提出新方法实现图像相似变换的亚像素级精确对齐。
Alignment of Similarity-Transformed Images Based on Fourier--Mellin Transform Using Auxiliary Function Method
- 分两阶段估计：先在对数极坐标中求尺度与旋转，再用辅助函数法精算平移。
- 仿真结果表明，尺度、旋转、平移误差均低于传统傅里叶-梅林方法。
- 适合高精度图像配准场景，如遥感、医学影像分析。
本文提出一种算法，用于以亚像素精度估计两幅图像间的相似变换（平移、缩放、旋转）。图像配准是不同视角和成像条件下对齐图像的基础技术，基于最大化离散互相关的方法中，傅里叶-梅林配准具有代表性。然而，当需要亚像素级估计时，傅里叶-梅林方法往往无法达到足够精度。所提方法结合了（i）在对数极坐标表示下的傅里叶幅度谱进行尺度与旋转估计，以及（ii）基于辅助函数法的最大化相位仅相关性。该融合实现了两阶段估计流程：首先在不受平移影响的情况下估计尺度与旋转，然后在空间域中利用校正后的图像对以亚像素精度估计平移。针对随机相似变换图像对的仿真实验表明，相比使用离散互相关的傅里叶-梅林配准方法，该方法在尺度、旋转和平移估计上的误差均有降低。
原文摘要 · Abstract (English)
This paper proposes an algorithm for estimating the similarity transformation, namely translation, scale, and rotation, between two images with subpixel accuracy. Image registration is a fundamental technique for aligning images acquired under different viewpoints and imaging conditions, and a representative approach based on maximizing discrete cross-correlation is the Fourier--Mellin registration. However, the Fourier--Mellin approach often fails to achieve sufficient alignment accuracy when subpixel-level estimation is required. The proposed method integrates (i) scale-and-rotation estimation from the Fourier magnitude spectrum in a log-polar representation and (ii) maximization of phase-only correlation based on the auxiliary function method. This integration enables a two-stage estimation procedure: it first estimates scale and rotation without being affected by translation, and then estimates translation with subpixel precision in the spatial domain using the corrected image pair. A simulation experiment on image pairs subjected to random similarity transformations demonstrates that the proposed method reduces estimation errors in scale, rotation, and translation compared with Fourier--Mellin-based registration methods using discrete cross-correlation.
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