Image Log-Polar Coordinate Transformation

Image log-polar coordinate transformation is a geometric transformation method that converts images from Cartesian coordinates to log-polar coordinates, commonly used in computer vision and image analysis. This transformation simulates the human visual system's characteristic of higher resolution perception in central regions while offering unique advantages when handling image transformations such as rotation and scaling.

Implementing log-polar transformation in MATLAB typically involves these key algorithmic steps: First, determine the transformation center point, usually selected at the image's center position; then define a polar coordinate grid where each polar coordinate point is mapped to corresponding Cartesian coordinates; finally, obtain transformed pixel values through interpolation methods. The distinctive feature of log-polar coordinates lies in using logarithmic scaling for radial coordinates, which magnifies details in central regions while compressing peripheral areas, aligning with human visual characteristics.

A practical MATLAB implementation should address computational efficiency by employing vectorized operations to avoid explicit loops, while judiciously selecting interpolation methods (such as bilinear interpolation) to balance transformation quality and computational complexity. Key functions involved may include coordinate mapping using meshgrid, logarithmic scaling calculations, and interp2 for 2D interpolation. The log-polar transformation proves particularly useful in applications like object recognition and image registration, as it converts image rotation and scaling into simple translation operations, significantly simplifying subsequent processing pipelines.