Accurate image registration based on image interpolation

图像内插是从给定的数字图像重建连续或离散信号的一种方法。正则化方法具有良好的内插能力，是一种有用的图像内插工具。提出了利用离散余弦变换(DCT)快速求解两个图像内插问题的方法。我们证明了径向基函数(RBF)插值法的频率响应与理想SINC插值法的频率响应是渐近等价的，并且RBF插值法比三次样条法和Lanczos插值法更接近理想SINC插值法。另一个问题是高分辨率(HR)图像复原，即基于正则化从下采样的低分辨率图像恢复HR图像。证明了下采样过程在DCT域以标量形式表示，导出了HR恢复问题的解析解，发展了利用DCT的快速计算方法，并利用径向基函数插值技术导出了一种亚像素精度的匹配参数估计方法。该估计方法使用径向基函数插值从同一场景的数字图像生成连续图像，然后最小化一个非线性代价函数来估计图像之间的平移、旋转、比例因子和强度变化。径向基函数插值可以生成精确的连续图像。我们将高斯权重函数引入到代价函数中，以获得特定区域周围匹配参数的局部估计。我们解析地计算了代价函数中的二重积分，并注意到高斯函数迅速衰减，从而降低了优化的计算复杂性。

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.