Linear Interpolation Implemented in MATLAB

Linear interpolation, nearest neighbor interpolation, and bicubic spline interpolation implemented in MATLAB are commonly used image interpolation methods. Linear interpolation works by calculating new pixel values along straight lines between two known pixels using the formula: pixel_value = (1-t)*pixel1 + t*pixel2, where t represents the interpolation parameter between 0 and 1. This method can be implemented using MATLAB's interp1 function or custom grid-based calculations. Nearest neighbor interpolation assigns each new pixel the value of the closest known pixel, which can be efficiently coded using rounding operations and distance calculations with minimal computational overhead. Bicubic spline interpolation employs a series of cubic polynomial functions to approximate grayscale values, typically using 16 neighboring pixels to compute each new pixel value through weighted averaging. MATLAB's imresize function with the 'bicubic' parameter implements this algorithm, which involves solving cubic convolution equations for smoother transitions. These interpolation techniques play crucial roles in image processing by significantly enhancing image resolution and quality, resulting in clearer and more realistic images through appropriate pixel value estimation algorithms.