Log-Polar Coordinate Transformation of an Image

Performing log-polar coordinate transformation on an image serves as preparation for Fourier-Mellin transform, converting rotation parameters into translation parameters. This transformation helps better understand rotational characteristics of images and provides additional information for subsequent image processing and analysis. By converting rotation parameters to translation parameters, we can process images more conveniently and achieve better results in rotation invariance. In code implementation, this typically involves remapping image coordinates from Cartesian (x,y) to log-polar (ρ,θ) space using interpolation methods like bilinear or bicubic interpolation. The transformation algorithm calculates ρ = log√(x²+y²) and θ = atan2(y,x), effectively converting rotational changes in the original image to horizontal shifts in the transformed domain. This technique has wide applications in computer vision and image processing fields, being used for tasks such as object recognition, image matching, and image retrieval where rotation-invariant features are crucial. The transformation can be implemented using OpenCV's cv2.logPolar() function or custom MATLAB scripts handling coordinate conversion and interpolation operations.