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翻译：李睿钦假名标注snapdragon you too指导老师：刘文军
Medical image registration with partial data
Senthil Periaswamyxsysinfo， Hany Farid
psalter
The goal of image registration is to find a transformation that aligns one image to another. Medical image registration has emerged from this broad area of rearch as a particularly active field. This activity is due in part to the many clinical applications including diagnosis, longitudinal studies, and surgical planning, and to the need for registration across different imaging modalities (e.g., MRI, CT, PET, X-ray, etc.). Medical image registration, however, still prents many challenges. Several notable difficulties are (1) the transformation between images can vary widely and be highly non-rigid in nature; (2) images acquired from different modalities may differ significantly in overall appearance and resolution; (3) there may not be a one-to-one correspondence between the images (missing/partial data); 阿根廷 英文
and (4) each imaging modality introduces its own unique challenges, making it difficult to develop a single generic registration algorithm.
In estimating the transformation that aligns two images we must choo: (1) to estimate the transformation between a small number of extracted features, or between the complete unprocesd intensity images; (2) a model that describes the geometric transformation; (3) whether to and how to explicitly model intensity changes; (4) an error metric that incorporates the previous three choices; and (5) a minimization technique for minimizing the error metric, yielding the desired transformation.
Feature-bad approaches extract a (typically small) number of corresponding landmarks or features between the pair of images to be registered. The overall transformation is estimated from the features. Common features include corresponding points, edges, contours or surfaces. The features may be specified manually or extracted automatically. Fiducial markers may also be ud as features; the markers are usually lected to be visible in different modalities. Feature-bad approaches have the advanta
recently时态ge of greatly reducing computational complexity. Depending on the feature extraction process, the approaches may also be more robust to intensity variations that ari during, for example, cross modality registration. Also, features may be chon to help reduce nsor noi. The approaches can be, however, highly nsitive to the accuracy of the feature extraction. Intensity-bad approaches, on the other hand, estimate the transformation between the entire intensity images. Such an approach is typically more computationally demanding, but avoids the difficulties of a feature extraction stage.英文大写字母
Independent of the choice of a feature- or intensity-bad technique, a model describing the geometric transform is required. A common and straightforward choice is a model that embodies a single global transformation. The problem of estimating a global translation and rotation parameter has been studied in detail, and a clod form solution was propod by Schonemann. Other clod-form solutions include methods bad on singular value decomposition (SVD), eigenvalue-eigenvector decomposition and unit quaternions. One idea for a global transformation model is to u polynomials. For exam
ple, a zeroth-order polynomial limits the transformation to simple translations, a first-order polynomial allows for an affine transformation, and, of cour, higher-order polynomials can be employed yielding progressively more flexible transformations. For example, the registration package Automated Image Registration (AIR) can employ (as an option) a fifth-order polynomial consisting of 168 parameters (for 3-D registration). The global approach has the advantage that the model consists of a relatively small number of parameters to be estimated, and the global nature of the model ensures a consistent transformation across the entire image. The disadvantage of this approach is that estimation of higher-order polynomials can lead to an unstable transformation, especially near the image boundaries. In addition, a relatively small and local perturbation can cau disproportionate and unpredictable changes in the overall transformation. An alternative to the global approaches are techniques that model the global transformation as a piecewi collection of local transformations. For example, the transformation between each local region may be modeled with a low-order polynomial, and global consistency is enforced via some form of a smoothness constraint. The advan
tage of such an approach is that it is capable of modeling highly nonlinear transformations without the numerical instability of high-order global models. The disadvantage is one of computational inefficiency due to the significantly larger number of model parameters that need to be estimated, and the need to guarantee global consistency. Low-order polynomials are, of cour, only one of many possible local models that may be employed. Other local models include B-splines, thin-plate splines, and a multitude of related techniques. The package Statistical Parametric Mapping (SPM) us the low-frequency discrete cosine basis functions, where a bending-energy function is ud to ensure global consistency. Physics-bad techniques that compute a local geometric transform include tho bad on the Navier–Stokes equilibrium equations for linear elastici and tho bad on viscous fluid approaches.
Under certain conditions a purely geometric transformation is sufficient to model the transformation between a pair of images. Under many real-world conditions, however, the images undergo changes in both geometry and intensity (e.g., brightness and contrast). Many registration techniques attempt to remove the intensity differences with a pre-pro
清远盛兴中英文学校cessing stage, such as histogram matching or homomorphic filtering. The issues involved with modeling intensity differences are similar to tho involved in choosing a geometric model. Becau the simultaneous estimation of geometric and intensity changes can be difficult, few techniques build explicit models of intensity differences. A few notable exceptions include AIR, in which global intensity differences are modeled with a single multiplicative contrast term, and SPM in which local intensity differences are modeled with a basis function approach.
Having decided upon a transformation model, the task of estimating the model parameters begins. As a first step, an error function in the model parameters must be chon. This error function should embody some notion of what is meant for a pair of images to be registered. Perhaps the most common choice is a mean square error (MSE), defined as the mean of the square of the differences (in either feature distance or intensity) between the pair of images. This metric is easy to compute and often affords simple minimization techniques. A variation of this metric is the unnormalized correlation coefficient applicable to intensity-bad techniques. This error metric is defined as the su
m of the point-wi products of the image intensities, and can be efficiently computed using Fourier techniques. A disadvantage of the error metrics is that images that would qualitatively be considered to be in good registration may still have large errors due to, for example, intensity variations, or slight misalignments. Another error metric (included in AIR) is the ratio of image uniformity (RIU) defined as the normalized standard deviation of the ratio of image intensities. Such a metric is invariant to overall intensity scale differences, but typically leads to nonlinear minimization schemes. Mutual information, entropy and the Pearson product moment cross correlation are just a few examples of other possible error functions. Such error metrics are often adopted to deal with the lack of an explicit model of intensity transformations .
