Abstract: The performance of existing edge detection methods in images corrupted by noise is not satisfying.Aiming at the edge detection problem in images corrupted by moderate noise,an image edge detection method based on improved nonlinear structure tensor using steering kernel is proposed.First the tensor products of the noisy image are computed.Then the tensor products are diffused according to the derivatives of the image which depends on the tensor product itself.The diffusivity matrix in the diffusion equation is composed of the tensor products which are spatially adaptive averaged using a steering kernel instead of isotropic filtered using a gaussian kernel.Finally,the eigenvalues and eigenvectors of the diffused tensor products are computed in order to detect the image edge.Experimental results show that,compared with image edge detection methods based on linear structure tensor,nonlinear structure tensor diffused according to the derivatives of the tensor,nonlinear structure tensor diffused according to the derivatives of the image,the proposed method can get clearer edges with smaller amount of noise.

Key words: Edge detection, Eigenvalue analysis, Iterative filtering, Linear structure tensor, Nonlinear structure tensor, Partial differential equation, Steering kernel, Tensor product