Department of Electronic Engineering, Yonsei University, Seoul, Korea.
IEEE Trans Image Process. 1998;7(5):679-92. doi: 10.1109/83.668025.
The standard interpolation approach to image resizing is to fit the original picture with a continuous model and resample the function at the desired rate. However, one can obtain more accurate results if one applies a filter prior to sampling, a fact well known from sampling theory. The optimal solution corresponds to an orthogonal projection onto the underlying continuous signal space. Unfortunately, the optimal projection prefilter is difficult to implement when sine or high order spline functions are used. We propose to resize the image using an oblique rather than an orthogonal projection operator in order to make use of faster, simpler, and more general algorithms. We show that we can achieve almost the same result as with the orthogonal projection provided that we use the same approximation space. The main advantage is that it becomes perfectly feasible to use higher order models (e.g. splines of degree n=or>3). We develop the theoretical background and present a simple and practical implementation procedure using B-splines. Our experiments show that the proposed algorithm consistently outperforms the standard interpolation methods and that it provides essentially the same performance as the optimal procedure (least squares solution) with considerably fewer computations. The method works for arbitrary scaling factors and is applicable to both image enlargement and reduction.
图像缩放的标准插值方法是用连续模型拟合原始图像，并以所需的速率对函数进行重采样。然而，如果在采样前应用滤波器，可以获得更精确的结果，这是采样理论中众所周知的事实。最优解对应于到基础连续信号空间的正交投影。不幸的是，当使用正弦或高阶样条函数时，很难实现最优的投影预滤波器。我们建议使用斜投影算子而不是正交投影算子来调整图像大小，以便利用更快、更简单、更通用的算法。我们表明，只要我们使用相同的逼近空间，我们就可以获得几乎与正交投影相同的结果。主要优点是，使用更高阶的模型（例如，阶数 n=or>3 的样条函数）变得完全可行。我们开发了理论背景，并提出了一种使用 B 样条的简单实用的实现过程。我们的实验表明，所提出的算法始终优于标准插值方法，并且与计算量少得多的最优方法（最小二乘解）提供基本相同的性能。该方法适用于任意缩放因子，可用于图像放大和缩小。
