Moment invariants have found many applications in pattern recognition. The main difficulty in the application of moment invariants is their computation. The presented paper is devoted to elaboration of new methods of image invariant recognition in Euclidean and non-Euclidean 2-, 3 and n-dimensional spaces, based on the theory of Clifford hypercomplex numbers that allow to work out efficient algorithms. Algebraic invariant pattern recognition have been discussed in the literature, however the Clifford algebra based method allows a more elegant reformulation providing greater geometrical insight.