ABSTRACT
This chapter introduces mathematical preliminaries for performing digital watermarking techniques for different embedding purposes and domains. It presents some commonly used operations in digital watermarking, including least-significant-bit substitution, discrete Fourier transform, discrete cosine transform, discrete wavelet transform, random sequence generation, the chaotic map, error correction code, and set partitioning in hierarchical tree. Least-significant-bit (LSB) substitution is often used in image watermarking for embedding watermarks into a host image. The idea of LSB substitution is to replace the LSB of a pixel with the watermark, because this has little effect on the appearance of the carrier message. The Fourier series was originally motivated by the problem of heat conduction, and later found a vast number of applications as well as providing a basis for other transforms, such as discrete cosine transform (DCT). Many video and image compression algorithms apply the DCT to transform an image to the frequency domain and perform quantization for data compression.
