By Makoto Nagao

It is correct that the 1st quantity to seem within the sequence "Advanced functions in trend reputation" can be this monograph through Nagao and Matsuyama. The paintings defined here's a deep unification and synthesis of the 2 primary ways to pat tern reputation: numerical (also often called "statistical") and struc tural ("linguistic," "syntactic"). the facility and team spirit of the meth odology circulation from the it seems that easy and traditional use of the knowledge-base framework illuminated via the easiest result of synthetic intelligence learn. a vital part of the paintings is the algorithmic answer of many hitherto incompletely or clumsily taken care of difficulties. It was once at the get together of a laboratory stopover at in reference to the 4th IJCPR (of ~hich Professor Nagao was once the very capable application Chairman) that I observed in operation the process defined right here. instant I expressed the need to determine the paintings defined for the inter nationwide technical viewers during this sequence and the authors have been type sufficient to conform to give a contribution to a brand new and unknown sequence. With the booklet of this monograph at the eve of the fifth ICPR my want is fu1fi11~d. i need to thank the following the authors and Plenum Publishing company for making this quantity and the sequence a reality.

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**Example text**

5 shows the results of the edge-preserving smoothing of a simple pattern, which has been artifically generated on a 100 x 100 grid and quantized to 256 gray levels. The original picture has three different regions with the average gray levels 48, 108, and 168, respectively. Gaussian noise has been added to this pattern with the standard deviations of (a) 10, (b) 20, (c) 30, (d) 40, and (e) 50, respectively. The noisy pictures on the top row of Fig. 5 hav~ been made by this operation. The pictures on the middle row show the results of the edge-preserving smoothing after ten iterations.

Step 2: Detect'the position of the mask where its graylevel variance is minimum. Step 3: Give the average gray-level of the mask at the selected position to the point (X, Y). Step 4: Apply the Steps 1 - 3 to all points in a picture. Step 5: Iterate the above process until the gray-levels of almost all points in a picture do not change. In order to remove the noise without blurring sharp edges, averaging must not be applied to an area which contains an'edge because it blurs the edge. Thus the most homogeneous neighborhood is to be found around a point to be smoothed.

Let a point (X, Y) belong to Rl. If (X, Y) is located at the central part of Rl, its gray-level approaches to the average graylevel of Rl (in this case 0) after several iterations of smoothing. On the other hand, if (X, Y) is near the boundary, there exist two kinds of neighborhoods, one of which is completely included in Rl 36 3. SOME BASIC TECHNIQUES IN PICTURE PROCESSING while the other includes parts of both Rl and R2. ab out a 2 • t h e f ormer 1S 1 culated as follows. The variance of The variance a 2 of the latter can be cal- Let N1 and N2 denote the numbers of points be- longing to Rl and R2, respectively, which are contained in this neighborhood.