Amplitude-only log Radon transform for geometric invariant shape descriptor

•We propose a new shape descriptor based on Radon transform•This descriptor needs no normalizations.•It is invariant to geometric transformations (rotation scale and translation) and robust to noise.•The rotation angle, the scaling factor and the position shift can be easily determined.

A shape descriptor combining the Radon transform, the amplitude extraction, and the log-mapping is proposed in this paper. It is invariant to shape rotation, scaling, and translation. Invariance to translation is achieved by amplitude extraction on the radial coordinate. Rotation and scaling are log-mapped into two-dimensional translations and recovered with the phase-only correlation function. In addition, all transformation parameters (rotating angle, scaling factor, and position shift) can be determined also. The efficiency of the proposed descriptor compared to existing methods is shown experimentally on different kind of datasets.