1. Introduction
Multi-Resolution multi-orientation decompositions are one of the foundational techniques of image analysis. The idea of analyzing image structure separately at every scale and orientation originated from a number of sources: measurements of the physiology of mammalian visual systems [1]–[3], principled reasoning about the statistics and coding of visual information [4]–[7] (Gabors, DOGs, and jets), harmonic analysis [8] [9] (wavelets), and signal processing [9] [10] (multirate filtering). Such representations have proven effective for visual processing tasks such as denoising [11], image enhancement [12], texture analysis [13], stereoscopic correspondence [14], motion flow [15] [16], attention [17], boundary detection [18] and recognition [19]–[21].