使用方向参数的双三次图像内插方法

传统的双三次内插方法仅在水平和垂直方向估计丢失的像素，易在边缘或纹理区域产生抖动、振铃等现象。为了克服这种现象，提出一种新的使用方向参数的双三次图像内插方法。对待内插的像素，首先在其邻域计算水平、垂直、45°和135°四个方向的梯度，以提取图像局部边缘的强度和方向。对强边缘上的像素，直接沿边缘方向采用对应方向的双三次内插模型估计像素值；否则，先分别沿梯度较大的两个方向采用相应方向的双三次内插模型估计像素，然后采用适当的权系数对所得结果加权平均。此外，为减小计算复杂度，方法中还根据图像局部方差的大小，动态使用双线性内插方法。相比于双三次内插，提出的方法能有效地保存图像边缘和细节；同时，提出的方法还能够实现任意倍数的放大。实验结果表明，与现有的边缘导向的图像内插方法相比，提出的方法具有更好的主观和客观效果，同时计算复杂度并不高。 

A Method of Bicubic Image Interpolation with Direction Parameter

Traditional bicubic interpolation only interpolates missing pixels in horizontal or vertical directions and incurs blurring, ringing artifacts along edges or textures easily. Aiming at this problem, a method of bicubic image interpolation with direction parameter is proposed. This method detects local directions and strengths by means of computing gradients along horizontal, vertical, 45°and 135° in the first. If pixels are on strong edges, 1D bicubic interpolation with corresponding direction is used directly. Otherwise, first interpolate along two directions with the biggest gradients respectively and then combine them with appropriate weights. Besides, in order to decrease computational complexity, bilinear interpolation is used dramatically based on local variance in this paper. Compared with bicubic method, the proposed method preserves sharp edges and details better and can accommodate arbitrary scaling factors as well. Experiments show that the proposed method is better than modern edge-directed interpolations in terms of subjective (such as PSNR) and objective (such as SSIM) measures, and the computational complexity is also relatively low.