We have not yet completed the automatic recognition of facial parts by image processing. Even if once we get the edge image for the contour of facial parts, due to the existence of the noise, the results are quite frequently not sufficient both in local and global aspects. This is caused mainly by the lack the top-down mechanism for compensating the insufficient Bottom-Up mechanism of image processing. Then, in this paper, a curve fitting mechanism in the image processing is introduced as a top-down processing for enforcing the total performance of contour extraction of the facial parts. An experiment for extracting the contour line extraction of the jaw was done and some preliminary experimental results were presented in this paper, because jaw contour was especially hard to detect at the field test of EXPO2005 Exhibition. Furthermore the possibility of the new deformation basis for the facial caricature is prospected so that the parameter space of the analytical curve could be introduced.