Abstract
Multistable illusions occur when the visual system interprets the same image in two different ways. We model illusions using dynamic systems based on Wilson networks, which detect combinations of levels of attributes of the image. In most examples presented here, the network has symmetry, which is vital to the analysis of the dynamics. We assume that the visual system has previously learned that certain combinations are geometrically consistent or inconsistent, and model this knowledge by adding suitable excitatory and inhibitory connections between attribute levels. We first discuss 4-node networks for the Necker cube and the rabbit/duck illusion. The main results analyze a more elaborate model for the Necker cube, a 16-node Wilson network whose nodes represent alternative orientations of specific segments of the image. Symmetric Hopf bifurcation is used to show that a small list of natural local geometric consistency conditions leads to alternation between two global percepts: cubes in two different orientations. The model also predicts brief transitional states in which the percept involves impossible rectangles analogous to the Penrose triangle. A tristable illusion generalizing the Necker cube is modelled in a similar manner.
Highlights
Visual perception involves puzzling phenomena when ambiguous or incomplete information is presented to one or both eyes, Blake and Logothetis [1]. (Binocular) rivalry occurs when two different images, presented one to each eye, lead to alternating percepts, possibly of neither image separately, see for example Breese [2], Wilson [3,4]
We summarize the main results of Stewart [50,51] needed for the analysis, namely: the relation between eigenvalues and eigenvectors of the adjacency matrix and those of the Jacobian of the rate model; preservation of spatiotemporal symmetry; relation between the first symmetry-breaking Hopf bifurcation and the largest eigenvalue of the adjacency matrix
We show how to model the perception of illusions using Wilson networks with natural geometric consistency conditions, and that such networks naturally generate global percepts such as a cube from local information
Summary
Visual perception involves puzzling phenomena when ambiguous or incomplete information is presented to one or both eyes, Blake and Logothetis [1]. (Binocular) rivalry occurs when two different images, presented one to each eye, lead to alternating percepts, possibly of neither image separately, see for example Breese [2], Wilson [3,4]. Our intention is to analyze schematic aspects of simple neuronal networks, showing how their structure proves a natural way to enable the recognition of images from incoming optical stimuli, based on geometric consistency. Illusions occur when this system ‘recognizes’ two or more alternatives in the same image, and this phenomenon provides insights into the underlying dynamics in normal image-recognition processes, Yoon and Shen [12]. Diekman and Golubitsky [19] provide an algorithmic construction for networks modelling rivalry, based on the combinations of attribute levels in the two images This approach is not applicable to illusions because there is only one image. Geometric consistency conditions, and employ plausible constraints of this kind
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
