58,214 research outputs found
Traditional and new principles of perceptual grouping
Perceptual grouping refers to the process of determining which regions and parts of the visual scene belong together as parts of higher order perceptual units such as objects or patterns. In the early 20th century, Gestalt psychologists identified a set of classic grouping principles which specified how some image features lead to grouping between elements given that all other factors were held constant. Modern vision scientists have expanded this list to cover a wide range of image features but have also expanded the importance of learning and other non-image factors. Unlike early Gestalt accounts which were based largely on visual demonstrations, modern theories are often explicitly quantitative and involve detailed models of how various image features modulate grouping. Work has also been done to understand the rules by which different grouping principles integrate to form a final percept. This chapter gives an overview of the classic principles, modern developments in understanding them, and new principles and the evidence for them. There is also discussion of some of the larger theoretical issues about grouping such as at what stage of visual processing it occurs and what types of neural mechanisms may implement grouping principles
Favoured Local Structures in Liquids and Solids: a 3D Lattice Model
We investigate the connection between the geometry of Favoured Local
Structures (FLS) in liquids and the associated liquid and solid properties. We
introduce a lattice spin model - the FLS model on a face-centered cubic lattice
- where this geometry can be arbitrarily chosen among a discrete set of 115
possible FLS. We find crystalline groundstates for all choices of a single FLS.
Sampling all possible FLS's, we identify the following trends: i) low symmetry
FLS's produce larger crystal unit cells but not necessarily higher energy
groundstates, ii) chiral FLS's exhibit to peculiarly poor packing properties,
iii) accumulation of FLS's in supercooled liquids is linked to large crystal
unit cells, and iv) low symmetry FLS's tend to find metastable structures on
cooling.Comment: 11 pages, 6 figure
GRASS: Generative Recursive Autoencoders for Shape Structures
We introduce a novel neural network architecture for encoding and synthesis
of 3D shapes, particularly their structures. Our key insight is that 3D shapes
are effectively characterized by their hierarchical organization of parts,
which reflects fundamental intra-shape relationships such as adjacency and
symmetry. We develop a recursive neural net (RvNN) based autoencoder to map a
flat, unlabeled, arbitrary part layout to a compact code. The code effectively
captures hierarchical structures of man-made 3D objects of varying structural
complexities despite being fixed-dimensional: an associated decoder maps a code
back to a full hierarchy. The learned bidirectional mapping is further tuned
using an adversarial setup to yield a generative model of plausible structures,
from which novel structures can be sampled. Finally, our structure synthesis
framework is augmented by a second trained module that produces fine-grained
part geometry, conditioned on global and local structural context, leading to a
full generative pipeline for 3D shapes. We demonstrate that without
supervision, our network learns meaningful structural hierarchies adhering to
perceptual grouping principles, produces compact codes which enable
applications such as shape classification and partial matching, and supports
shape synthesis and interpolation with significant variations in topology and
geometry.Comment: Corresponding author: Kai Xu ([email protected]
Stability of Soft Quasicrystals in a Coupled-Mode Swift-Hohenberg Model for Three-Component Systems
In this article, we discuss the stability of soft quasicrystalline phases in
a coupled-mode Swift-Hohenberg model for three-component systems, where the
characteristic length scales are governed by the positive-definite gradient
terms. Classic two-mode approximation method and direct numerical minimization
are applied to the model. In the latter approach, we apply the projection
method to deal with the potentially quasiperiodic ground states. A variable
cell method of optimizing the shape and size of higher-dimensional periodic
cell is developed to minimize the free energy with respect to the order
parameters. Based on the developed numerical methods, we rediscover decagonal
and dodecagonal quasicrystalline phases, and find diverse periodic phases and
complex modulated phases. Furthermore, phase diagrams are obtained in various
phase spaces by comparing the free energies of different candidate structures.
It does show not only the important roles of system parameters, but also the
effect of optimizing computational domain. In particular, the optimization of
computational cell allows us to capture the ground states and phase behavior
with higher fidelity. We also make some discussions on our results and show the
potential of applying our numerical methods to a larger class of mean-field
free energy functionals.Comment: 26 pages, 13 figures; accepted by Communications in Computational
Physic
Coordinated optimization of visual cortical maps : 1. Symmetry-based analysis
In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of orientation columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about a hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference. From basic symmetry assumptions we obtain a comprehensive phenomenological classification of possible inter-map coupling energies and examine representative examples. We show that each individual coupling energy leads to a different class of OP solutions with different correlations among the maps such that inferences about the optimization principle from map layout appear viable. We systematically assess whether quantitative laws resembling experimental observations can result from the coordinated optimization of orientation columns with other feature maps
A tensor network study of the complete ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice
Using infinite projected entangled pair states, we study the ground state
phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square
lattice directly in the thermodynamic limit. We find an unexpected partially
nematic partially magnetic phase in between the antiferroquadrupolar and
ferromagnetic regions. Furthermore, we describe all observed phases and discuss
the nature of the phase transitions involved.Comment: 27 pages, 15 figures; v3: adjusted sections 1 and 3, and added a
paragraph to section 5.2.
Spontaneous symmetry breaking and the formation of columnar structures in the primary visual cortex II --- Local organization of orientation modules
Self-organization of orientation-wheels observed in the visual cortex is
discussed from the view point of topology. We argue in a generalized model of
Kohonen's feature mappings that the existence of the orientation-wheels is a
consequence of Riemann-Hurwitz formula from topology. In the same line, we
estimate partition function of the model, and show that regardless of the total
number N of the orientation-modules per hypercolumn the modules are
self-organized, without fine-tuning of parameters, into definite number of
orientation-wheels per hypercolumn if N is large.Comment: 36 pages Latex2.09 and eps figures. Needs epsf.sty, amssym.def, and
Type1 TeX-fonts of BlueSky Res. for correct typo in graphics file
Merging diabolical points of a superconducting circuit
We present the first theoretical study of the merging of diabolical points in
the context of superconducting circuits. We begin by studying an analytically
solvable four-level model which may serve as theoretical pattern for such a
phenomenon. Then, we apply it to a circuit named Cooper pairs pump, whose
diabolical points are already known.Comment: 11 pages, 6 figure
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