Mach Equations Research Articles

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.