图像待插像素用其邻域内连续方向上像素的Tyler展开可以得到较好的近似，但是沿着灰度连续和不连续方向(跨越图像边缘方向)的Tyler展开近似的线性平均会增加图像边缘宽度，引起图像边缘的视觉模糊以及产生锯齿边缘。为此，通过一个与灰度距离相关的权函数，自适应选择待插像素邻域内的Tyler展开，提出一个邻域滤波图像插值方法。与待插像素位于图像边缘同侧的像素权函数的值较大，像素的Tyler展开被选择为待插像素的近似；反之则权函数的值较小，像素的Tyler展开不用作待插像素的Tyler展开。实验结果表明，该方法避免了跨越图像边缘的Tyler展开的线性平均，可减小插值图像边缘的宽度，增加边缘斜坡坡度，从而获得清晰的插值图像边缘。%The interpolated pixel can be expanded along the direction on which image grey is continuously varied by Tyler expansion. But the linear average of these Tyler expansions along the continuous and discontinuous direction will enlarge the width of image edges and introduce blurring and zigzag effects. In this paper, a neighborhood filtering for image interpolation is proposed. A weighted function based on grey distance adaptively selects the Tyler expansions in the neighborhood of interpolated pixel. The principle of the method is that the weight of the pixel which lies on the same lateral of image edges with the interpolated pixel is large,so its Tyler expansion is selected,vice versa,the weight is small and its Tyler expansion is not selected. It avoids the average of the expansions which cross the image edges, and can reduce width of edge and increase slope,which produce scrip edges.
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