A new noise-robust edge detector is proposed, which combines a small-scaled isotropic Gaussian kernel and large-scaled anisotropic Gaussian kernels (ANGKs) to obtain edge maps of images. Its main advantage is that noise reduction is attained while maintaining high edge resolution. From the ANGKs, anisotropic directional derivatives (ANDDs) are derived to capture the locally directional variation of an image. The ANDD-based edge strength map (ESM) is constructed. Its noise-robustness is determined by the scale alone and its edge resolution by the ratio of the scale to the anisotropic factor. Moreover, the edge stretch effect in anisotropic smoothing is revealed. The ANDD-based ESM and the gradient-based ESM with a small-scaled isotropic Gaussian kernel are fused into a noise-robust ESM with high edge resolution and little edge stretch. Embedding the fused ESM into the routine of Canny detector, a noise-robust edge detector is developed, which includes two additional modifications: contrast equalization and noise-dependent lower threshold. The aggregate test receiver-operating-characteristic (ROC) curves and the Pratt's Figure of Merit (FOM) are used to evaluate the proposed detector by abundant experiments. The experimental results show that the proposed detector can obtain high-quality edge maps for noise-free and noisy images.