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Edge detection is a process of identifying and detecting sharp discontinuities in an image. The discontinuities are abrupt changes in pixel intensity gray level value. The traditional method of edge detection involves convolving the image with an operator (2-D filter) which is constructed to be sensitive to noise. Edge detector is a collection of very important local image processing method to locate sharp changes in the intensity value. Edge detection is an important technique in many image processing applications such as object recognition, motion analysis, pattern recognition, medical image processing etc. This paper shows the comparison of edge detection techniques under different conditions showing advantages and disadvantages of these algorithms. This was done under Matlab. Further work would be to detection of liver tumor with the help of new developed algorithm.