A field theory for geometrical pattern identification is developed based on the postulate that various modified patterns are identified via invariant characteristics of pattern transformations. The invariant characteristics of geometrical patterns are written as the functional of the light intensity distribution of pattern, its spatial gradient, and also its spatial curvature. Some definite expressions of the invariant characteristic functional for two dimensional linear transformation are derived, and their invariant and feature extracting property are examined numerically. It is also shown that the invariant property is conserved even when patterns are deformed locally by introducing a "gauge field" as new degree of freedom in the functional in form of a covariant derivative. Based on this idea, we discuss a field theoretical model for pattern identification performed in biological systems.