Algorithm Implementation for Converting Images from Cartesian to Polar Coordinate System in MATLAB

Implementing image transformation from Cartesian to polar coordinate systems in MATLAB is a common image processing task, particularly useful for analyzing circular or rotationally symmetric features in images. The core principle involves remapping each pixel from XY Cartesian coordinates to radius-and-angle-based polar coordinates. The conversion process consists of two main steps: coordinate remapping and interpolation processing. Since polar grid points don't perfectly align with original Cartesian pixel locations, interpolation methods must be used to calculate pixel values in the new coordinate system. In MATLAB implementation, this typically involves using functions like `meshgrid` to create polar coordinate grids and `interp2` for interpolation operations. In practical MATLAB implementation, we typically create a polar coordinate grid where the horizontal axis represents angle (usually ranging from 0 to 2π) and the vertical axis represents radius (from 0 to the maximum distance from the image center to corners). The algorithm then calculates corresponding positions in the original Cartesian coordinate system for each point in this polar grid, using methods like bilinear interpolation to obtain pixel values. This can be implemented using coordinate transformation formulas: x = r*cos(θ) and y = r*sin(θ), with careful handling of coordinate shifts to align with image center. Several key considerations are crucial during implementation: first, determining the polar coordinate origin, typically set at the image center using `floor(size(image)/2)`; second, handling boundary conditions, especially when polar radius exceeds original image boundaries, which can be managed through zero-padding or boundary replication; third, selecting appropriate interpolation methods where different choices (nearest-neighbor, bilinear, bicubic) significantly impact output image quality. This transformation finds widespread applications in medical image processing (such as ocular image analysis), industrial inspection (like bearing surface defect detection), and computer vision (including panoramic image stitching). Through this conversion, features that are difficult to analyze in Cartesian coordinates may become intuitively visible in polar coordinates. After completing the transformation, users can perform further processing on polar images, such as unwrapping circular features along the angular axis using `unwrap` function, or applying specific filtering operations in polar coordinate space using MATLAB's image processing toolbox functions. The entire process can be encapsulated into a reusable function with parameters for center point selection, interpolation method, and output resolution control.