Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-20T00:52:29.532Z Has data issue: false hasContentIssue false

4 - Fast correlation and phase correlation

from PART II - Similarity Metrics for Image Registration

Published online by Cambridge University Press:  03 May 2011

By
Harold S. Stone
Edited by
Jacqueline Le Moigne ,
Nathan S. Netanyahu  and
Roger D. Eastman
Harold S. Stone
Affiliation:
NEC Research Laboratory Retiree, New Jersey
Jacqueline Le Moigne
Affiliation:
NASA-Goddard Space Flight Center
Nathan S. Netanyahu
Affiliation:
Bar-Ilan University, Israel and University of Maryland, College Park
Roger D. Eastman
Affiliation:
Loyola University Maryland
Get access

Summary

Abstract

Correlation is an extremely powerful technique for finding similarities between two images. This chapter describes why correlation has proved to be a valuable tool, how to implement correlation to achieve extremely high performance processing, and indicates the limits of correlation so that it can be used where it is appropriate. Section 4.1 gives the underlying theory for fast correlation, which is the well-known convolution theorem. It is this theory that gives correlation a huge processing advantage in many applications. Also covered is normalized correlation, which is a form of correlation that allows images to be matched in spite of differences in the images due to uniform changes of intensity. Section 4.2 treats the practical implementation of correlation, including the use of masks to eliminate irrelevant or obscured portions of images. The implementations described in this section treat images that differ only by translation, and otherwise have the same orientation and scale. Section 4.3 introduces an extension of the basic algorithm to allow for small differences of scale and orientation as well as translation. Section 4.4 presents very high precision registration. This section shows how to make use of Fourier phase to determine translational differences down to a few hundredths of a pixel. The images must be oriented and scaled identically and have a translational difference that does not exceed half of a pixel. Section 4.5 deals with fast rotational registration that uses phase correlation to discover the rotational difference between two images.

Type
Chapter
Information
Image Registration for Remote Sensing , pp. 79 - 111
Publisher: Cambridge University Press
Print publication year: 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Agarwal, R. C. and Cooley, J. W. (1977). New algorithms for digital convolution. IEEE Transactions on Acoustics, Speech, and Signal Processing, 25, 392–410.CrossRefGoogle Scholar
Alliney, S. and Morandi, C. (1986). Digital image registration using projections. IEEE Pattern Analysis and Machine Intelligence, 8(2), 222–233.CrossRefGoogle ScholarPubMed
Alliney, S., Cortelazzo, G., and Mian, G. A. (1996). On the registrations of an object translating on a static background. Pattern Recognition, 29(1), 131–141.CrossRefGoogle Scholar
Anuta, P. (1970). Spatial registration of multispectral and multitemporal digital imager using fast Fourier transform techniques. IEEE Transactions on Geoscience Electronics, 8, 353–368.CrossRefGoogle Scholar
Chang, S. H., Chen, F. H., Hsu, W. H., and Wu, G. Z. (1997). Fast algorithm for point pattern matching: Invariant to translations, rotations and scale changes. Pattern Recognition, 30(2), 311–320.CrossRefGoogle Scholar
Chen, Q.-S., Defrise, M., and Deconinck, F. (1994). Symmetric phase-only matched filtering of Fourier-Mellin transforms for image registration and recognition. IEEE Pattern Analysis and Machine Intelligence, 16(12), 1156–1168.CrossRefGoogle Scholar
Cooley, J. W. (1966). Harmonic Analysis Complex Fourier Series. SHARE Program Library No. SDA 3425.
Cooley, J. W. and Tukey, J. W. (1965). An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation, 19(90), 297–301.CrossRefGoogle Scholar
Dasgupta, B. and Chatterji, B. N. (1996). Fourier-Mellin transform based image matching algorithm. Journal of the Institution of Electronics and Telecommunication Engineers, 42(1), 3–9.Google Scholar
Castro, E. and Morandi, C. (1987). Registration of translated and rotated images using finite Fourier transforms. IEEE Pattern Analysis and Machine Intelligence, 9(52), 700–703.CrossRefGoogle ScholarPubMed
Edwards, A. L. (1976). The correlation coefficient. In An Introduction to Linear Regression and Correlation. San Francisco, CA: W. H. Freeman, pp. 33–46.Google Scholar
Good, I. J. (1958). The interaction algorithm and practical Fourier analysis. Journal of the Royal Statistical Society, Series B (Methodological), 20(2), 361–372.Google Scholar
Levenberg, K. (1944). A method for the solution of certain problems in least squares. Quarterly of Applied Mathematics, 2, 164–168.CrossRefGoogle Scholar
Marquardt, D. (1963). An algorithm for least-squares estimation of nonlinear parameters. Journal of Applied Mathematics, 11, 431–441.Google Scholar
Shannon, C. E. (1949). Communication in the presence of noise. Professional Institute of Radio Engineers, 37(1), 10–21; reprinted in Proceedings of the IEEE, 86(2), 447–457.Google Scholar
Shekarforoush, H., Berthod, M., and Zerubia, J. (1996). Subpixel image registration by estimating the polyphase decomposition of cross power spectrum. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 532–537.CrossRefGoogle Scholar
Singleton, R. C. (1967). On computing the fast Fourier transform. Communications of the ACM, 10(10), 647–654.CrossRefGoogle Scholar
Stone, H. S. (1998). Convolution theorems for linear transforms. IEEE Transactions on Signal Processing, 46(10), 2819–2821.CrossRefGoogle Scholar
Stone, H. S. (1999). Progressive wavelet correlation using Fourier techniques. IEEE Transactions on Signal Processing, 47(1), 97–107.CrossRefGoogle Scholar
Stone, H. S. and Li, C.-S. (1996). In Image matching by means of intensity and texture matching in the Fourier domain. In Proceedings of the SPIE Conference on Image and Video Databases, Storage and Retrieval for Still Image and Video Databases IV, San Jose, CA, Vol. 2670, pp. 337–344.CrossRefGoogle Scholar
Stone, H. S. and Shamoon, T. (1997). Search by content of partially occluded images. International Journal on Digital Libraries, 1(4), 329–343.CrossRefGoogle Scholar
Stone, H. S., Orchard, M., Chang, E.-C., and Martucci, S. (2001). A fast direct Fourier-based algorithm for subpixel registration of images. IEEE Transactions on Geoscience and Remote Sensing, 39(10), 2235–2243.CrossRefGoogle Scholar
Stone, H. S., Tao, B., and McGuire, M. (2003). Analysis of image registration noise due to rotationally dependent aliasing. Journal of Visual Communication and Image Representation, 14(2), 114–135.CrossRefGoogle Scholar
Strang, G. (1986). Introduction to Applied Mathematics. Wellesley, MA: Wellesley-Cambridge Press.Google Scholar
Unser, M. (2000). Sampling – 50 years after Shannon. Proceedings of the IEEE, 88(4), 569–587.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×