An edge detection algorithm based on the multi-direction shear transform

Wavelet multi-resolution analysis allows us to detect edges at different scales. However, the wavelet transform can only capture edge information in three directions, horizontal, vertical and diagonal. In addition, the extracted edges are discontinuous. A new edge detection method to solve these problems is proposed in his paper. Firstly, the image is extended symmetrically by applying horizontal and vertical reflections. Secondly, shear transform is taken on the extended images according to various shear matrixes. Thirdly, the edges of the sheared images are detected by means of wavelet transform. The edges detected in different directions have some difference and can complement each other, so we fuse them with a fusion rule. Finally, a threshold is set to refine the edges. The proposed method works efficiently on the images, and the continuity of the edge is getting better. Besides, the method is able to distinguish the real edges from the noise.

► We apply the shear transform to capture more directional information of the edges.
► We adopt an edge fusion rule to fuse the edge information in different directions.
► A threshold is set to refine the rough edges of the fused image.
► We apply horizontal and vertical reflections to extend the image symmetrically.