We survey the framework of morphological edge detection. Morphological gradients are hybrid operators: they are constructed with set and arithmetic operations. After a short introduction
to gradients in digital images, we present the gradients available in mathematical morphology: morphological gradients, half gradients, and directional gradients. These gradients are based on dilations and erosions. We present a new directional gradient based on graytone thinning/thickening and a new multiscale gradient called the regularized gradient. Morphological gradients have a considerable
advantage with respect to classical edge detection paradigms: they are easier to generalize to any type of space in which dilation can be defined. We describe the gradient operators in image sequences,
3-D images, and graphs. We propose a new operator on graphs, the mosaic gradient.