To improve the edge detecting effect of the pressed character, a novel method based on facet model and topographic structures is proposed. Firstly, the discrete gray scale image is approximated by a bivariate cubic function, then, the concerned features of the continuous function are computed to describe the discrete image. After every pixel in the image has been defined to Peak, Ridge, Saddle, Flat, Ravine, Pit or Hillside, the edge of the character is detected. To reduce the time in computing the coefficients of cubic function, an efficient separable algorithm is presented. In addition, an image enhancement method prior to edge detection is adopted to improve the detecting effect. The tests show that the proposed method is more suitable for complex edge detecting problems than common methods.