Local and global gestalt laws: A neurally based spectral approach

A mathematical model of figure-ground articulation is presented, taking into account both local and global gestalt laws. The model is compatible with the functional architecture of the primary visual cortex (V1). Particularly the local gestalt law of good continuity is described by means of suitable connectivity kernels, that are derived from Lie group theory and are neurally implemented in long range connectivity in V1. Different kernels are compatible with the geometric structure of cortical connectivity and they are derived as the fundamental solutions of the Fokker Planck, the Sub-Riemannian Laplacian and the isotropic Laplacian equations. The kernels are used to construct matrices of connectivity among the features present in a visual stimulus. Global gestalt constraints are then introduced in terms of spectral analysis of the connectivity matrix, showing that this processing can be cortically implemented in V1 by mean field neural equations. This analysis performs grouping of local features and individuates perceptual units with the highest saliency. Numerical simulations are performed and results are obtained applying the technique to a number of stimuli.Comment: submitted to Neural Computatio

Influence of cold-rolling reduction on retained austenite texture in cold-rolled and intercritically annealed TRIP-assisted steel

The newly developed multiphase transformation-induced plasticity (TRIP) steels are of interest for industrial applications because of their excellent combination of high strength and ductility. Their performance can be successfully controlled by designing an optimum balance in the volume fractions of ferrite, bainite and retained austenite. The characteristics of the retained austenite are considered to be the main key to achieving the desired final properties. Against this background, the effects of retained austenite characteristics, such as volume fraction, carbon concentration, size and shape, on the behaviour of TRIP steels have been studied. The crystallographic orientation of the retained austenite was measured by electron backscattered diffraction (EBSD). The effect of initial cold-rolling reduction on the microtexture development of the retained austenite was studied on an aluminium-containing TRIP steel. The results show that, by increasing the cold-rolling reduction before the final austempering, the main components of the face-centred cubic phase, i.e. copper, brass and Goss, dominate the texture of the retained austenite. In contrast, the copper and Goss components of the retained austenite are absent in the texture of lightly deformed sheets. The features of the preferred orientation of the retained austenite are discussed and explained in terms of the annealing texture of the recrystallized ferrite and bainite

A geometric model of multi-scale orientation preference maps via Gabor functions

In this paper we present a new model for the generation of orientation preference maps in the primary visual cortex (V1), considering both orientation and scale features. First we undertake to model the functional architecture of V1 by interpreting it as a principal fiber bundle over the 2-dimensional retinal plane by introducing intrinsic variables orientation and scale. The intrinsic variables constitute a fiber on each point of the retinal plane and the set of receptive profiles of simple cells is located on the fiber. Each receptive profile on the fiber is mathematically interpreted as a rotated Gabor function derived from an uncertainty principle. The visual stimulus is lifted in a 4-dimensional space, characterized by coordinate variables, position, orientation and scale, through a linear filtering of the stimulus with Gabor functions. Orientation preference maps are then obtained by mapping the orientation value found from the lifting of a noise stimulus onto the 2-dimensional retinal plane. This corresponds to a Bargmann transform in the reducible representation of the $\text{SE}(2)=\mathbb{R}^2\times S^1$ group. A comparison will be provided with a previous model based on the Bargman transform in the irreducible representation of the $\text{SE}(2)$ group, outlining that the new model is more physiologically motivated. Then we present simulation results related to the construction of the orientation preference map by using Gabor filters with different scales and compare those results to the relevant neurophysiological findings in the literature

Computer vision for real-time orbital operations. Center directors discretionary fund

Machine vision research is examined as it relates to the NASA Space Station program and its associated Orbital Maneuvering Vehicle (OMV). Initial operation of OMV for orbital assembly, docking, and servicing are manually controlled from the ground by means of an on board TV camera. These orbital operations may be accomplished autonomously by machine vision techniques which use the TV camera as a sensing device. Classical machine vision techniques are described. An alternate method is developed and described which employs a syntactic pattern recognition scheme. It has the potential for substantial reduction of computing and data storage requirements in comparison to the Two-Dimensional Fast Fourier Transform (2D FFT) image analysis. The method embodies powerful heuristic pattern recognition capability by identifying image shapes such as elongation, symmetry, number of appendages, and the relative length of appendages

An aperiodic hexagonal tile

We show that a single prototile can fill space uniformly but not admit a periodic tiling. A two-dimensional, hexagonal prototile with markings that enforce local matching rules is proven to be aperiodic by two independent methods. The space--filling tiling that can be built from copies of the prototile has the structure of a union of honeycombs with lattice constants of $2^n a$, where $a$ sets the scale of the most dense lattice and $n$ takes all positive integer values. There are two local isomorphism classes consistent with the matching rules and there is a nontrivial relation between these tilings and a previous construction by Penrose. Alternative forms of the prototile enforce the local matching rules by shape alone, one using a prototile that is not a connected region and the other using a three--dimensional prototile.Comment: 32 pages, 24 figures; submitted to Journal of Combinatorial Theory Series A. Version 2 is a major revision. Parts of Version 1 have been expanded and parts have been moved to a separate article (arXiv:1003.4279

Discrimination of orientation-defined texture edges

AbstractPreattentive texture segregation was examined using textures composed of randomly placed, oriented line segments. A difference in texture element orientation produced an illusory, or orientation-defined, texture edge. Subjects discriminated between two textures, one with a straight texture edge and one with a “wavy” texture edge. Across conditions the orientation of the texture elements and the orientation of the texture edge varied. Although the orientation difference across the texture edge (the “texture gradient”) is an important determinant of texture segregation performance, it is not the only one. Evidence from several experiments suggests that configural effects are also important. That is, orientation-defined texture edges are strongest when the texture elements (on one side of the edge) are parallel to the edge. This result is not consistent with a number of texture segregation models including feature- and filter-based models. One possible explanation is that the second-order channel used to detect a texture edge of a particular orientation gives greater weight to first-order input channels of that same orientation

Geometry and dimensionality reduction of feature spaces in primary visual cortex

Some geometric properties of the wavelet analysis performed by visual neurons are discussed and compared with experimental data. In particular, several relationships between the cortical morphologies and the parametric dependencies of extracted features are formalized and considered from a harmonic analysis point of view