Local and Global Gestalt Laws: A Neurally Based Spectral Approach

Abstract

A mathematical model of figure-ground articulation is presented, which takes into account both local and global gestalt laws and is compatible with the functional architecture of the primary visual cortex (V1). The local gestalt law of good continuation is described by means of suitable connectivity kernels, that are derived from Lie group theory, and quantitatively compared with long range connectivity in V1. Global gestalt constraints are then introduced in terms of spectral analysis of connectivity matrix derived from these kernels. This analysis performs grouping of local features and individuates perceptual units with the highest saliency. Numerical simulations are performed and results are obtained applying the technique to a number of stimuli.

A psychophysically-tuned computational model of human primary visual cortex produces geometric optical illusions

“…A fine tuning of the parameters detailed above helped to compromise between the contribution of intracortical connectivity and long-range connectivity: the need for large-size ( ሻ receptive fields has been identified by means of the model, pointing out the likely contribution of higher-level visual processes such as those in V2 and perhaps elsewhere (Murray & Herrmann, 2013b). The strength of neuro-geometrical models give a clear and elegant framework to explain the cellular organization and construction of visual percepts, which can be easily applied to other illusions, such as the Kanizsa triangle (Citti & Sarti, 2006) or basic perceptual phenomena (line completion) (Favali, Citti, & Sarti, 2017).…”

Neurogeometry of Perception: Isotropic and Anisotropic Aspects

“…As such it introduces a geometric intrinsic notion of shape based on the property of the cortex. Figure 8: The result of the grouping process applied from left to right to the Kanizsa square (as in [33]) , to the Kanizsa diamond and to an other image.…”

“…The result of the grouping process applied from left to right to the Kanizsa square (as in[33]) , to the Kanizsa diamond and to an other image.…”

A Neuromathematical Model for Geometrical Optical Illusions

“…The functional architectures built in R 2 ×S 1 correspond to the neural connectivity measured by Angelucci et al in [1] and Bosking et al in [2]. For a qualitatively and quantitative comparison between the kernels and the connectivity patterns see Favali et al in [10]. In our work a local formulation of the kernel presented in [10] will be used.…”

“…For a qualitatively and quantitative comparison between the kernels and the connectivity patterns see Favali et al in [10]. In our work a local formulation of the kernel presented in [10] will be used. Furthermore, it has been shown by Sanguinetti et al in [32] that the geometry of fuctional architecture formally introduced in 3 is naturally encoded in the statistics of natural images.…”