Brightness perception: one simple model explaines most if not all effects

Few models can explain Mach bands (Pessoa, 1996 Vision Research 36 3205-3227) . Our own employs multiscale line and edge coding by simple and complex cells. Lines are interpreted by Gaussian functions, edges by bipolar, Gaussian-truncated errorfunctions. Widths of these functions are coupled to the scales of the underlying cells and the amplitudes are determined by their responses.

Estimating fuzzy membership functions parameters by the levenberg-marquardt algorithm

In previous papers from the authors fuzzy model identification methods were discussed. The bacterial algorithm for extracting fuzzy rule base from a training set was presented. The Levenberg-Marquardt algorithm was also proposed for determining membership functions in fuzzy systems. In this paper the Levenberg-Marquardt technique is improved to optimise the membership functions in the fuzzy rules without Ruspini-partition. The class of membership functions investigated is the trapezoidal one as it is general enough and widely used. The method can be easily extended to arbitrary piecewise linear functions as well.

Looking through the eyes of the painter: from visual perception to non-photorealistic rendering

In this paper we present a brief overview of the processing in the primary visual cortex, the multi-scale line/edge and keypoint representations, and a model of brightness perception. This model, which is being extended from 1D to 2D, is based on a symbolic line and edge interpretation: lines are represented by scaled Gaussians and edges by scaled, Gaussian-windowed error functions. We show that this model, in combination with standard techniques from graphics, provides a very fertile basis for non-photorealistic image rendering.

Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in

We study the Riemann boundary value problem , for analytic functions in the class of analytic functions represented by the Cauchy-type integrals with density in the spaces with variable exponent. We consider both the case when the coefficient is piecewise continuous and it may be of a more general nature, admitting its oscillation. The explicit formulas for solutions in the variable exponent setting are given. The related singular integral equations in the same setting are also investigated. As an application there is derived some extension of the Szegö-Helson theorem to the case of variable exponents.