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Recognition of three-dimensional objects independent of size, position, and orientation is an important and difficult problem of scene analysis. The use of three-dimensional moment invariants is proposed as a solution. The generalization of the results of two-dimensional moment invariants which had linked two-dimensional moments to binary quantics is done by linking three-dimensional moments to ternary quantics. The existence and number of nth order moments in two and three dimensions is explored. Algebraic invariants of several ternary forms under different orthogonal transformations are derived by using the invariant property of coefficients of ternary forms. The result is a set of three-dimensional moment invariants which are invariant under size, orientation, and position change. This property is highly significant in compressing the data which are needed in three-dimensional object recognition. Empirical examples are also given.