Image Processing Based on Polynomial Interpolation

In this document, I will provide detailed information about MATLAB implementations for image processing based on polynomial interpolation. Beyond bicubic interpolation and spline interpolation, several other interpolation methods are available for implementation.

First, let's examine bicubic interpolation. This widely-used interpolation method is commonly employed for image scaling (both enlargement and reduction). It generates new pixel values by performing smooth interpolation between existing pixels, thereby enhancing image quality. In MATLAB implementation, this typically involves using the imresize function with the 'bicubic' parameter, which calculates new pixel values using a weighted average of 16 surrounding pixels through cubic convolution.

Another common interpolation approach is spline interpolation. This method generates new pixel values by fitting smooth curves between data points, producing more continuous and natural-looking image results. MATLAB's spline interpolation can be implemented using functions like interp2 with 'spline' option, which constructs piecewise polynomial functions that pass through known data points while maintaining continuity in derivatives.

In addition to these two methods, there are other polynomial interpolation techniques for image processing, such as Lagrange interpolation and Newton interpolation. Each method has distinct advantages and specific application scenarios. For instance, Lagrange interpolation provides exact polynomial fitting at data points but may suffer from Runge's phenomenon with high-degree polynomials, while Newton interpolation offers computational efficiency through divided differences. These can be implemented in MATLAB using custom functions that handle the respective polynomial basis functions and coefficient calculations.

I hope these detailed explanations help you better understand the content and implementation approaches of polynomial interpolation-based image processing techniques in MATLAB.