Design of B-spline multidimensional deformable models in the frequency domain

Deformable models are mathematical tools which are able to emulate physical characteristics of objects in image processing. In the original formulation, 1D and 2D models are defined in the spatial domain. These models use the finite element method (FEM) for the spatial discretization. Subsequent work proposes a frequency-based approach of the deformable models, also based on the FEM, which leads to a simple formulation and design. The Fourier-based approach offers important computational savings. In addition, each frequency component of the model acts as a system which is independent of the rest of components. This allows us to generalize the formulation of multidimensional deformable models, which are presented in this paper using B-spline as shape function for the FEM. This process allows us to obtain a computationally efficient iterative system in matrix form, suitable for models of any number of dimensions. These models can be used for fast segmentation and tracking of 2D and 3D objects with non-rigid motion or deformation. Other applications such as simulation of soft-tissue deformation are also feasible. © 2012 Elsevier Ltd.