Gradient and Laplacian Edge Detection

To use the gradient or the Laplacian approaches as the basis for practical image edge detectors, one must extend the process to two dimensions, adapt to the discrete case, and somehow deal with the difficulties presented by real images. Relative to the 1D edges, edges in 2D images have the additional quality of direction. One usually wishes to find edges regardless of direction, but a directionally sensitive edge detector can be useful at times. Also, the discrete nature of digital images requires the use of an approximation to the derivative. Finally, there are a number of problems that can confound the edge detection process in real images. These include noise, crosstalk or interference between nearby edges, and inaccuracies resulting from the use of a discrete grid. False edges, missing edges, and errors in edge location and orientation are often the result. An edge detector based solely on the zero crossings of the continuous Laplacian produces closed edge contours if the image, meets certain smoothness constraints. The contours are closed because edge strength is not considered, so even the slightest, most gradual intensity transition produces a zero crossing. In effect, the zero crossing contours define the boundaries that separate regions of nearly constant intensity in the original image.