Abstract 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 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.

This paper introduces the robust internal-loop compensator based sliding mode control (SMRIC) scheme for multiple-input multiple-output (MIMO) nonlinear systems subjected to mismatched uncertainties, which are time-varying and non-vanishing with non-constant steady-state values. The proposed approach extends an application area of the robust internal-loop compensator (RIC), as well as a class of mismatched uncertainties that could be imposed on the system. The developed SMRIC technique allows substantial alleviation of the chattering phenomenon in the presence of disturbances while retaining the nominal performance of the system in the absence of disturbances. The stability analysis of the closed-loop system is performed using the Lyapunov-based approach. The proposed SMRIC method guarantees the finite-time convergence of the system trajectories to the sliding surface and provides asymptotic stability of the equilibrium. The simulation results of the numerical example and both simulation and experimental results of the application example show that the proposed SMRIC technique exhibits, in comparison with the concurrent algorithms, excellent tracking performance and robustness properties in the presence of modeling uncertainties, parameter variations, external disturbances, and mismatched uncertainties.