By using the angular spectrum representation, the propagation law of the second intensity moment are given for the axially symmetric paraxial and nonparaxial scalar beam.

Based on the angular spectrum representation and the theory of the second intensity moment of non-paraxial scalar beam,the beam waist radius,the far-field divergence angle and the beam quality factor of non-paraxial scalar sinh-Gaussian(ShG) beams were calculated.

By taking the vectorial property of time average energy flow density and the accurate formula of the light intensity into accout, the first and second intensity moments of the nonparaxial scalar beams are defined.

In addition, it is found that in free space for small a the mean-squared width of the spectral degree of coherence w_c can be either larger or smaller than that of the spectral density w_i depending on ε, and critical value ε_0 increases with increasing α.

Based on the propagation law of the second-order moments matrix,the focusing of twisted anisotropic Gaussian-Schell model (AGSM) beams through a lens is studied.

Inspired by image salient area detection model,A model for extracting local invariant feature is proposed based on salient measurement of local second moment matrix.

Affine invariant feature is constructed based on scale space and second moment matrix, image registration is performed using pyramid method and distance calculation acceleration, and reliability is ensured by registration probability model.