Frequency domain formulation of active parametric deformable models

Abstract

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.

Frequency-domain active contours solution to evaluate intima–media thickness of the common carotid artery

“…Initialization includes speckle reduction, correlation with a model and morphological processing. After that, the Fourier domain implementation of the snakes algorithm is applied, which produces relevant computational cost savings [14]. Final contours are smooth due to the use of B-splines as shape function.…”

“…To reduce it, the proposal by Weruaga et al [14] of using a frequency formulation is implemented. The computational savings vary from N 2 in the classical formulation to N log 2 N, being N the number of nodes.…”

Automatic Active Contour-Based Segmentation and Classification of Carotid Artery Ultrasound Images

“…An alternative formulation has been proposed by Weruaga et al [17] for translation of the energy function (9) in frequency domain. In this procedure, matrix inversion is avoided because in frequency domain, it becomes a point-wise inversion.…”

Automatic Carotid Artery Image Segmentation using Snake Based Model

“…But an alternative formulation has been proposed by Weruaga et al [13] for translation of the energy function (7) into frequency domain. Matrix inversion is avoided through this procedure because it becomes a point-wise inversion in frequency domain.…”