Abstract
AbstractWe 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 co-efficients 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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