Accurate image registration based on image interpolation

图像插值是一种从给定的数字图像重建连续或离散信号的方法。正则化以其优异的插值性能成为图像插值的有效工具之一。本文提出了用离散余弦变换（DCT）快速求解两种图像插值问题的方法。我们证明了径向基函数（RBF）插值的频率响应渐近等价于理想正弦插值，并且RBF插值比三次样条插值和Lanczos插值更接近于理想正弦插值。另一个问题是高分辨率（HR）图像恢复，它是基于正则化从下采样的低分辨率图像恢复高分辨率图像。我们证明了下采样过程在DCT域中以标量形式表示，推导了HR恢复问题的解析解，并开发了利用DCT的快速计算方法。利用RBF内插技术，提出了一种亚像素精度的匹配参数估计方法。该估计方法利用RBF插值从同一场景的数字图像中生成连续图像，然后最小化非线性代价函数来估计图像之间的平移、旋转、缩放因子和强度变化。RBF插值可以生成精确的连续图像。我们在代价函数中引入了高斯加权函数，以获得特定区域周围匹配参数的局部估计。我们在代价函数中解析计算了一个二重积分，并注意到高斯函数衰减迅速，从而降低了优化的计算复杂度。

Image interpolation is a method of reconstructing a continuous or discrete signal from a given digital image. Regularization is one of useful tools for image interpolation due to its excellent interpolation capability. We have proposed fast methods for two image interpolation problems by using the discrete cosine transform (DCT). We have shown that the frequency response of the radial basis function (RBF) interpolation is asymptotically equivalent to the ideal sinc interpolation, and that the RBF interpolation is closer to the ideal sinc interpolation than the cubic spline and Lanczos interpolations. The other problem is the high resolution (HR) image restoration, which restores the HR image from a downsampled low resolution image based on the regularization. We have shown that the downsampling process is expressed in a scalar form in the DCT domain, have derived the analytical solution to the HR restoration problem, hand have developed the fast computation method by using the DCT.A matching parameter estimation method with subpixel accuracy is derived by using the RBF in-terpolation technique. The estimation method uses the RBF interpolation to generate the continuous images from the digital images taken from the same scene, and then minimizes a nonlinear cost function to estimate translation, rotation, scaling factor, and intensity change between images. The RBF inter-polation can generate accurate continuous images. We have introduced a Gaussian weighting function into the cost function to obtain a local estimate of the matching parameters around a specific region. We have analytically computed a double integral in the cost function, and have reduced the computational complexity of the optimization by noticing that the Gaussian function decays rapidly.