A novel shape representation and registration method based on Hough spectrum is developed in this paper. The weighted-average Hough spectrum(WAHS) is defined for the representation of arbitrary shapes

and the translation

rotation

scale and periodic properties of WAHS are summarized and proved. When registration

the parameters of rotation and scale can be estimated easily from the phase and amplitude of WAHS

and the parameter of translation can be estimated in the Hough density space. Experiments show that the method is effective to estimate the parameters of translation

rotation and scale

and is immune to noise and overlapping.