Abstract
This paper presents a method for constructing symmetric and transitive algorithms for registration of image sequences from image registration algorithms that do not have these two properties. The method is applicable to both rigid and nonrigid registration and it can be used with linear or periodic image sequences. The symmetry and transitivity properties are satisfied exactly (up to the machine precision), that is, they always hold regardless of the image type, quality, and the registration algorithm as long as the computed transformations are invertable. These two properties are especially important in motion tracking applications since physically incorrect deformations might be obtained if the registration algorithm is not symmetric and transitive. The method was tested on two sequences of cardiac magnetic resonance images using two different nonrigid image registration algorithms. It was demonstrated that the transitivity and symmetry errors of the symmetric and transitive modification of the algorithms could be made arbitrary small when the computed transformations are invertable, whereas the corresponding errors for the nonmodified algorithms were on the order of the pixel size. Furthermore, the symmetric and transitive modification of the algorithms had higher registration accuracy than the nonmodified algorithms for both image sequences.
Highlights
The process of aligning images so that the corresponding features can be related is called image registration [1]
While the result of the previous section holds for any registration operator that generates invertable transformations, here we illustrate the approach on two sequences of cardiac magnetic resonance images using two nonrigid image registration algorithms
Theorem 1 says that reference-based modification of any registration operator satisfies identity, symmetry, and transitivity on an image sequence
Summary
The process of aligning images so that the corresponding features can be related is called image registration [1]. Image registration methods have been discussed and classified in books [1,2,3,4] and surveys [5,6,7,8,9,10]. Most registration methods are ad hoc with assumptions often violated in practical applications. This results in a behavior that is often not predictable. A way to reduce the ad hoc nature of registration methods is to require them to satisfy certain properties. In [11], Ashburner et al proposed an approximately symmetric image registration method that uses symmetric priors. In [12], Christensen and Johnson proposed a registration algorithm that approximately satisfies the symmetry property. In [12], Christensen and Johnson proposed a registration algorithm that approximately satisfies the symmetry property. (Christensen and Johnson used the term “inverse consistency” for what we refer to as “symmetry.”) Their idea is to estimate the forward and reverse transformation simultaneously by minimizing an objective function composed of terms that measure the similarity between the two images and the consistency of the forward and reverse transformations
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