The problem of detecting edges in gray level digital images is considered. A literature survey of the existing methods is presented. Based on the survey, two methods that are well accepted by a majority of investigators are identified. The methods selected are: 1) Laplacian of Gaussian (LoG) operator, and 2) An optimal detector based on maxima in gradient magnitude of a Gaussian-smoothed image. The latter has been proposed by Canny[], and will be referred as Canny's method. The purpose of the thesis is to compare the performance of these popular methods. In order to increase the scope of such comparison, two additional methods are considered. First is one of the simplest methods, based on the first order approximation of the first derivative of the image. This method has the advantage of relatively low amount of computations. Second is an attempt to develop an edge fitting method based on eigenvector least-squared error fitting of an intensity profile. This method is developed with an intent to keep the edge localization errors small. All the four methods are coded and applied on several digital images, actual as well as synthesized. Results show that the LoG method and Canny's method perform quite well in general, and that demonstrates popularity of these methods. On the other hand, even the simplest method of first derivative is found to perform well if applied properly. Based on the results of the comparative study several critical issues related to edge detection are pointed out. Results also indicate feasibility of the proposed method based on eigenvector fit. Improvements and recommendation for further work are made.