A New Framework for Image Invariants using Basis Expansion

We propose a general framework for computing invariant features from images. The proposed approach is based on a simple concept of basis expansion. It is widely applicable to many popular basis representations, such as wavelets 4, 5, 24, 25], short-time Fourier analysis 15, 30], and splines 2, 6, 33]. Exploiting formulations that use both global and local information about shape and color, the new approach is neither strictly global nor local. It has the advantage of tolerating a certain degree of occlusion (unlike global analysis) and does not require estimating high-order derivatives in computing invariants (unlike local analysis), whence is more robust. Furthermore, it enables a quasi-localized, hierarchical shape analysis which is not possible with other known invariant techniques. Unlike most current research on image invariants which concentrates on either geometry or illumination invariants, the proposed framework is very general and produces invariants which are insensitive to rigid motion, general aane transform, changes of parameterization and scene illumination, and perspective transform.