The magnitude-based Fourier descriptors (FD) are frequently used in shape-based image retrieval, due to their efficiency and effectiveness. Unlike the phase-preserving Fourier descriptors, the magnitude-based Fourier descriptors are inherently invariant under rotation and starting point change, but they discard all valuable information contained in the phase of the Fourier coefficients (FCs). In
... [Show full abstract] order to preserve the coefficients’ phase, the orientation and starting point of the shape must be determined. In this paper, we conducted a comprehensive evaluation of different state-of-the-art methods for determining nominal shape orientation, which can be used to extract phase-preserving Fourier descriptors: the point of maximal radius, the axis of least inertia (moments), the phase of the first harmonic, the cross-correlation, the Procrustes distance and the pseudomirror points. The methods were compared in terms of sensitivity to non-rigid transformations, retrieval performance, computational complexity and computational time. The experimental results give insight into the pros and cons of all analyzed methods.