Multi-scale cortical keypoint representation for attention and object detection

Keypoints (junctions) provide important information for focus-of-attention (FoA) and object categorization/recognition. In this paper we analyze the multi-scale keypoint representation, obtained by applying a linear and quasi-continuous scaling to an optimized model of cortical end-stopped cells, in order to study its importance and possibilities for developing a visual, cortical architecture.We show that keypoints, especially those which are stable over larger scale intervals, can provide a hierarchically structured saliency map for FoA and object recognition. In addition, the application of non-classical receptive field inhibition to keypoint detection allows to distinguish contour keypoints from texture (surface) keypoints.

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.