图像插值是图像处理中的一个基本问题,为了获得更合理的图像插值权函数,从1维函数中插值的有关思想出发,通过梯度信息在图像插值中的应用研究,构造了一种基于图像梯度信息的加权插值方法。该方法利用图像为分片连续的光滑函数的先验信息,通过建立一个与各点梯度值成反比的权函数来完成对图像的插值,同时对涉及的有关参数选择问题进行了讨论,给出了一种合理的参数选取方法。仿真计算表明,该方法对一般图像均具有较好的插值效果,尤其适用于对比度较强,且边缘简单的图像,插值后的图像边缘更清晰。

Image interpolation is a basic problem of image processing,in order to get a more reasonable weight function,the paper studies the application of gradients in one-dimensional signal interpolation,and generalizes it to the interpolation of image,then obtains a method for image interpolation based on gradients.In linear interpolation model,the weighted function is only dependent on the distance of the pixels,but not on the gradient,which often leads to the blurring of the image.Since image is a piecewise continual function,the gray value of an unknown pixel is closer to the pixel with smaller gradient than the pixel with bigger gradient,so a decreased weighted function of gradient is constructed in this method to interpolate the unknown pixels.It also discusses the selection of the related parameter in the model,and obtains a reasonable parameter based on the distribution of the gradient.The algorithm is tested on two images,all results show that the new method has higher peak signal to noise ratio and better intensity of image than known methods,and that it suits to simple image especially.