Abstract: In order to protect more image detail features, an image matching algorithm based on
fractional-order gradient operator to construct nonlinear scale space was proposed. The
fractional-order gradient operator was introduced in conductivity function of classic nonlinear
diffusion equation. In this process, the recent numerical schemes called fast explicit diffusion (FED)
was used to build the nonlinear scale space. And the sequence of the FED time step sizes was
rearranged by Leja ordering. In addition, a new interest point operator from the Hessian matrix was
exploited to detect the keypoints and local intensity order pattern (LIOP) descriptor was applied in
feature description. The experimental results show that compared with the state-of-the-art algorithm,
the proposed algorithm has better performance in many geometric and photometric transformations.

Key words: image matching, fractional-order gradient operator, fast explicit diffusion, Leja ordering;
local intensity order pattern