1. An edge enhancement apparatus in digital image scalar-up circuit, comprising: a buffer for temporarily storing input image pixels to be processed; a profile detecting unit including: a directional filter for performing a band-pass filtering to the input image pixel in multiple directions to obtain multiple sum-of-border values for the input image pixel in the directions; an adder for summing up the sum-of-border values to obtain an overall sum-of-border value; and a selector for selecting a first gain and a second gain according to the value of the overall sum-of-border value; and an outline analytic processing unit including: a high-pass filter and a low-pass filter for filtering the input image pixel to obtain border component and plain component of the input image pixel, respectively; and a first gain device and a second gain device for multiplying the border component and the plain component by the first gain and the second gain, respectively, which are summed and added to the original pixel for obtaining a new pixel.