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Single-Band Amplitude Demodulation of Müller-Lyer Illusion Images

Published online by Cambridge University Press:  10 April 2014

Vicente Sierra-Vázquez
Universidad Complutense, Madrid
Ignacio Serrano-Pedraza
University of Newcastle
E-mail address:


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.

La percepción de la ilusión de Müller-Lyer ha sido explicada como resultado del filtrado visual paso-bajo de las imágenes en las que aparece, aunque, de hecho, la ilusión se percibe en imágenes paso-banda y paso-alto carentes de bajas frecuencias espaciales. Una nueva manera de pensar acerca del procesamiento visual espacial sugiere que la percepción de la estructura espacial global de una imagen se corresponde con el componente de amplitud modulada (AM) o envolvente resultante de su descomposición AM-FM (o, alternativamente, de su descomposición AM-PM). En este trabajo, la envolvente de imágenes de la ilusión de Müller-Lyer se estimó mediante dos algoritmos de demodulación: el algoritmo AMPM de Daugman y Downing (1995) y DESA de Maragos & Bovik (1995). Las imágenes de Müller-Lyer utilizadas presentan la configuración clásica de la ilusión en diferentes versiones espaciales y con diferente contenido en frecuencia espacial. Para cada una de las imágenes utilizadas, incluidas aquellas en las que su filtrado paso-bajo es inútil para obtener su estructura global, la envolvente estimada mediante la demodulación de la amplitud presenta distorsiones físicas que se corresponden con la ilusión percibida. Es poco plausible que el sistema visual humano implemente cualquiera de los dos algoritmos utilizados. Sin embargo, se muestra que el modelo de mecanismos visuales de segundo orden propuesto para la segregación preatencional de la textura puede recuperar la envolvente de los estímulos visuales, explicándose así la percepción de la ilusión de Müller-Lyer aún en imágenes carentes de bajas frecuencias espaciales.

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