MATLAB Implementation of Bicubic Interpolation for Standard Lena Test Image

Bicubic interpolation is a high-quality image scaling technique that calculates interpolated values by computing weighted averages of 16 neighboring pixels around the target pixel, preserving more detail compared to bilinear interpolation. When implementing this algorithm in MATLAB, the following core logic needs to be addressed: Image Reading and Preprocessing First, load the standard Lena test image (built-in MATLAB image in earlier versions, requires manual import in newer versions). Convert the original image to grayscale or maintain RGB channels for separate processing, ensuring the data format is double-precision floating-point for accurate calculations. In code implementation, this typically involves using `imread()` followed by `im2double()` conversion. Coordinate Mapping and Weight Calculation For each pixel in the output image, perform reverse mapping to floating-point coordinates in the input image to determine the surrounding 4x4 pixel region. Use cubic spline functions (such as BiCubic basis functions) to calculate weights for 16 adjacent pixels, where weights depend on the distance between the target point and each neighboring pixel. The implementation requires nested loops for coordinate transformation and weight matrix generation using mathematical functions like `abs()` and power operations. Boundary Handling and Pixel Composition When interpolation points approach image edges, handle out-of-bound coordinates through mirror padding or truncation methods. For RGB images, calculate interpolation results independently for each channel, then merge channels and clamp pixel values within the 0-255 range. Code implementation typically uses conditional statements for boundary checks and `cat()` function for channel merging. Extension Concepts Performance Optimization: MATLAB's `imresize` function natively supports bicubic interpolation and can be called directly, but custom implementation helps understand algorithm details and allows for parameter customization. Application Comparison: Compared to nearest-neighbor interpolation (visible aliasing) and bilinear interpolation (edge blurring), bicubic interpolation better preserves texture details and sharpness when enlarging images. Variant Improvements: Adjust basis function parameters or combine with edge detection algorithms to further optimize interpolation results. Potential code enhancements include implementing Lanczos filters or adaptive interpolation based on local image characteristics. (Note: Actual code implementation requires coordinate transformation loops, weight matrix generation, and pixel value calculation steps - this description focuses on the logical framework and implementation approach.)