The 3D object representation method is a key problem on computer vision. The existent methods of 3D object representation have applied for 3D object recognition. But

they have themselves drawback. The 3D object representation method based on aspect graph is a kind of means on a center of the observant. It completely describes the 3D object by a finite set of 2D views of the object from different viewpoint. According to geometry structure of object

the set of viewpoint on the viewing space is partitioned into regions such that in each region the equivalent structure of the line drawing is consistent. An aspect is defined for the same of qualitative structure of topology of the line drawing. The 3D object representation method based on aspect graph makes 3D object recognition become problem on matching 2D image and 2D aspect. To begin with

The thesis defines a principle of equivalent structure of topology for the line drawing. In addition

it studies the partition theory and structure method of aspect graph for 3D object of transparent under perspective projection. At last

according to the principle of equivalent structure of topology

the aspect graph for 3D object of opaque and aspect are established. At the same time

it is proved for example of 3D object.