newton-type directions for the underlying optimization problem. The Newton-type speed function is found by solving an elliptic problem on the current active contour in every time step. Numerical experiments comparing the classical gradient method with Newton's method are presented.

The paper discusses the detection of weaknesses and defects on photolithographic masks by cellular neural networks. The detection by cellular neural networks is performed with the advantages of their massive parallel architecture. First a survey is given of actual methods for the detections of weaknesses and defects. Then the relations between the structures of the mask layouts and the real structures of the masks are defined by local design rules. These local design rules can also indirectly be used to detect most weaknesses and defects. After that, the design of the operators for the detection of weaknesses and defects are executed on the basis of the local design rules, using the method of Galias that is practicable by cellular neural networks. Then some examples of weakness and defect detections on real mask images by cellular neural networks are presented. Finally the results and future aims are discussed. >

There are many cases where image processing is performed using the neural network. The content of this Chapter is implementation of CNN (Cellular Neural Network) on a chip in a new original digital approach. First, testing of some features of the proposed cell of the neural network is evaluated. Then the design of the basic circuit containing the cell for the CNN will be introduced. The idea is to use it for a more complex chip with image processing application. CNN have been extensively used in various image processing applications. One of the most important problems in signal processing is noise removal. The input signals mostly arrive from the real world and therefore they contain relatively high amounts of noise. The CNN circuits are capable of removing this noise partly. The possibility of noise removing depends on the template (weight) coefficients between the cells. CNN networks are based on relatively simple principles, very similar to biological neurons. The input signals are multiplied by appropriate weights, the weight matrix being given intuitively, as it is typical for CNN networks. Then they are added and multiplied by the transfer function. We describe also the settings of weights coefficients. CNN have been extensively used in various image processing applications ( Matsumoto & Yokohama, 1990 ) or ( Sziranyi & Csicsvari, 1993 ). The main problem of CNN implementations on a chip is the chip area consumption. The most area is reserved for the multiplexer, so we looked for alternative multiplications. We describe the achieved results with the designed chip. During the creation of the chip architecture we proposed and introduced special original coding for the weight coefficients. After simulations we recognized that the results were better with rounding than without it, but we found that the rounding during multiplication was not as important as we previously expected. Therefore we decided – instead of a hardware multiplexer – to use multiplication realized by simple gate timing of the special signal. The circuit was designed as a digital synchronized circuit. For the design and simulation we used the Xilinx tool. The cell is based on sub-circuits as it will be shown in detail. The Chapter describes the designed circuit. We introduce also our novel simulator for the CNN using the program tool Visual Basic for Application, and its algorithm which was based on the same principle as the planned designed circuit. The network can process the patterns with 400 points of recognition. O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

This paper develops and validates through a series of presentable examples, a comprehensive high-precision, and ultrafast computing concept for solving nonlinear ordinary differential equations (ODEs) and partial differential equations (PDEs) with cellular neural networks (CNN). The core of this concept is a straightforward scheme that we call "nonlinear adaptive optimization (NAOP),” which is used for a precise template calculation for solving nonlinear ODEs and PDEs through CNN processors. One of the key contributions of this work is to demonstrate the possibility of transforming different types of nonlinearities displayed by various classical and well-known nonlinear equations (e.g., van der Pol-, Rayleigh-, Duffing-, Rössler-, Lorenz-, and Jerk-equations, just to name a few) unto first-order CNN elementary cells, and thereby enabling the easy derivation of corresponding CNN templates. Furthermore, in the case of PDE solving, the same concept also allows a mapping unto first-order CNN cells while considering one or even more nonlinear terms of the Taylor's series expansion generally used in the transformation of a PDE in a set of coupled nonlinear ODEs. Therefore, the concept of this paper does significantly contribute to the consolidation of CNN as a universal and ultrafast solver of nonlinear ODEs and/or PDEs. This clearly enables a CNN-based, real-time, ultraprecise, and low-cost computational engineering. As proof of concept, two examples of well-known ODEs are considered namely a second-order linear ODE and a second order nonlinear ODE of the van der Pol type. For each of these ODEs, the corresponding precise CNN templates are derived and are used to deduce the expected solutions. An implementation of the concept developed is possible even on embedded digital platforms (e.g., field programmable gate array (FPGA), digital signal processor (DSP), graphics processing unit (GPU), etc.). This opens a broad range of applications. Ongoing works (as outlook) are using NAOP for deriving precise templates for a selected set of practically interesting ODEs and PDEs equation models such as Lorenz-, Rössler-, Navier Stokes-, Schrödinger-, Maxwell-, etc.

Cellular neural networks for welding arc thermograms segmentation

This paper presents a new methodology for the deformation of soft objects by drawing an analogy between cellular neural network (CNN) and elastic deformation. An improved CNN model is developed to simulate the deformation of soft objects. A finite volume based method is presented to derive the discrete differential operators over irregular nets for obtaining the internal elastic forces. The proposed methodology not only models the deformation dynamics in continuum mechanics, but it also simplifies the complex deformation problem with simple setting CNN templates.

A background robust active appearance model using active contour technique

During the last decade, Active Contour Models had been greatly developed and were used in image edge detection, image segmentation and classification, image registration, 3D reconstruction and many other areas. In the meantime, Active Contour Models themselves had also been enriched and completed. Various typed Active Contour Models had emerged, such as Sobolev Active Contour Model(SACM). SACM was considered as a global model and showed great promise in application. It out-performs the traditional model for the same energy in many cases. SACM is a new model, so there are few cases of its application was reported. But it was believed that SACM will be a very important tool for image segmentation. SACM covers vast areas of study such as Soloblev space, Steepest decent methods, Variation of functionals, Riesz representing theorem, Riemannian geometry, PDE, and Image procession. This paper tries to clarify the relationships among those different areas of studies. Especially, the paper had introduced new formulae for the calculation of Soloblev gradients, because the formulae initiated by Sundaramoorthi are not strict mathematically.

The concept of the active contour model has been extensively utilized in the segmentation and analysis of images. This technology has been effectively employed in identifying the contours in object recognition, computer graphics and vision, biomedical processing of images that is normal images or medical images such as Magnetic Resonance Images (MRI), X-rays, plus Ultrasound imaging. Three colleagues, Kass, Witkin and Terzopoulos developed this energy, lessening “Active Contour Models” (equally identified as Snake) back in 1987. Being curved in nature, snakes are characterized in an image field and are capable of being set in motion by external and internal forces within image data and the curve itself in that order. The present study proposes the use of a hybrid image segmentation technique to acquire precise segmentation outcomes, while engaging “Alpha Shape (α-Shape)” in supposition to derive the original contour, followed by a refining process through engaging a conventional active contour model. Empirical results show high potential in the suggested computational method. Trials indicate that the primary contour is capable of being precisely set next to the objective contour and effectively have these objective contours extracted, devoid of any contour instigation. Some of the benefits associated with the novel hybrid contour include minimized cost of computation, enhanced anti-jamming capability, as well as enlarged utilization array of snake model.

The cellular neural network (CNN) method is applied to solve the Pennes bioheat transfer equation, and its feasibility is demonstrated. Numerical solutions were obtained for a cellular neural network for a two-dimensional steady-state temperature field obtained from focused and unfocused ultrasound heat sources. Transient-state temperature fields were also studied and compared with experimental results obtained elsewhere. The cellular neural networks' key features of asynchronous parallel processing, continuous-time dynamics and local interaction enable real-time temperature field estimation for clinical hyperthermia.

The application of cellular neural network (CNN) has made great progress in image processing. When the selected objects extraction (SOE) CNN is applied to gray scale images, its effects depend on the choice of initial points. In this paper, we take medical images as an example to analyze this limitation. Then an improved algorithm is proposed in which we can segment any gray level objects regardless of the limitation stated above. We also use the gradient information and contour detection CNN to determine the contour and ensure the veracity of segmentation effectively. Finally, we apply the improved algorithm to tumor segmentation of the human brain MR image. The experimental results show that the algorithm is practical and effective.

This paper presents a novel class of cellular neural networks (CNNs), where output of a cell in the CNN is given by the piecewise-linear (PWL) function having multiple constant regions or a quantization function. CNNs with one of these output functions allow us to extend CNNs to image processing with multiple gray levels. Since each cell of the original CNN has the PWL output function with two saturation regions, the image-processing tasks are mainly developed for black and white output images. Hence, the proposed architecture will extend the promising nature of the CNN further. Moreover, the hysteresis characteristics are introduced for these functions, which make tolerance to a noise robust. It is demonstrated mathematically that under a mild assumption, the stability of the CNN, which has an output function with hysteresis characteristics, is guaranteed, and the impressive simulation results are also presented.

Currently, the mechanical dynamics of soft tissue deformation is achieved by numerical time integrations such as the explicit or implicit integration; however, the explicit integration is stable only under a small time step, whereas the implicit integration is computationally expensive in spite of the accommodation of a large time step. This paper presents a cellular neural network method for stable simulation of soft tissue deformation dynamics. The non-rigid motion equation is formulated as a cellular neural network with local connectivity of cells, and thus the dynamics of soft tissue deformation is transformed into the neural dynamics of the cellular neural network. Results show that the proposed method can achieve good accuracy at a small time step. It still remains stable at a large time step, while maintaining the computational efficiency of the explicit integration. The proposed method can achieve stable soft tissue deformation with efficiency of explicit integration for surgical simulation.

In this paper, a mixed‐mode polynomial‐type cellular neural network (CNN) for analysing brain electrical activity in epilepsy is presented. The principles and design characteristics of this application are overviewed. The main difference of the requirements of this application compared to conventional CNN realizations is that in addition to linear, cells are also coupled with polynomial‐type couplings. A mixed‐mode CNN is shown to be suitable for the realization of a polynomial‐type CNN in the brain electrical activity analysis application. In a mixed‐mode CNN multiplication is done in analog domain, whereas the integration and storage are digital. Suitability of different integration methods for cell level realization are studied and cell and network level design of a mixed‐mode CNN is described. First‐, second‐ and third‐order polynomial feedback terms are included in the cell and Heun's integration method is used. In order to reduce the cell count, the array is designed so that it can process input data that has been divided into blocks. The whole input data is stored in parallel with the cells so that all input/output operations during processing are local. Cell structure is shown along with register connections between edge cells of the network. Analog power consumption and computing speed are estimated by HSPICE simulations using 0.25 µm digital CMOS process parameters. The die area of a network with 2×72 cells with 36 layers in each was determined by drawing the layout. Copyright © 2002 John Wiley & Sons, Ltd.