Level Set Method for Image Processing: Narrow Band Technique Implementation in MATLAB

The level set method is a partial differential equation-based image segmentation technique that transforms curve evolution problems into higher-dimensional level set function evolution. Its core principle involves implicitly representing moving interfaces, thereby eliminating topological constraints associated with parametric curve representation.

The narrow band technique serves as a critical optimization strategy for improving computational efficiency in level set methods. By updating only pixels within the interface's proximity (the narrow band region), it significantly reduces computational load. Unlike traditional level set approaches that require computations across the entire image domain, the narrow band technique confines calculations to a 5-10 pixel-wide strip surrounding the active contour. This is complemented by reinitialization operations to maintain the signed distance property of the level set function.

MATLAB implementation typically involves several key steps: First, initialize the level set function as a signed distance function using MATLAB's bwdist function. Then construct a velocity field based on image gradient information through functions like imgredient. During each iteration, update level set values only within the narrow band region using logical indexing, and solve the partial differential equation through finite difference methods (e.g., using central differences). To prevent level set function distortion, periodic reinitialization is implemented through distance transform recalculation or PDE-based reinitialization schemes.

Compared to conventional methods, this technique achieves 3-5 times faster computation speeds, making it particularly suitable for large-scale image processing scenarios like medical image segmentation. Narrow band width selection requires balancing computational efficiency against segmentation accuracy - excessively narrow bands may cause contour leakage while overly wide bands diminish acceleration benefits. Modern enhancements include adaptive narrow band techniques utilizing MATLAB's regionprops for dynamic band adjustment, and fast marching methods for efficient distance computation.