Variational B-spline level-set: a linear filtering approach for fast deformable model evolution.

Area of Science:

• Computer Vision
• Image Processing
• Computational Mathematics

Background:

• Traditional level-set active contours often rely on discrete representations of implicit functions.
• This can limit flexibility and introduce discretization errors in image segmentation.

Purpose of the Study:

• To propose a novel continuous formulation for level-set active contours using B-spline basis functions.
• To develop an efficient and intrinsically smoothing image segmentation algorithm based on this formulation.

Main Methods:

• Modeling the implicit function of active contours as a continuous parametric function on a B-spline basis.
• Restricting the variational problem to the B-spline space for direct minimization of the energy functional.
• Expressing minimization steps as convolution operations, leveraging B-spline separability for efficient 1-D convolutions.

Main Results:

• The formulation allows direct minimization in terms of B-spline coefficients.
• Each minimization step can be efficiently computed via separable 1-D convolutions.
• The level-set evolution is interpreted as filtering with a B-spline kernel, providing controllable intrinsic smoothing.

Conclusions:

• The proposed B-spline-based active contour model offers an efficient and stable approach to image segmentation.
• The intrinsic smoothing is explicitly controllable via B-spline degree and scale.
• The method demonstrates effectiveness on both simulated and experimental image data across various domains.