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Announcing the arrival of Valued Associate Extraction of boundary is discussed in Section 4. The issue of detecting the corner points is discussed in Section 5. The Section 7 summarizes the discussion.

The algorithm Our proposed algorithm of automatic approximation of the boundary of digital character images consists of the following steps: Getting a digitized image.

Extracting of boundary contour from the digitized image. Detecting corner points. Fitting parametric cubic Bezier.

This is an iterative process. In the following sections, we explain the above steps.

Getting digitized image Digitized image of a character can be obtained directly from some electronic device or by scanning an image. We used both the methods. The quality of digitized scanned image depends on various factors such as image on paper, scanner and attributes set during scanning. The quality of digitized image obtained directly from electronic device depends on the resolution of device, source of image, type of image, etc.

Some of the digitized images are shown in Figs. Digitized image 'Samar' character. Extracting of boundary Boundary of digitized image is extracted by using some boundary detection algorithm. There are numerous algorithms for detecting the boundary [2]. We have used the algorithm in [11]. The corner points are those points which partition the outline into various segments. There has been a good amount of work done for the de- tection of corner points given the boundary of an image. A number of ap- proaches have been proposed by researchers [1,6,12].

These include the Curvature analysis with numerical techniques and some signal processing methods. In [12] some of the possible ways to detect corners in an image are presented. The curvature can be analyzed using some numerical approaches. The detection of corner actually depends on the actual resolution of the image and processing width to calculate the curvature. For the detection of corners, in this paper, we adopted the technique used in [7]; algorithm sometimes gives Fig.

Detected boundary consists of two pieces. The value of k depends on several factors such as the resolution of the original digital image. The algorithm is demonstrated in Fig. The division is based on corner points.

It means that if there are m corner points cp1 ;. Corner points. Last segment has all the contour points between corner point cpm and corner point cp1 inclusive. Of course corner points obey the order of contour points. The situation is illustrated in Fig.

If contour points of the kth segment are pu ;.

Finding intermediate control points The Bezier form of cubic polynomial curve segment has four control points P0 , P1 , P2 and P3. The Bezier curve interpolates the two end control points P0 and P3 and approximates the two intermediate points P1 and P2. The two end control points are the two corner points of the curve segment. The description of the cubic Bezier curve is given as fol- lows: Division of contour into segments.

Then 3 can be expressed as follows: We will use chord-length parameterization to estimate the parametric value t associated with each point pi. Optimal curve Recall that our goal is to approximate the digitized curve by a parametric curve in the best way. For this purpose, we use the least square method. Mathematically we can write: The solution will give us values of P1 and P2 that approximate the digitized curve by a parametric curve in the best optimal way for given values of t.