Zig-Zag Transformation and Inverse Transformation for Grayscale Images of Arbitrary Size

This article explores the implementation of zig-zag transformation and inverse transformation for grayscale images of arbitrary dimensions, as well as applying zig-zag scanning to DCT-processed images to identify frequency domain information. The implementation involves creating a custom algorithm that tracks coordinates in a zig-zag pattern through nested loops or coordinate mapping functions. For the inverse transformation, we reconstruct the image matrix by reversing the scanning pattern using index mapping techniques. When processing DCT-transformed images, the zig-zag scan systematically rearranges coefficients from low to high frequencies, allowing efficient extraction of mid-frequency components through array slicing operations. The article delves into practical MATLAB or Python implementations using matrix manipulation functions like reshape() and advanced indexing, demonstrating how to handle edge cases in non-square matrices through conditional boundary checks. Through this comprehensive guide, you'll gain insights into image processing techniques that can be applied to real-world problems such as image compression and frequency analysis, with detailed explanations of key functions like zigzag scanning algorithms and coefficient reorganization methods.