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Registration is a technique nowadays commonly used in medical imaging. A drawback of most of the current registration schemes is that all tissue is being considered as non-rigid (Staring et al., Proceedings of the SPIE 2006, vol. 6144, pp. 1–10, ). Therefore, rigid objects in an image, such as bony structures or surgical instruments, may be transformed non-rigidly. In this paper, we integrate the concept of local rigidity to the FLexible Image Registration Toolbox (FLIRT) (Haber and Modersitzki, in SIAM J. Sci. Comput. 27(5):1594–1607, 2006; Modersitzki, Numerical Methods for Image Registration, ). The idea is to add a penalty for local non-rigidity to the cost function and thus to penalize non-rigid transformations of rigid objects. As our examples show, the new approach allows the maintenance of local rigidity in the desired fashion. For example, the new scheme can keep bony structures rigid during registration. We show, how the concept of local rigidity can be integrated in the FLIRT approach and present the variational backbone, a proper discretization, and a multilevel optimization scheme. We compare the FLIRT approach to the B-spline approach. As expected from the more general setting of the FLIRT approach, our examples demonstrate that the FLIRT results are superior: much smoother, smaller deformations, visually much more pleasing. [ABSTRACT FROM AUTHOR]

The physical (microtomy), optical (microscopy), and radiologic (tomography) sectioning of biological objects and their digitization lead to stacks of images. Due to the sectioning process and disturbances, movement of objects during imaging for example, adjacent images of the image stack are not optimally aligned to each other. Such mismatches have to be corrected automatically by suitable registration methods. Here, a whole brain of a Sprague Dawley rat was serially sectioned and stained followed by digitizing the 20 μm thin histologic sections. We describe how to prepare the images for subsequent automatic intensity based registration. Different registration schemes are presented and their results compared to each other from an anatomical and mathematical perspective. In the first part we concentrate on rigid and affine linear methods and deal only with linear mismatches of the images. Digitized images of stained histologic sections often exhibit inhomogenities of the gray level distribution coming from staining and/or sectioning variations. Therefore, a method is developed that is robust with respect to inhomogenities and artifacts. Furthermore we combined this approach by minimizing a suitable distance measure for shear and rotation mismatches of foreground objects after applying the principal axes transform. As a consequence of our investigations, we must emphasize that the combination of a robust principal axes based registration in combination with optimizing translation, rotation and shearing errors gives rise to the best reconstruction results from the mathematical and anatomical view point. Because the sectioning process introduces nonlinear deformations to the relative thin histologic sections as well, an elastic registration has to be applied to correct these deformations. In the second part of the study a detailed description of the advances of an elastic registration after affine linear registration of the rat brain is given. We found quantitative evidence that affine linear registration is a suitable starting point for the alignment of histologic sections but elastic registration must be performed to improve significantly the registration result. A strategy is presented that enables to register elastically the affine linear preregistered~ rat brain sections and the first one hundred images of serial histologic sections through both occipital lobes of a human brain (6112 images). Additionally, we will describe how a parallel implementation of the elastic registration was realized. Finally, the computed force fields have been applied here for the first time to the morphometrized data of cells determined automatically by an image analytic framework. [ABSTRACT FROM AUTHOR]

In this paper, we suggest a variational model for optic flow computation based on non-linearised and higher order constancy assumptions. Besides the common grey value constancy assumption, also gradient constancy, as well as the constancy of the Hessian and the Laplacian are proposed. Since the model strictly refrains from a linearisation of these assumptions, it is also capable to deal with large displacements. For the minimisation of the rather complex energy functional, we present an efficient numerical scheme employing two nested fixed point iterations. Following a coarse-to-fine strategy it turns out that there is a theoretical foundation of so-called warping techniques hitherto justified only on an experimental basis. Since our algorithm consists of the integration of various concepts, ranging from different constancy assumptions to numerical implementation issues, a detailed account of the effect of each of these concepts is included in the experimental section. The superior performance of the proposed method shows up by significantly smaller estimation errors when compared to previous techniques. Further experiments also confirm excellent robustness under noise and insensitivity to parameter variations. [ABSTRACT FROM AUTHOR]

An image registration algorithm is developed to estimate dense motion vectors between two images using the coarse-to-fine wavelet-based motion model. This motion model is described by a linear combination of hierarchical basis functions proposed by Cai and Wang ( SIAM Numer. Anal., 33(3):937–970, 1996). The coarser-scale basis function has larger support while the finer-scale basis function has smaller support. With these variable supports in full resolution, the basis functions serve as large-to-small windows so that the global and local information can be incorporated concurrently for image matching, especially for recovering motion vectors containing large displacements. To evaluate the accuracy of the wavelet-based method, two sets of test images were experimented using both the wavelet-based method and a leading pyramid spline-based method by Szeliski et al. (International Journal of Computer Vision, 22(3):199–218, 1996). One set of test images, taken from Barron et al. (International Journal of Computer Vision, 12:43–77, 1994), contains small displacements. The other set exhibits low texture or spatial aliasing after image blurring and contains large displacements. The experimental results showed that our wavelet-based method produced better motion estimates with error distributions having a smaller mean and smaller standard deviation. [ABSTRACT FROM AUTHOR]

In clinical practice, Digital Subtraction Angiography (DSA) is a powerful technique for the visualization of blood vessels in the human body. The diagnostic relevance of the images is often reduced by artifacts which arise from the misalignment of successive images in the sequence, due to patient motion. In order to improve the quality of the subtraction images, several registration techniques have been proposed. However, because of the required computation times, it has never led to algorithms that are fast enough so as to be acceptable for integration in clinical applications. In this paper, a new approach to the registration of digital angiographic images is proposed. It involves an edge-based selection of control points for which the displacement is computed by means of template matching, and from which the complete displacement vector field is constructed by means of interpolation. The final warping of the images according to the calculated displacement vector field is performed real-time by graphics hardware. Experimental results with several clinical data sets show that the proposed algorithm is both effective and very fast. [ABSTRACT FROM AUTHOR]