Frequency domain formulation of active parametric deformable models

Active deformable models are simple tools, very popular in computer vision and computer graphics, for solving ill-posed problems or mimic real physical systems. The classical formulation is given in the spatial domain, the motor of the procedure is a second-order linear system, and rigidity and elasticity are the basic parameters for its characterization. This paper proposes a novel formulation based on a frequency-domain analysis: The internal energy functional and the Lagrange minimization are performed entirely in the frequency domain, which leads to a simple formulation and design. The frequency-based implementation offers important computational savings in comparison to the original one, a feature that is improved by the efficient hardware and software computation of the FFT algorithm. This new formulation focuses on the stiffness spectrum, allowing the possibility of constructing deformable models apart from the elasticity and rigidity-based original formulation. Simulation examples validate the theoretical results.