Application of Riesz transforms to the isotropic AM-PM decomposition of geometrical-optical illusion images.

The existence of a special second-order mechanism in the human visual system, able to demodulate the envelope of visual stimuli, suggests that spatial information contained in the image envelope may be perceptually relevant. The Riesz transform, a natural isotropic extension of the Hilbert transform to multidimensional signals, was used here to demodulate band-pass filtered images of well-known visual illusions of length, size, direction, and shape. We show that the local amplitude of the monogenic signal or envelope of each illusion image conveys second-order information related to image holistic spatial structure, whereas the local phase component conveys information about the spatial features. Further low-pass filtering of the illusion image envelopes creates physical distortions that correspond to the subjective distortions perceived in the illusory images. Therefore the envelope seems to be the image component that physically carries the spatial information about these illusions. This result contradicts the popular belief that the relevant spatial information to perceive geometrical-optical illusions is conveyed only by the lower spatial frequencies present in their Fourier spectrum.

[1]  Dennis Gabor,et al.  Theory of communication , 1946 .

[2]  Hans Knutsson,et al.  Signal processing for computer vision , 1994 .

[3]  A. Papoulis,et al.  The Fourier Integral and Its Applications , 1963 .

[4]  Michael Felsberg,et al.  The monogenic signal , 2001, IEEE Trans. Signal Process..

[5]  J. Horváth.  Sur Les Fonctions Conjuguées À Plusieurs Variables , 1953 .

[6]  Alfredo Restrepo,et al.  Localized measurement of emergent image frequencies by Gabor wavelets , 1992, IEEE Trans. Inf. Theory.

[7]  R. Gregory.  Eye and Brain: The Psychology of Seeing , 1966 .

[8]  R. Müller,et al.  Die Hilberttransformation und ihre Verallgemeinerung in Optik und Bildverarbeitung , 1999 .

[9]  Thomas Bülow,et al.  A Novel Approach to the 2D Analytic Signal , 1999, CAIP.

[10]  M. Georgeson,et al.  Sensitivity to contrast modulation: the spatial frequency dependence of second-order vision , 2003, Vision Research.

[11]  J G Daugman,et al.  Demodulation, predictive coding, and spatial vision. , 1995, Journal of the Optical Society of America. A, Optics, image science, and vision.

[12]  R. Bracewell.  The Fourier transform. , 1989, Scientific American.

[13]  Michael Felsberg,et al.  Optical Flow Estimation from Monogenic Phase , 2004, IWCM.

[14]  M. Carrasco,et al.  A Test of the Spatial-Frequency Explanation of the Müller-Lyer Illusion , 1986, Perception.

[15]  E. Stein,et al.  Introduction to Fourier Analysis on Euclidean Spaces. , 1971 .

[16]  M. A. Oldfield,et al.  Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[17]  W. James,et al.  The Principles of Psychology. , 1983 .

[18]  B. Skottun.  Amplitude and Phase in the MüLler-Lyer Illusion , 2000, Perception.

[19]  D. H. Kelly.  Spatial frequency selectivity in the retina , 1975, Vision Research.

[20]  Stanley Coren,et al.  Seeing is Deceiving , 2020 .

[21]  Ignacio Serrano Pedraza,et al.  Single-Band Amplitude Demodulation of Müller-Lyer Illusion Images , 2007 .

[22]  Michael S. Landy,et al.  Orthogonal Distribution Analysis: A New Approach to the Study of Texture Perception , 1991 .

[23]  Michael Felsberg,et al.  The Monogenic Scale-Space: A Unifying Approach to Phase-Based Image Processing in Scale-Space , 2004, Journal of Mathematical Imaging and Vision.

[24]  Michael Felsberg,et al.  A New Extension of Linear Signal Processing for Estimating Local Properties and Detecting Features , 2000, DAGM-Symposium.

[25]  D. Hubel,et al.  Receptive fields, binocular interaction and functional architecture in the cat's visual cortex , 1962, The Journal of physiology.

[26]  Alan C. Bovik,et al.  Am-fm image models , 1996 .

[27]  C Chubb,et al.  Second-order processes in vision: introduction. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[28]  Michael Felsberg,et al.  Structure Multivector for Local Analysis of Images , 2000, Theoretical Foundations of Computer Vision.

[29]  Franz Clemens Brentano.  Über ein optisches Paradoxon , 2008 .

[30]  C. R. Carlson,et al.  Visual illusions without low spatial frequencies , 1984, Vision Research.

[31]  C L Baker,et al.  A processing stream in mammalian visual cortex neurons for non-Fourier responses. , 1993, Science.

[32]  J. O. Robinson.  The Psychology of Visual Illusion , 1972 .

[33]  E. Stein.  Singular Integrals and Di?erentiability Properties of Functions , 1971 .

[34]  Arthur P Ginsburg,et al.  Visual Information Processing Based on Spatial Filters Constrained by Biological Data. , 1978 .

[35]  I Mareschal,et al.  Cortical processing of second-order motion , 1999, Visual Neuroscience.

[36]  Michael Felsberg,et al.  Disparity from Monogenic Phase , 2002, DAGM-Symposium.

[37]  Michael Felsberg,et al.  The Multidimensional Isotropic Generalization of Quadrature Filters in Geometric Algebra , 2000, AFPAC.

[38]  Irvin Rock,et al.  The description and analysis of object and event perception. , 1986 .

[39]  Stanley Coren,et al.  Perceptual Phenomena. (Book Reviews: Seeing Is Deceiving. The Psychology of Visual Illusions) , 1978 .

[40]  Arthur P. Ginsburg,et al.  Spatial filtering and visual form perception. , 1986 .

[41]  E. Adelson,et al.  Early vision and texture perception , 1988, Nature.

[42]  Michael Felsberg,et al.  GET: The Connection Between Monogenic Scale-Space and Gaussian Derivatives , 2005, Scale-Space.

[43]  Kieran Larkin,et al.  Uniform estimation of orientation using local and nonlocal 2-D energy operators. , 2005, Optics express.

[44]  A. Zygmund.  On Singular Integrals , 1956 .

[45]  Antonio Torralba,et al.  Modeling the Shape of the Scene: A Holistic Representation of the Spatial Envelope , 2001, International Journal of Computer Vision.

[46]  A. Zygmund,et al.  On the existence of certain singular integrals , 1952 .

[47]  R. Bracewell.  The Fourier Transform and Its Applications , 1966 .

[48]  John Daugman,et al.  Demodulation: a new approach to texture vision , 1994 .

[49]  D. Burr,et al.  Feature detection in human vision: a phase-dependent energy model , 1988, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[50]  Petros Maragos,et al.  Image demodulation using multidimensional energy separation , 1995 .

[51]  Mark A. Georgeson,et al.  Edges and bars: where do people see features in 1-D images? , 2005, Vision Research.

[52]  C. Baker,et al.  First- and second-order information in natural images: a filter-based approach to image statistics. , 2004, Journal of the Optical Society of America. A, Optics, image science, and vision.

[53]  F. Zöllner.  Ueber eine neue Art von Pseudoskopie und ihre Beziehungen zu den von Plateau und Oppel beschriebenen Bewegungsphänomenen , 1860 .

[54]  M. García-Pérez.  Visual phenomena without low spatial frequencies: A closer look , 1991, Vision Research.

[55]  I. Serrano-Pedraza,et al.  Single-Band Amplitude Demodulation of Müller-Lyer Illusion Images , 2007, The Spanish Journal of Psychology.

[56]  Stanley Coren,et al.  The influence of optical aberrations on the magnitude of the Poggendorff illusion , 1969 .

[57]  J A Solomon,et al.  Channel selection with non-white-noise masks. , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.