The field of computer vision is concerned with extracting features and information from images in order to make analysis of images easier, so that more and more information can be extracted. The primary goal of this thesis is to obtain the useful edges from the images and also removes the speckle noise if present before detects the edges in the presence of speckle noise. The proposed method uses mathematical morphology for edge detection and also for removing noise. An edge may be defined as a set of connected pixels that forms a boundary between two disjoint regions. Edge detection is basically, a method of segmenting an image into regions of discontinuity. The edge detection has been used by object recognition, target tracking, segmentation, and etc. Therefore, the edge detection is one of the most important parts of image processing. This paper describes detection of edges in the image with noise and also without noise using mathematical morphology. The existence of speckle is unwanted since it disgraces image quality. Eliminating such noise is an important preprocessing step. If such noise is present in the image the method will remove the noise before edge detection.