Several values of different anisotropic factors.

This paper presents a novel multi-scale, noise-robust edge detection method that employs multi-scale automatic anisotropic morphological Gaussian kernels to extract edge maps from input images. It addresses the issue of cross-edge detection failure in the Canny edge detector. Compared to other edge detection methods, the proposed approach offers significant advantages in maintaining noise robustness while achieving high edge resolution and accuracy. The paper is structured into five key sections. First, we propose a multi-scale automatic anisotropic morphological directional derivative (AMDD) to capture local gray-level variations around each pixel at multiple scales. Second, a new fused edge strength map (ESM) is introduced based on the multi-scale AMDD. Third, we analyze why the Canny isotropic Gaussian kernel detector fails to detect cross edges. Additionally, the edge contour is extracted by incorporating the fused ESMs and the edge direction map (EDM), which are processed through spatial and directional matching filters, into the standard Canny detection framework. Finally, we evaluate the proposed method using precision-recall (PR) curves and Pratt’s Figure of Merit (FOM). We compare its performance with existing state-of-the-art detectors on a standard dataset. Experimental results demonstrate that the proposed method effectively reduces noise, mitigates irrelevant signal interference, and smooths the image, showing competitive performance in edge detection tasks.