When working sequences of images, registration of the frames to a common point of reference is an essential prerequisite for many types of image analysis. The phase correlation method (PCM) is a popular Fourier domain method to register two images. It computes a phase difference map that (ideally) contains a single peak. The location of the peak is proportional to the relative translation [dx, dy] between the two images. The PCM is resilient to noise and image defects and is readily automated.

The importance of Accurate Frame Registration is depicted in an IKONOS satellite image of Venice, Italy (top). The green vs. red color ratio for this image was computed by extracting the green and red components of the image and performing simple element-by-element matrix division (R1 = Green/Red). The color ratio was computed a second time (R2) using a green image with a (deliberate) subpixel registration error of 0.1 pixel. At right is the quantity (R2-R1)/R1, which is the normalized error in color ratio. Although the registration error is small, the color ratio error is as large as 15%.
The accuracy of PCM registration depends upon the content and quality of the images. There are representative tradeoffs of accuracy versus image noise and array size. Perhaps the most prominent advantage of the PCM is that it is exceptionally robust against noise.

The PCM is strictly applicable to images that obey periodic boundary conditions. However, images of this kind are unphysical. An essential feature of the present work is that it uses realistic images that do not obey periodic boundary conditions. In addition to nonperiodic boundary conditions, real images are subject to noise and frequency aliasing. In addition, some focal plane arrays have dead space between the pixels. If one is concerned with registering images to within only ±1 pixel, these real-world effects are generally inconsequential. However, they become significant as one attempts to push the PCM to subpixel accuracy.

A reliable algorithm for subpixel accuracy frame registration is needed to accurately process multispectral imagery. Three different extensions of the popular PCM to subpixel frame registration were evaluated using a common set of satellite images. The test images derived from the satellite images include real-world effects such as nonperiodic boundary conditions, dead space between pixels, and additive noise.

The GTF (Guizar-Sicairos, Thurman, and Fienup) method and its two minor variants performed best, with registration errors consistently on the order of 0.05 pixels or less. This registration accuracy pertains to 256 × 256 images with rms noise levels as high as 10%. The RVJ (Ren, Vlachos, and Jiang) method performed inconsistently. It worked as well as GTF for most images, but poorly for others. The Hoge method is not recommended in its present form. However, the mathematical basis is sound, and with minor changes, it might be made to perform as well as the other methods.

Attempts to further increase the accuracy of registration by preprocessing the images (e.g., by taking gradients or by performing histogram equalization of the intensities) led to only minor gains in accuracy.

This work was done by Robert A. Reed of the Aerospace Testing Alliance. AFRL-0163

This Brief includes a Technical Support Package (TSP).
Comparison of Subpixel Phase Correlation Methods for Image Registration

(reference AFRL-0163) is currently available for download from the TSP library.

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