The edge detection process serves to simplify the analysis of images by drastically reducing the amount of data to be processed, while preserving useful structural informations about object boundaries. At first, this paper proposes an edge detection algorithm to reduce the amount of computation. The gradients of pixels are calculated by using first order differential equations on the pixels with even rows and even columns or odd rows and odd columns, and they are compared with a threshold to decide edges. As a result, the computational complexity is reduced to one third or one forth compared with the provious ones. To enhance the accuracy of edge detection, a method with the adaptive threshold for each pixel window which is calculated by using characteristic values is proposed. In this case, the performance can be improved since the threshold is calculated properly for each window according to the local characteristics of corresponding window.