Existing Fuzzy-based CNN Models and CNN Integrated Systems

To make a CNN or a set of CNNs have the ability of reasoning functions, several fuzzy-based CNN models were proposed [5]-[9], which are fuzzy cellular neural network (FCNN) proposed by Yang et al [5], [6], fuzzy reasoning implemented on CNN proposed by Balsi et al [7], [8]. To make a set of CNNs in parallel achieve higher-level information processing, several integrated CNN systems are proposed [9]-[11], which are cellular neuro-fuzzy networks (CNFNs) proposed by Colodro [9], and fuzzy-type CNN proposed by Rekeczky [10], [11] and Szatmári et al. [4]. In the following, we will survey these related papers.

1.3.1.1. Existing Fuzzy-based CNN Models

Yang et al. [5], [6] first proposed a FCNN model in 1996. Such architecture had the same structure as a CNN with nonlinear connections, but the connection functions were stated in terms of fuzzy logic operators, so that the model departed from the trend towards standardization and simplification of connection functions to be realized in future CNN universal machine (CNN-UM) chips. The authors gave an example for edge detection. The characteristics of Yang’s FCNN are to integrate fuzzy logic into the structure of traditional CNN and maintains local connection among cells, but its drawback is that it is too complex to implement in the short term.

Balsi et al. [7], [8] proposed a fuzzy reasoning method implemented on CNN-UM in 1999. Such architecture has the same structure as a conventional CNN.

The authors showed that standard fuzzy logic could be straightforwardly implemented in the CNN-UM framework without any architectural modifications. The authors showed several examples for edge detection and noise removal. One of them concerned the edge detection in the presence of impulse noise. Experimental result showed the edge could be detected even impulse noise existed with appropriate fuzzy rules. The characteristic of Balsi’s FCNN is to map a standard Sugeno-style fuzzy-rule-based image processing algorithm into a standard CNN-UM analogic (analog and logic) algorithm. However, the fuzzy rules must be obtained by domain experts.

Yang et al. [5], [6] and Balsi et al. [7], [8] were devoted to make a CNN or a set of CNNs have the ability of fuzzy reasoning. However, the other authors [4], [9]-[11]

were devoted to make a set of CNNs in parallel achieve higher-level information processing, which is the main research subject in this thesis. The related papers are described in the following subsection.

1.3.1.2. Existing CNN Integrated Systems

In 1996, Colodro et al. [9] proposed a new class of cellular networks called cellular neuro-fuzzy networks (CNFNs), which the linear combination and piece-wise linear function of a CNN were replaced by an arithmetic fuzzy-logic unit. To demonstrate the capabilities of the proposed CNFN, the authors gave an application example for edge detection. The example used eight fuzzy rules and its CNFN templates were well-known Sobel masks to detect edge. The characteristic of Colodro’s CNFN is to provide a new architecture based on CNN and FIS to solve problem. Its drawbacks are the templates cannot be learned and the fuzzy rules must be obtained by domain experts. Though Colodro et al. showed a simple example for edge detection, they presented an approach to integrate different CNN template sets to solve problem.

Rekeczky et al. [10], [11] developed a common CNN framework for various adaptive non-linear filters [10]. Their experimental results indicated that impulsive noise elimination will be more robust if both the pixel intensity and the edge-like local property is taken into consideration and exploited in a fuzzy-type decision.

Rekeczky et al. [11] also proposed a CNN-based spatio-temporal approach to find the endocardial (inner) boundary of the left ventricle from a sequence of echocardiographic images. The kernel of the left ventricle was located and the boundary was found using a fuzzy-adaptive technique. Boundary dislocation, area and smoothness constraints were transformed into the transient length of the CNN while the a priori knowledge about the heart morphology was built into the spatial template parameters. The authors showed the architecture of the processing steps of a fuzzy-type CNN analogic algorithm. As observed by Rekeczky et al. [11], it was not necessary to use a specialized CNN model [5], [6] in order to exploit fuzzy logic

concepts. The reasons were as follows. First, elementary fuzzy-type computations, such as the min and max operator, are already defined in CNN-based gray-scale morphology and require only simple non-linear templates with sigmoid-type nonlinear interactions. Second, higher level fuzzy strategies can also be synthesized using ‘conventional’ linear and non-linear CNN templates. The characteristic of Rekeczky’s fuzzy-type CNN analogic algorithm is to use FIS to integrate different CNNs to detect fuzzy boundary of a given object. Similarly, its drawbacks are the corresponding templates cannot be learned and must be assigned in advance, and the fuzzy rules must be obtained by domain experts.

In 2003, Szatmári et al. [4] proposed an image flow processing mechanism for visual exploration systems. The goal of this multi-channel topographic approach was to produce decision maps for salient feature localization and identification. According to a current biological study, mammalian visual systems process the world through a set of separate parallel channels. Each sub-channel can be regarded as a unique CNN.

The output of these sub-channels is then combined to form the new channel responses.

In the core of the algorithm crisp or fuzzy logic strategies define the global channel interaction and result in a unique binary image flow. Experimental results were shown for terrain exploration environment based on multiple feature extraction. The characteristic of Szatmári’s method is to use FIS to integrate different CNNs to extract features of a given object. Similarly, its drawbacks are the corresponding templates cannot be learned and the fuzzy rules must be obtained by domain experts.