The project deals with generalization of existing theory of moment invariants, with derivation of new invariants for object description and recognition, with proposal of stable and efficient numerical algorithms for their computation, and with their software implementation in a form of MATLAB toolbox. Theoretical part covers a design of invariants to image blurring as well as to geometric degradations of images. The first category is represented by invariants to convolution defined both in spatial and in frequency domain, where space domain invariants are intended mainly for binary object recognition while frequency domain invariants are more suitable for graylevel and color image matching. Geometrical invariance should deal with images, deformed by elastic transformation (invariants in the implicit form) or by 3D affine transform. Numerical algorithms for invariants will employ orthogonal polynomials and proper recurrent relations. Possible new areas of moment invariants application will be searched out and thoroughly studied.