A new Edge Detector Based on Parametric Surface Model: Regression Surface Descriptor

In this paper we present a new methodology for edge detection in digital images. The first originality of the proposed method is to consider image content as a parametric surface. Then, an original parametric local model of this surface representing image content is proposed. The few parameters involved in the proposed model are shown to be very sensitive to discontinuities in surface which correspond to edges in image content. This naturally leads to the design of an efficient edge detector. Moreover, a thorough analysis of the proposed model also allows us to explain how these parameters can be used to obtain edge descriptors such as orientations and curvatures. In practice, the proposed methodology offers two main advantages. First, it has high customization possibilities in order to be adjusted to a wide range of different problems, from coarse to fine scale edge detection. Second, it is very robust to blurring process and additive noise. Numerical results are presented to emphasis these properties and to confirm efficiency of the proposed method through a comparative study with other edge detectors.Comment: 21 pages, 13 figures and 2 table

Border collision bifurcations of stroboscopic maps in periodically driven spiking models

In this work we consider a general non-autonomous hybrid system based on the integrate-and-fire model, widely used as simplified version of neuronal models and other types of excitable systems. Our unique assumption is that the system is monotonic, possesses an attracting subthreshold equilibrium point and is forced by means of periodic pulsatile (square wave) function.\\ In contrast to classical methods, in our approach we use the stroboscopic map (time-$T$ return map) instead of the so-called firing-map. It becomes a discontinuous map potentially defined in an infinite number of partitions. By applying theory for piecewise-smooth systems, we avoid relying on particular computations and we develop a novel approach that can be easily extended to systems with other topologies (expansive dynamics) and higher dimensions.\\ More precisely, we rigorously study the bifurcation structure in the two-dimensional parameter space formed by the amplitude and the duty cycle of the pulse. We show that it is covered by regions of existence of periodic orbits given by period adding structures. They do not only completely describe all the possible spiking asymptotic dynamics but also the behavior of the firing rate, which is a devil's staircase as a function of the parameters

A survey of visual preprocessing and shape representation techniques

Many recent theories and methods proposed for visual preprocessing and shape representation are summarized. The survey brings together research from the fields of biology, psychology, computer science, electrical engineering, and most recently, neural networks. It was motivated by the need to preprocess images for a sparse distributed memory (SDM), but the techniques presented may also prove useful for applying other associative memories to visual pattern recognition. The material of this survey is divided into three sections: an overview of biological visual processing; methods of preprocessing (extracting parts of shape, texture, motion, and depth); and shape representation and recognition (form invariance, primitives and structural descriptions, and theories of attention)