Moment patterns in the Radon space: Invariance to blur

Previously, we introduced the idea of moment patterns in the Radon space and described normalization procedures to render the patterns invariant to translation, rotation, and amplitude and geometric scaling. We extend our work toward rendering the patterns invariant also to blurring, which is modeled as a convolution by a linear shift-invariant filter. This is achieved by considering blur-invariant functions of the central moments of the projections, and normalizing them to eliminate the effects of both amplitude and geometric scaling. Results of simulation are presented to demonstrate the invariance of the new moment-based functions in the Radon space to translation, rotation, amplitude and geometric scaling, and blur.