Bicubic Interpolation: Principles and MATLAB Source Code Implementation

Bicubic interpolation is a high-precision interpolation method commonly used in image processing. By considering 16 neighboring pixels around the target pixel and applying cubic polynomial weighting calculations, it produces smoother results compared to bilinear interpolation. This method is particularly suitable for image processing scenarios requiring high-quality enlargement.

In implementation principles, bicubic interpolation consists of two core components: basis function calculation and interpolation operations. The basis function typically uses the BiCubic function, which reaches its maximum at x=0 and gradually decays as the absolute value of x increases. This characteristic ensures that the influence of neighboring pixels on the target pixel decreases with distance.

In MATLAB implementation, the algorithm is typically decomposed into two files: a main file responsible for controlling the interpolation calculation flow, and a separate file implementing the basis function calculation. This modular design creates clearer code structure and facilitates debugging and maintenance. The main function would handle coordinate mapping and pixel weighting, while the basis function file would compute coefficients using cubic convolution algorithms.

In practical applications, the bicubic interpolation algorithm needs to handle boundary conditions and may require preprocessing of input images. Due to its high computational complexity, algorithm performance optimization is a key consideration during implementation. By designing appropriate data structures and computation flows, such as vectorizing pixel operations and precomputing basis coefficients, the execution efficiency of bicubic interpolation can be significantly improved.