We present an information-theoretic approach to registration of DWI with explicit optimization over the orientational scale, with an additional focus on normalized mutual information as a robust information-theoretic similarity measure for DWI. The framework is an extension of the LOR-DWI density-based hierarchical scale-space model, that varies and optimizes over the integration, spatial, directional, and intensity scales. We extend the model to non-rigid deformations and show that the formulation provides intrinsic regularization through the orientational information. Our experiments illustrate that the proposed model deforms ODFs correctly and is capable of handling the classic complex challenges in DWI-registrations, such as the registration of fiber-crossings along with kissing, fanning and interleaving fibers. Our results clearly illustrate a novel promising regularizing effect, that comes from the nonlinear orientation-based cost function. We illustrate the properties of the different image scales, and show that including orientational information in our model make the model better at retrieving deformations compared to standard scalar-based registration.
Image registration refers to a process that transforms data into a shared coordinate system. For DWI, the common way to register two images is to use scalar-based methods on quantitative measures, such as the fractional anisotropy (FA) or the mean diffusivity (MD) @cite_27 . However, as such methods disregard most of the directional information in DWI, methods have been developed to also account for the reorientation of the diffusion profile. Most of these are created on top of scalar-based methods and iteratively reorients the gradients after changing the deformation field. Some of the most popular methods can be found in @cite_19 @cite_5 @cite_26 @cite_29 . However, registration frameworks have also been designed with an objective function that explicitly optimizes over the reorientation of the gradients, such as DTI-TK @cite_15 , DT-REFineD @cite_23 , and the more recent DR-TAMAS @cite_18 . These frameworks have been shown to generally outperform scalar-based frameworks for DWI @cite_14 @cite_13 @cite_35 @cite_25 .
@cite_35 @cite_18 @cite_26 @cite_14 @cite_29 @cite_19 @cite_27 @cite_23 @cite_5 @cite_15 @cite_13 @cite_25
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Abstract Registration plays an important role in group analysis of diffusion-weighted imaging (DWI) data. It can be used to build a reference anatomy for investigating structural variation or tracking changes in white matter. Unlike traditional scalar image registration where spatial alignment is the only focus, registration of DWI data requires both spatial alignment of structures and reorientation of local signal profiles. As such, DWI registration is much more complex and challenging than scalar image registration. Although a variety of algorithms has been proposed to tackle the problem, most of them are restricted by the diffusion model used for registration, making it difficult to fit to the registered data a different model. In this paper we describe a method that allows any diffusion model to be fitted after registration for subsequent multifaceted analysis. This is achieved by directly aligning DWI data using a large deformation diffeomorphic registration framework. Our algorithm seeks the optimal coordinate mapping by simultaneously considering structural alignment, local signal profile reorientation, and deformation regularization. Our algorithm also incorporates a multi-kernel strategy to concurrently register anatomical structures at different scales. We demonstrate the efficacy of our approach using in vivo data and report detailed qualitative and quantitative results in comparison with several different registration strategies. Registration is a prerequisite for fusion of geometrically distorted images. Traditionally, intensity-based image registration methods are preferred to feature-based ones due to higher accuracy of the former than that of the latter. To reduce computational load, image registration is often carried out using the approximate-level coefficients of a wavelet-like transform. Directional selectivity of the transform and the objective function used for the coefficients play vital roles in the alignment process of images. This paper introduces an image registration algorithm that uses the approximate-level coefficients of the curvelet transform, directional selectivity of which is better than many wavelet-like transforms. A conditional entropy-based objective function is developed for registration using a suitable probabilistic model of the curvelet coefficients of images. Suitability of the probability distribution of the coefficients is validated using a standard method to assess goodness of fit. To align the distorted images, the affine transformation that possesses parameters related to the translation, rotation, scaling, and shearing is used. Extensive experimentations are carried out to test the performance of the proposed registration method considering that the images are synthetically or naturally distorted. Experimental results show that performance of the proposed registration method is superior to existing methods in terms of commonly used performance metrics. 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 A to image B being the inverse of the optimal mapping from B to A. The method does not require that landmarks be specified, and the minimizer of the distance functional involved is uniques 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 L2 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 extend this method to take into account changes in intensity, and show that it is well suited for applications such as image morphing. In this paper, we propose the DT-REFinD algorithm for the diffeomorphic nonlinear registration of diffusion tensor images. Unlike scalar images, deforming tensor images requires choosing both a reorientation strategy and an interpolation scheme. Current diffusion tensor registration algorithms that use full tensor information face difficulties in computing the differential of the tensor reorientation strategy and consequently, these methods often approximate the gradient of the objective function. In the case of the finite-strain (FS) reorientation strategy, we borrow results from the pose estimation literature in computer vision to derive an analytical gradient of the registration objective function. By utilizing the closed-form gradient and the velocity field representation of one parameter subgroups of diffeomorphisms, the resulting registration algorithm is diffeomorphic and fast. We contrast the algorithm with a traditional FS alternative that ignores the reorientation in the gradient computation. We show that the exact gradient leads to significantly better registration at the cost of computation time. Independently of the choice of Euclidean or Log-Euclidean interpolation and sum of squared differences dissimilarity measure, the exact gradient achieves better alignment over an entire spectrum of deformation penalties. Alignment quality is assessed with a battery of metrics including tensor overlap, fractional anisotropy, inverse consistency and closeness to synthetic warps. The improvements persist even when a different reorientation scheme, preservation of principal directions, is used to apply the final deformations.