Implementation and Comparative Analysis of Three Shock Filters in MATLAB

This article presents MATLAB implementations and comparative analysis of three prominent shock filters: Osher-Rudin [OR90], Alvarez-Mazorra [AM94], and Gilboa-Sochen-Zeevi [GSZ02eccv, GSZ04pami]. We provide detailed explanations of each filter's underlying principles and algorithms, supplemented with implementation approaches using MATLAB's image processing toolbox. Key implementation aspects include gradient computation using central differences, Laplacian estimation for edge detection, and time-step optimization for numerical stability. The comparative evaluation examines performance across various scenarios including noise reduction, edge enhancement, and texture preservation. Through systematic testing with standardized image datasets, we analyze computational efficiency, qualitative results, and parameter sensitivity. This comparison provides valuable insights into the strengths and limitations of each filter, serving as a reference for researchers and engineers in selecting appropriate shock filtering techniques for computer vision and image processing applications. The accompanying MATLAB code demonstrates practical implementation details, featuring modular function design and parameter tuning methodologies.