平面图形的几何变换

为了对畸变的图象进行纠正,我们建立了畸变过程的数学模型,并由此推导出了它的逆变换模型,再根据此模型进一步设计了它的算法.算法的核心内容是位置坐标的插值和灰度值的插值.位置坐标的插值用于变换后图象象素点的定位,而灰度值插值用于确定象素点的灰度值.经过这两步插值,便可得到变换后的新图象.本文将给出两种算法,它们在位置坐标的插值方法上有所不同,适用的范围也不同.该方法的主要数学工具是双线性插值.

Geometric Variations of Image

In order to rectify the image with distortion, we have to set up a mathematical model for the distortion, and derive an inverse transformation formula from it, then design an algorithm according to the model. The key content of the algorithm is the interpolation of the position coordinate and the interpolation of grey scale. The interpolation of the position coordinate determines the position of pixels, and the interpolation of grey scale determines the grey scale of pixels. We can acquire a new image through these two steps. In this paper, we will give two algorithms, they are different in the method of interpolation of the position coordinate, and the suited ranges are different too. The main mathematical tool of this method is bilinear interpolation. This method is not only suitable for rectifying the image with distortion, but also can be applied to the decoration of images, make some peculiar result.