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Optimal mass transport for registration and warping (2004)
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| Venue: | International Journal on Computer Vision |
| Citations: | 58 - 9 self |
BibTeX
@ARTICLE{Haker04optimalmass,
author = {Steven Haker and Lei Zhu and Allen Tannenbaum and Sigurd Angenent},
title = {Optimal mass transport for registration and warping},
journal = {International Journal on Computer Vision},
year = {2004},
volume = {60},
pages = {225--240}
}
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Abstract
Image registration is the process of establishing a common geometric reference frame between two or more image data sets possibly taken at different times. In this paper we present a method for computing elastic registration and warping maps based on the Monge–Kantorovich theory of optimal mass transport. This mass transport method has a number of important characteristics. First, it is parameter free. Moreover, it utilizes all of the grayscale data in both images, places the two images on equal footing and is symmetrical: the optimal mapping from image to ¡ image being the inverse of the optimal mapping ¡ from to £ ¢ The method does not require that landmarks be specified, and the minimizer of the distance functional involved is unique; there are no other local minimizers. Finally, optimal transport naturally takes into account changes in density that result from changes in area or volume. Although the optimal transport method is certainly not appropriate for all registration and warping problems, this mass preservation property makes the Monge-Kantorovich approach quite useful for an interesting class of warping problems, as we show in this paper. Our method for finding the registration mapping is based on a partial differential equation approach to the minimization of ¤¦ ¥ the Kantorovich–Wasserstein or “Earth Mover’s Distance ” under a mass preservation constraint. We show how this approach leads to practical algorithms, and demonstrate our method with a number of examples, including those from the medical field. We also extended this method to take into account changes in intensity, and show that it is well suited for applications such as image morphing. A. Image Registration I.
Keyphrases
optimal mass transport account change optimal mapping image registration grayscale data monge-kantorovich approach medical field monge kantorovich theory warping problem local minimizers optimal transport method registration mapping important characteristic partial differential equation approach kantorovich wasserstein elastic registration common geometric reference frame mass preservation property equal footing interesting class image morphing different time practical algorithm mass preservation constraint earth mover image data set optimal transport mass transport method
