We propose a regular method for constructing integral invariants under geometric image transformations. The method allows us to find invariant features for arbitrary one-parameter groups of 2D-transformations. Our theoretical results provide a constructive synthesis of functional invariants. We illustrate method by examples involving shear maps and projective transformations. Furthermore, in the same way action of multi-parameter groups can be used for the analysis of image sequences on time intervals when the transformation coefficients are known and constant. The time at which the image appears is also as a parameter. A general form of such one-parameter groups is obtained for six-parameter planar affine transformations. Invariants for one-parameter Euclidean similarity group are found.
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