Jpn. J. Appl. Phys. Vol. 39 (2000) pp. 2278–2286 Part 1, No. 4B, April 2000 c 2000 The Japan Society of Applied Physics Cellular ν MOS Circuits Performing Edge Detection with Difference-of-Gaussian Filters Tatsuhiko SUNAYAMA, Masayuki I KEBE, Tetsuya ASAI ∗ and Yoshihito AMEMIYA Department of Electrical Engineering, Hokkaido University, Kita 13, Nishi 8, Sapporo, 060-8628, Japan (Received October 22, 1999; accepted for publication December 21, 1999) Aiming at the development of high-speed image processors, we propose a cellular ν MOS circuit that performs the pro- cessing of edge detection. The proposed circuit uses neuron MOS (ν MOS) transistors for analog convolution operations with Gaussian-shaped kernel functions, which makes the circuit organization extremely simple as compared with that of conven- tional convolution circuits. Performances of the proposed circuit are evaluated by simulation program with integrated circuit emphasis (SPICE). The results show the usefulness of the cellular ν MOS circuit in image-processing applications. KEYWORDS: cellular automaton, difference-of-Gaussian filter, edge detection, ν MOS transistor ∗ E-mail address: asai@sapiens-ei.eng.hokudai.ac.jp 2278 1. Introduction One of the promising research areas in microelectronics is the development of intelligent image sensors based on parallel processing architectures. Among various image-processing architectures, the cellular automaton (CA) is expected to pro- vide high-speed image-processing systems because of its in- herent parallel operations. 1) Recently, a number of CA algo- rithms for extracting various image features have been pro- posed and successfully demonstrated, 2) which show the great potential of CA in image-processing applications. Aiming at the development of CA-based high-speed pro- cessors, a number of large-scale integrated circuits (LSIs) have been proposed and fabricated. 3–8) The important require- ment in developing such CA LSIs is that the LSI must be implemented on one chip in a fully parallel construction. Be- cause image-processing applications need a large number of pixels, the unit processor (pixel circuit) has to be constructed as compactly as possible. To meet this requirement, a func- tional metal-oxide semiconductor (MOS) device, known as the ν MOS transistor, was recently developed and has been ap- plied to various image-processing applications. 9, 10) And the authors have developed a number of CA circuits using the ν MOS transistors (cellular ν MOS circuits) for morphological processing on binary images and demonstrated that functions required for the processing can be successfully achieved with compact pixel circuits. 11–14) In this paper, we propose a CA algorithm for perform- ing difference-of-Gaussian (DoG) filtering and develop the ν MOS circuit that performs edge detection on gray scale (ana- log) images on the basis of the DoG filtering. The cellular ν MOS circuit is useful for analog image processing as well as for binary image processing. The proposed circuit uses the ν MOS transistor for analog convolution operations with Gaussian-shaped kernel functions, which makes the circuit organization extremely simple as compared with that of con- ventional convolution circuits. This paper is organized as follows. In §2, we outline the CA and the DoG filters for edge detection. In §3, we propose a method of edge detection by the CA. Section 4 shows the cellular ν MOS circuit for edge detection. Section 5 shows the behaviors of the ν MOS circuit, using a simulation pro- gram with integrated circuit emphasis (SPICE). Section 6 is devoted to a summary. C 1, 1 C n,1 C n, m C 1, m C i, j Fig. 1. A cellular automaton (CA) consisting of m-by-n cells with local connections among neighboring cells. Nine cells represented by the filled box are the neighboring cells of the cell C i, j , including the cell. 2. The Cellular Automaton and DoG Filters 2.1 Pattern transformation using the cellular automaton A cellular automaton (CA) is a discrete dynamical system whose behavior is completely specified in terms of finite lo- cal interactions. 1, 2) The CA consists of many identical cells (processors) and local connections among the cells. These cells are regularly arrayed on a two-dimensional rectangular grid. Figure 1 shows a CA consisting of m-by-n cells with local interactions among the neighboring cells. Nine cells represented by the gray boxes are the neighboring cells of cell C i , j , including the cell. Each cell has a binary, multiple- valued, or continuous state. All the cells change their states synchronously in an update cycle. During the cycle, the cur- rent frame, represented by all the cell-state planes, is replaced by a new frame according to a given transition rule. The CA can be used for various image processing applica- tions by regarding each cell and its state as a pixel and the pixel-luminance value, respectively. As an example, edge de- tection by means of the CA is demonstrated in Fig. 2. A bi- nary pixel state (0 or 1) is assumed in the example. Figures 2(a) and 2(b) show an original frame and an edged frame pro- cessed by the CA, respectively. The original frame is updated to the edged frame according to the transition rule given in