中文字帖書法字之描述

Abstract

書法是我們中國國粹之一，為了保存我們傳統的固有文化，在本篇論文中提出了一個自動將點陣圖向量化的系統，如此一來，我們便可以防止在字體放大時鉅齒狀的現象，我們的系統的輸入影像為二值化的點陣圖像。 這個系統包括兩個主要的模組: 字形輪廓切割之擷取與字形輪廓切割之描述。在字形輪廓切割之擷取部分，我們先將字形輪廓變平滑以防止字形輪廓有凹凸不平的現象並去除字中的白色小雜點，接著找出字形輪廓，在輪廓上找出曲率變化較大的點當作輪廓線的斷點，這些斷點將每一個輪廓線切成數個輪廓線段。在字形輪廓切割之描述部分，首先我們先決定每一個輪廓線段的描述形態，看是用直線描述或用貝茲曲線來描述，若是使用貝茲曲線來描述，首先估計每一個曲線控制點的起始位置，接著定義一個判斷函數，看曲線與輪廓線段的密合度，若由此判斷函數得知曲線與輪廓線段的差異大，則移動曲線的控制點讓曲線更接近原輪廓線段，詳細的說，我們先找出通過控制點且與輪廓線段兩端點相垂直的直線，還有此直線與輪廓線段和曲線的各自交點，利用交點的距離來移動控制點往左往右或增加斷點，藉此讓曲線更接近輪廓線段，當每一個輪廓線段和曲線都很接近的時候，這表示我們可以用這些曲線來描述原來的字形輪廓而且可以描述得很好。 在我們的實驗中，對於一個含有4500個輪廓線段的A4影像，曲線描述的處理時間約為5秒，成功描述輪廓線段的平均移動次數為1.32次。

The calligraphy is one of the quintessence of Chinese culture. In this thesis, we design an automatic system to vectorize the digital images of the Chinese characters in calligraphy documents. Thus, we can prevent the zigzag phenomena when enlarge characters. The input of our system is binary calligraphy images without noises. Our system contains two major modules: contour segment extraction and contour segment description. In the contour segment extraction module, we first perform image smoothing to avoid rough contours and remove white pixels inside characters. We then trace contour by recording the contour points of characters. The high curvature points on contours are next detected as corner points that divide each contour into several contour segments. In the contour segment description module, we first determine to describe the segment by a straight line or a cubic Bezier curve. For the latter, after we locate initial control points, we find the curve. we define a cost function to evaluate the curve fitness. If the cost is large, we adjust the control points to fit the contour segment better. In details, we find the intersection points of the two lines passing through two control points perpendicular to the line between two end points, and intersected with both the Bezier curve and the contour segment. We use the distance between the intersection points and both the Bezier curve and the contour segment to move the control points up or down, and left or right, or to add a new corner point. When the cost between each contour segment and Bezier curve is small, we have the best shape descriptions. In our experiments, the processing time of curve fitting is about 5 second per A4 image around 4500 contour segments. The average number of iterations of successful fitting contour segments is 1.32.