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

机译：基于多方向剪切变换的边缘检测算法

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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.
机译：小波多分辨率分析使我们能够检测不同比例的边缘。但是，小波变换只能捕获水平，垂直和对角线三个方向的边缘信息。另外，提取的边缘是不连续的。他的论文提出了一种解决这些问题的新的边缘检测方法。首先，通过施加水平和垂直反射来对称地扩展图像。其次，根据各种剪切矩阵对扩展图像进行剪切变换。第三，通过小波变换检测剪切图像的边缘。在不同方向上检测到的边缘存在一些差异，并且可以彼此互补，因此我们将它们融合在一起。最后，设置阈值以细化边缘。所提出的方法在图像上有效地工作，并且边缘的连续性越来越好。此外，该方法能够从噪声中区分出真实边缘。

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