Insensitivity of Fourier Descriptors to Rotation, Translation, and Other Motions

Fourier descriptors enable more accurate target recognition due to their inherent invariance to rotational and translational motions. As a frequency-domain analysis method, Fourier descriptors represent object contours as sequences of complex numbers, effectively capturing shape characteristics and structural features. The key advantage lies in their mathematical properties that remain unchanged under Euclidean transformations - specifically, the descriptor magnitudes are rotation-invariant while phase information can be normalized for translation invariance. In practical implementation, the process typically involves: contour extraction using edge detection algorithms, coordinate conversion to complex-number representation, application of Fast Fourier Transform (FFT), and descriptor normalization through magnitude-based feature vector creation. This methodology maintains high recognition accuracy even when targets undergo spatial transformations, making Fourier descriptor-based approaches widely adopted in computer vision and image processing applications such as shape matching, object classification, and motion-invariant pattern recognition systems.