Some Insights Into Brightness Perception of Images in the Light of a New Computational Model of Figure–Ground Segregation

The excitatory-inhibitory visual receptive-field model may be looked upon as a classical structuralist approach to vision that relies upon brightness-contrast information of the image as a preliminary step toward visual representation. The corresponding mathematical operator (Laplacian) was first proposed by the empiricist Ernst Mach on the basis of the Mach band illusion. The Helmholtz´s constructivist approach, on the other hand, argues that perception is the product of unconscious inference. Propagating a sort of intermediate stance between these two viewpoints led to the emergence of the Gestalt school for whom perception follows a minimum principle and is at the same time holistic, based on certain coherence criteria. In this paper, we have modeled the extraclassical receptive field through an eigenfunction-based generalization of the Gaussian derivative approach that resulted in a modification of Mach´s equation, introducing a higher order isotropic derivative (Bi-Laplacian) of Gaussian and a fourth-moment operator. The proposed computational model draws its inspiration from the structuralist approach, performs figure-ground segregation in Gestalt sense, and also provides cues toward brightness perception in tune with the constructivist notion of unconscious inference.