Watermark Embedding in Images After Contourlet Transform

In the original context, we can further elaborate to describe in greater detail the process of watermark embedding after Contourlet transformation of images. Initially, through Contourlet transform – a multi-scale and directional image representation method – we decompose the image into multiple subbands with enhanced resolution and superior localized feature characterization. This transformation can be implemented using MATLAB's contourlet toolbox or custom algorithms involving pyramidal directional filter banks (PDFB). Subsequently, we apply digital watermarking techniques to the transformed coefficients, embedding hidden information into specific directional subbands. This embedding process typically involves modifying coefficient values in selected frequency domains using quantization-based or spread-spectrum approaches, ensuring visual imperceptibility through psycho-visual models and energy threshold constraints. Finally, during verification, we employ corresponding decoding algorithms that reverse the transformation process and extract watermark information using correlation detection or statistical analysis methods, thereby validating image integrity and authenticity through embedded signature matching.