In this paper

two problems are researched.First

we propose five topology characteristics and geometry characteristics that are invariant under perspective transformation to describe polygon.Then the definition of homograph is given in terms of these characteristics.On the basis of this definition

we give a procedure for recognizing homographs.Second

a new algorithm for recognizing polyhedrons from a perspective line drawing based on principle of homograph is presented.Homograph as defined by us can be employed to distinguish between surfaces with different characteristics and to classify the surfaces of polyhedron.As homographs' categories are few in number and as it is only necessary to put the polygon to be recognized in one of these few categories

efficiency of recognition is greatly raised.We introduced the topological structure to analyze homograph qualitatively

therefore the algorithm is insensitive to noises;and employ geometrical structure to analyze homograph quantitatively

thus the algorithms can show fine discrimination between polyhedrons.Thus

it can not only recognize polyhedrons of different shape but also distinguish between polyhedrons that are of the same shape but their sizes and proportions are different.Comparing with other recognition algorithms

our algorithm has obtained obvious improvement.The effectiveness of the algorithm is demonstrated preliminarily by computer simulation.