We propose invariant formulations that can potentially be combined into a single system. In particular, we describe a framework for computing invariant features which are insensitive to rigid motion, affine transform, changes of parameterization and scene illumination, perspective transform, and view point change. This is unlike most current research on image invariants which concentrates on either geometric or illumination invariants exclusively. The formulations are widely applicable to many popular basis representations, such as wavelets, short-time Fourier analysis, and splines. Exploiting formulations that examine information about shape and color at different resolution levels, the new approach is neither strictly global nor local. It enables a quasi-localized, hierarchical shape analysis which is rarely found in other known invariant techniques, such as global invariants. Furthermore, it does not require estimating high-order derivatives in computing invariants (unlike local invariants), whence is more robust. We provide results of numerous experiments on both synthetic and real data to demonstrate the validity and flexibility of the proposed framework.
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