Deformable template matching is a kind of useful method for contour extraction and image segmentation in the fields of computer vision and image analysis. In this paper

by utilizing the gradient trajectories of a two dimensional function

a novel analytical form based two dimensional parametric deformable template with three kinds of biological tissue bone

muscle and skin is built

which has more reasonable template structure used to control the template deformation. In order to improve the operational efficiency of the new matching method

a heterogeneous discretization scheme is adopted. Then the new definitions of similarity internal energy function

smoothness internal energy function and external energy function are presented to reduce the sensitivity to initial placement of the template. Gaussian function is used to widen the capturing scope of the external force in the external energy function definition. Finally

greedy optimization fast algorithm is used to obtain globally optimal solution with more acceptable complexity of computation than dynamic programming. The experimental results on real images show that our new matching method is efficient and robust to accurate contour extraction.