A New Class of Elastic Body Splines for Nonrigid Registration of Medical Images

3D ultrasound-CT registration of the liver using combined landmark-intensity information

“…The combined registration process might not be able to compensate the initial displacements in these regions. Other interpolating functions like GEBS ( [31]) are promising alternatives.…”

“…Pure non-rigid landmark registration has already been applied to MRI-ultrasound registration [26]. Usually thin-plate splines (TPS) [27][28][29] are used as transformations of non-rigid landmark registration, but promising advancements have been published: elastic body splines (EBS) [30] and Gaussian elastic body splines (GEBS) [31]. In addition, anisotropic localization uncertainties have been considered leading to approximating TPS [32] or GEBS [33].…”

Analysis of Compactly Supported Transformations for Landmark-based Image Registration

“…In order to test the different CSRBF transformation schemes, we obtain several numerical results on some test cases. Here, for brevity, we refer only to two examples in [10,15], which simulate typical medical cases where image portions scale or shift. These image portions represent rigid objects embedded in elastic material changing their position or form.…”

“…It may be viewed as a very schematic model for a tumor resection in surrounding elastic brain tissue. In this model (see [15]) the outer circle corresponds to the skull bone, which is assumed to be rigid. The inner circle represents the boundary of the tumor, whereas the space between the inner and the outer circle is assumed to be filled with elastic material, which corresponds to brain tissue.…”

“…Since using globally supported RBFs, as for example the thin plate spline or the Gaussian, a single landmark pair change may influence the whole registration result, in the last decade several methods have been presented to circumvent this disadvantage, such as Wendland's compactly supported radial basis functions (CSRBFs) [10], elastic body splines (EBSs) [15], the modified inverse distance weighted method (IDWM) [4,5], and a spline method [1,2]. These interpolation techniques, giving rise to compactly supported or local mappings, handle well images locally deformed.…”