Adaptive FEM-based nonrigid image registration using truncated hierarchical B-splines

Abstract

a b s t r a c tWe present an efficient approach of Finite Element Method (FEM)-based nonrigid image registration, in which the spatial transformation is constructed using truncated hierarchical B-splines (THB-splines). The image registration framework minimizes an energy functional using an FEM-based method and thus involves solving a large system of linear equations. This framework is carried out on a set of successively refined grids. However, due to the increased number of control points during subdivision, large linear systems are generated which are generally demanding to solve. Instead of using uniform subdivision, an adaptive local refinement scheme is carried out, only refining the areas of large change in deformation of the image. By incorporating the key advantages of THB-spline basis functions such as linear independence, partition of unity and reduced overlap into the FEM-based framework, we improve the matrix sparsity and computational efficiency. The performance of the proposed method is demonstrated on 2D synthetic and medical images.

Adjusting fictitious domain parameters for fairly priced image-based modeling: Application to the regularization of Digital Image Correlation

“…Finally, a series of other prospects could also be envisioned such as adaptive refinement for materials with multi-scale micro-structures [10,36], extension to multi-phase (> 2) materials using more advanced modellings such as those based on the Cut-FEM method [28]. In addition, we recall that the threshold value used for characterizing the geometric level-set is a user-defined parameter herein and is one of the crucial parameters.…”

“…We choose to adopt here the B-spline FCM due to its computational simplicity related to the tensor product nature of B-spline basis functions and its high regularity. That is also interesting for the regularization of image registration [36,61] (see Section 3 below). The B-spline FCM consists in embedding the domain of analysis in a simple rectangular domain and transferring the geometrical representation from the mesh to the integration scheme.…”

“…After a first step devoted to the identification of a level-set based smooth boundary of the specimen that is imaged, we suggest constructing an automated immersed boundary DIB model using a regular high order B-spline grid in the same spirit as in [10]. The spline support will then be used as the discretization basis for image registration (same idea as in [34,35,36,37] for instance). Returning to the area of DIB models, the contribution of our work is to adjust the modeling parameters (element size, polynomial degree, quadrature rule) so that the discretization error is comparable to that produced through the imaging (i.e., pixelation) of the real specimen.…”

Injective hierarchical free-form deformations using THB-splines

“…In contrast, THB-splines offer a clear hierarchical structure, which enables us to selectively hide control points from certain levels in the user interface [7,14], and offer polynomial basis functions with reduced supports when compared to non-truncated alternatives [13]. Their locality and numerical efficiency are ideally suited for FEMbased non-rigid image registration [25,26] and for performance-critical scenarios such as real-time FFDs performed on dense meshes. This also allows the use of more demanding techniques such as self-intersection detection and prevention [12] without sacrificing interactivity.…”

Non-rigid registration of medical images using a hierarchical framework with normalized mutual information

“…In the past decades, a large number of methods have been proposed for non-rigid registration, such as feature-based algorithms [5][6][7], intensity-based approaches [8][9][10], and physical models [11,12]. However, very few methods focus on registration of pelvis images with reasonable results.…”