Abstract: The comprehensive and recognition of 3D scene based on invariants are the most important
research areas in computer vision fields. The conventional studies of invariants are that these
invariants are derived for planar objects using points, lines, and conics from images. The invariants of
triangular, quadrilateral, pentagonal and hexagon are structured by use of triangular area from 2D
points perspective projection in this paper. And the computational methods of the invariants are
derived. The result of example shows that this formula is correct on the basis of studies.

Key words: computer vision, coplanar polygon, 3D invariant, computational methods