Classical Two-Dimensional Empirical Mode Decomposition

This presents a classical implementation of two-dimensional Empirical Mode Decomposition (EMD) code specifically designed for image decomposition applications. The algorithm decomposes images into multiple intrinsic mode functions (IMFs) through an iterative sifting process that identifies local extrema and interpolates envelopes using spline interpolation methods. Key implementation aspects include boundary handling techniques to minimize edge effects, stopping criteria based on standard deviation thresholds between consecutive sifting iterations, and efficient matrix operations for handling 2D spatial data. The decomposition process enables separation of image features at different spatial scales, allowing researchers to extract fine details, textures, and background components for advanced analysis and processing. This implementation demonstrates core EMD concepts including the sifting procedure, IMF extraction, and residue calculation, making it particularly valuable for individuals studying image processing, signal decomposition, and multi-scale analysis techniques. The code structure follows modular design principles with separate functions for extremum detection, envelope construction, and IMF validation, facilitating both educational understanding and practical adaptation for specific research needs. This robust implementation serves as an excellent foundation for exploring empirical mode decomposition concepts and their applications in digital image processing.