Single-band amplitude demodulation of Müller-Lyer illusion images

The perception of the Müller-Lyer illusion has previously been explained as a result of visual low band-pass spatial filtering, although, in fact, the illusion persists in band-pass and high-pass filtered images without visible low-spatial frequencies. A new theoretical framework suggests that our perceptual experience about the global spatial structure of an image corresponds to the amplitude modulation (AM) component (or its magnitude, also called envelope) of its AM-FM (alternatively, AM-PM) decomposition. Because demodulation is an ill-posed problem with a non-unique solution, two different AM-FM demodulation algorithms were applied here to estimate the envelope of images of Müller-Lyer illusion: the global and exact Daugman and Downing (1995) AMPM algorithm and the local and quasi-invertible Maragos and Bovik (1995) DESA. The images used in our analysis include the classic configuration of illusion in a variety of spatial and spatial frequency content conditions. In all cases, including those of images for which visual low-pass spatial filtering would be ineffective, the envelope estimated by single-band amplitude demodulation has physical distortions in the direction of perceived illusion. It is not plausible that either algorithm could be implemented by the human visual system. It is shown that the proposed second order visual model of pre-attentive segregation of textures (or "back-pocket" model) could recover the image envelope and, thus, explain the perception of this illusion even in Müller-Lyer images lacking low spatial frequencies.