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In order to describe color images, the use of the algebra of quaternions in combination with existing image orthogonal moments, meant for binary and grayscale images, has been widely investigated. This is because of their advantages in (1) gathering the three-channel color information in a single feature vector while preserving the correlation between them and in (2) eliminating shape information redundancy. However, the computation of these quaternary orthogonal moments depends on a unit pure quaternion parameter. The optimal value of this latter can be fixed only with the help of experiments and it is application-dependent. We propose a parameter-free formulation of the quaternary orthogonal moments. The general formula for the computation of the proposed moments, whose rotation invariance is achieved by retaining the modulus, is provided. Furthermore, experiments are conducted to evaluate the performance of the proposed modulus-based moment invariants for color image retrieval and recognition.

We introduce a hybrid fingerprint recognition method built from minutiae and quaternion orthogonal moments. The proposed algorithm includes four steps: extraction of the minutiae triplets (m-triplets), first pass of triplets minutiae matching, validation step of these triplets by characterizing their neighboring gray-level image information through feature vectors of quaternion radial moments, and an adequate similarity measure. By boosting the local minutiae matching step, we avoid consolidation and global matching. To show the added-value of our method, several algorithms for extracting and matching m-triplets are considered and an experimental comparison is established. Experiments are carried out using all four parts of the FVC2004 dataset. Results indicate that the combination of the geometrical features and the quaternion radial moments of the m-triplets leads to an improvement in the overall fingerprint matching performance and demonstrate the expected gain of integrating a validation step in an m-triplets based fingerprint matching algorithm.

A set of invariant quaternion moments based on an adaptation of the three-dimensional (3-D) spherical harmonic transform (SHT) for describing two-dimensional color shapes is proposed. The use of quaternions to deal with the color part is beneficial in the way the three color components are integrated in a single feature. An adequate mapping from the 3-D SHT to the unit disc allows a fast and accurate computation of the proposed moments. Experiments are conducted to evaluate the performance of the obtained moments in terms of color image reconstruction, robustness to geometric and photometric transformations, content-based color shape retrieval, and computation time. For this purpose, two image databases (COIL-100 and ALOI) are used. Results illustrate the effectiveness of the proposed moments in dealing with the color information.