H.S. Stiehl

Radial basis functions with compact support for elastic registration of medical images

Abstract Common elastic registration schemes based on landmarks and radial basis functions (RBFs) such as thin-plate splines or multiquadrics are global. Here, we introduce radial basis functions with compact support for elastic registration of medical images which have an improved locality, i.e. which allow to constrain elastic deformations to image parts where required. We give the theoretical background of these basis functions and compare them with other basis functions w.r.t. locality, solvability, and efficiency. A detailed comparison with the Gaussian as well as conditions for preserving topology is given. An important property of the used RBFs (Wendlands ψ-functions) is that they are positive definite. Therefore, in comparison to the use of the truncated Gaussian, the solvability of the resulting system of equations is always guaranteed. We demonstrate the applicability of our approach for synthetic as well as for 2D and 3D tomographic images.

Spline-based elastic image registration: integration of landmark errors and orientation attributes

We introduce a spline-based elastic registration scheme which is based on a well-defined minimizing functional for which the solution can be stated analytically. In this work, we consider the integration of anisotropic landmark errors as well as additional attributes at landmarks. As attributes we use orientations at landmarks and we incorporate the corresponding constraints through scalar products. With our approximation scheme it is thus possible to integrate statistical as well as geometric information as additional knowledge in elastic image registration. On the basis of synthetic as well as real tomographic images we show that this additional knowledge can significantly improve the registration result. In particular, we demonstrate that our scheme incorporating orientation attributes can preserve the shape of rigid structures (such as bone) embedded in an otherwise elastic material. This is achieved without selecting further landmarks and without a full segmentation of the rigid structures.

Elastic registration of medical images using radial basis functions with compact support

We introduce radial basis functions with compact support for elastic registration of medical images. With these basis functions the influence of a landmark on the registration result is limited to a circle in 2D and, respectively, to a sphere in 3D. Therefore, the registration can be locally constrained which especially allows to deal with rather local changes in medical images due to, e.g., tumor resection. An important property of the used RBFs is that they are positive definite. Thus, the solvability of the resulting system of equations is always guaranteed. We demonstrate our approach for synthetic as well as for 2D and 3D tomographic images.

Coupling of fluid and elastic models for biomechanical simulations of brain deformations using FEM

In order to improve the accuracy of image-guided neurosurgery, different biomechanical models have been developed to correct preoperative images with respect to intraoperative changes like brain shift or tumor resection. All existing biomechanical models simulate different anatomical structures by using either appropriate boundary conditions or by spatially varying material parameter values, while assuming the same physical model for all anatomical structures. In general, this leads to physically implausible results, especially in the case of adjacent elastic and fluid structures. Therefore, we propose a new approach which allows to couple different physical models. In our case, we simulate rigid, elastic and fluid regions by using the appropriate physical description for each material, namely either the Navier equation or the Stokes equation. To solve the resulting differential equations, we derive a linear matrix system for each region by applying the finite element method (FEM). Thereafter, the linear matrix systems are linked together, ending up with one overall linear matrix system. Our new approach has been tested and compared to a purely linear elastic model using synthetic as well as tomographic images. It turns out from our experiments, that the integrated treatment of rigid, elastic and fluid regions improves the physical plausibility of the predicted deformation results as compared to a purely linear elastic model.

Thin-plate spline approximation for image registration

The point-based registration technique of F.L. Bookstein (1989) can be seen as an interpolation problem. With this technique an elastic transformation based on thin-plate splines is determined which maps the source and target landmarks exactly to each other. However, in real applications the positions of the landmarks can only be determined approximately. Therefore, in this case an interpolation scheme is inadequate and should be substituted by an approximation scheme to take into account the localization errors. In this paper, the authors describe an approach for extending Booksteins method in this direction.

A comparison between BEM and FEM for elastic registration of medical images

The aim of medical image registration is to bring different images into the best possible spatial correspondence in order to obtain complementary information for clinical applications. When using physically-based techniques for image registration the transformation of images is typically obtained as the solution of partial differential equations of continuum mechanics. Because of the complexity of real boundary conditions, these equations can usually be solved with the help of numerical techniques only. One standard numerical method is the boundary element method (BEM) which allows to compute the solution exclusively through boundary integration. This paper investigates the applicability of BEM for registration of medical images and quantitatively assesses its advantages and disadvantages in comparison to the previously used finite element method (FEM).

A Biomechanical Model of the Human Head for Elastic Registration of MR-Images

The accuracy of image-guided neurosurgery generally suffers from brain deformations due to intraoperative changes, e.g. brain shift or tumor resection. In order to improve the accuracy, we developed a biomechanical model of the human head which can be employed for the correction of preoperative images. By now, the model comprises two different materials while the correction of the preoperative image is driven by a set of given landmark correspondences. Our approach has been tested on synthetic images and yields physically plausible results. Additionally, we carried out registration experiments with a preoperative MR image and a corresponding postoperative image simulating an intraoperative image. We found, that our approach yields good prediction results, even in the case when correspondences are given in a small area of the image only.