Abstract
For numerous applications in image registration, sub-pixel translation estimation is a fundamental task, and increasing attention has been given to methods based on image phase information. However, we have found that none of these methods is universal. In other words, for any one of these methods, we can always find some image pairs which will not be well matched. In this paper, by introducing the cyclic shift matrix (CSM), we present a new model for the translation matching problem and derive a least squares solution for the model. In addition, by repeatedly applying the CSM to the matching image, an iterative CSM method is proposed to further improve the matching accuracy. Furthermore, we show that the traditional phase-based matching algorithms can only achieve an exact solution when there is a cyclic shift relationship between the images to be matched. The proposed method is evaluated using simulated and real images and demonstrates a better performance in both accuracy and robustness compared with the state-of-the-art methods.
Highlights
T O ADDRESS the image translation registration problem, traditional cross-correlation methods, such as normalized cross correlation and zero-normalized cross correlation, are time-consuming and often inaccurate in many cases [1], [2]
By introducing the cyclic shift matrix (CSM), we propose a new model for the image translation matching problem (TMP) and obtain a least squares solution for the model, named the CSM method
In order to evaluate the accuracy of our algorithm, we compared the CSM method with five classical phase correlation methods: the traditional discrete FT (DFT) [7] method, the DFT with up-sampling (DFT-US) [13] method, the traditional singular value decomposition (SVD) method [17], the SVD-Ransac method [20] and Stone’s method [14]
Summary
As for the subpixel shift situation, some methods introduce the procedure of interpolation to achieve sub-pixel precision [11] These are affected by noise and other interference [12]. The other type of method directly uses the phase information of P matrix to estimate the pixel shift. The phase shift angle of the matrix P can be expressed as a linear function of the shift (x0, y0), and it represents a 2-D plane through the origin of the u-v coordinates Based on this fact, many methods have been proposed [5], [14], [15]. By introducing the cyclic shift matrix (CSM), we propose a new model for the image translation matching problem (TMP) and obtain a least squares solution for the model, named the CSM method.
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