A Replica Inference Approach to Unsupervised Multi-Scale Image Segmentation

We apply a replica inference based Potts model method to unsupervised image segmentation on multiple scales. This approach was inspired by the statistical mechanics problem of "community detection" and its phase diagram. Specifically, the problem is cast as identifying tightly bound clusters ("communities" or "solutes") against a background or "solvent". Within our multiresolution approach, we compute information theory based correlations among multiple solutions ("replicas") of the same graph over a range of resolutions. Significant multiresolution structures are identified by replica correlations as manifest in information theory overlaps. With the aid of these correlations as well as thermodynamic measures, the phase diagram of the corresponding Potts model is analyzed both at zero and finite temperatures. Optimal parameters corresponding to a sensible unsupervised segmentation correspond to the "easy phase" of the Potts model. Our algorithm is fast and shown to be at least as accurate as the best algorithms to date and to be especially suited to the detection of camouflaged images.Comment: 26 pages, 22 figure

Image restoration using the chiral Potts spin-glass

We report on the image reconstruction (IR) problem by making use of the random chiral q-state Potts model, whose Hamiltonian possesses the same gauge invariance as the usual Ising spin glass model. We show that the pixel representation by means of the Potts variables is suitable for the gray-scale level image which can not be represented by the Ising model. We find that the IR quality is highly improved by the presence of a glassy term, besides the usual ferromagnetic term under random external fields, as very recently pointed out by Nishimori and Wong. We give the exact solution of the infinite range model with q=3, the three gray-scale level case. In order to check our analytical result and the efficiency of our model, 2D Monte Carlo simulations have been carried out on real-world pictures with three and eight gray-scale levels.Comment: RevTex 13 pages, 10 figure

Bottlenecks in granular flow: When does an obstacle increase the flowrate in an hourglass?

Bottlenecks occur in a wide range of applications from pedestrian and traffic flow to mineral and food processing. We examine granular flow across a bottleneck using particle-based simulations. Contrary to expectations we find that the flowrate across a bottleneck actually increases if an opti- mized obstacle is placed before it. The dependency of flowrate on obstacle diameter is derived using a phenomenological velocity-density relationship that peaks at a critical density. This relationship is in stark contrast to models of traffic flow, as the mean velocity does not depend only on density but attains hysteresis due to interaction of particles with the obstacle.Comment: Submitted to Phys. Rev. Let

Statistical mechanics of image restoration and error-correcting codes

We develop a statistical-mechanical formulation for image restoration and error-correcting codes. These problems are shown to be equivalent to the Ising spin glass with ferromagnetic bias under random external fields. We prove that the quality of restoration/decoding is maximized at a specific set of parameter values determined by the source and channel properties. For image restoration in mean-field system a line of optimal performance is shown to exist in the parameter space. These results are illustrated by solving exactly the infinite-range model. The solutions enable us to determine how precisely one should estimate unknown parameters. Monte Carlo simulations are carried out to see how far the conclusions from the infinite-range model are applicable to the more realistic two-dimensional case in image restoration.Comment: 20 pages, 9 figures, ReVTe

The anisotropy of granular materials

The effect of the anisotropy on the elastoplastic response of two dimensional packed samples of polygons is investigated here, using molecular dynamics simulation. We show a correlation between fabric coefficients, characterizing the anisotropy of the granular skeleton, and the anisotropy of the elastic response. We also study the anisotropy induced by shearing on the subnetwork of the sliding contacts. This anisotropy provides an explanation to some features of the plastic deformation of granular media.Comment: Submitted to PR

Granular Solid Hydrodynamics

Granular elasticity, an elasticity theory useful for calculating static stress distribution in granular media, is generalized to the dynamic case by including the plastic contribution of the strain. A complete hydrodynamic theory is derived based on the hypothesis that granular medium turns transiently elastic when deformed. This theory includes both the true and the granular temperatures, and employs a free energy expression that encapsulates a full jamming phase diagram, in the space spanned by pressure, shear stress, density and granular temperature. For the special case of stationary granular temperatures, the derived hydrodynamic theory reduces to {\em hypoplasticity}, a state-of-the-art engineering model.Comment: 42 pages 3 fi

Effective null Raychaudhuri equation

The effects on Raychaudhuri's equation of an intrinsically-discrete or particle nature of spacetime are investigated. This is done through the consideration of null congruences emerging from, or converging to, a generic point of spacetime, i.e. in geometric circumstances somehow prototypical of singularity issues. We do this from an effective point of view, that is through a (continuous) description of spacetime modified to embody the existence of an intrinsic discreteness on the small scale, this adding to previous results for non-null congruences. Various expressions for the effective rate of change of expansion are derived. They in particular provide finite values for the limiting effective expansion and its rate of variation when approaching the focal point. Further, this results in a non-vanishing of the limiting cross-sectional area itself of the congruence.Comment: 7 pages; v2: some comparisons with other approaches adde

Spatial based Expectation Maximizing (EM)

<p>Abstract</p> <p>Background</p> <p>Expectation maximizing (EM) is one of the common approaches for image segmentation.</p> <p>Methods</p> <p>an improvement of the EM algorithm is proposed and its effectiveness for MRI brain image segmentation is investigated. In order to improve EM performance, the proposed algorithms incorporates neighbourhood information into the clustering process. At first, average image is obtained as neighbourhood information and then it is incorporated in clustering process. Also, as an option, user-interaction is used to improve segmentation results. Simulated and real MR volumes are used to compare the efficiency of the proposed improvement with the existing neighbourhood based extension for EM and FCM.</p> <p>Results</p> <p>the findings show that the proposed algorithm produces higher similarity index.</p> <p>Conclusions</p> <p>experiments demonstrate the effectiveness of the proposed algorithm in compare to other existing algorithms on various noise levels.</p

The most accurate determination of the 8B half-life

Beta decay is a primary source of information of the structure of a nucleus. An accurate measurement of the half-life of a nucleus is essential for the proper determination of the reduced Gammow-Teller transition probability B(GT). In this work, we present an experiment using a compact set-up of Si-telescope detectors to measure the half-life of the 8B nucleus. Three independent measurements have been analysed, obtaining the values 771.9(17) ms, 773.9(18) ms, and 770.9(27) ms. The value of the half-life obtained as the weighted averaged with the previous published measures is 771.17(94) ms which is a factor 3.2 of improvement in the uncertainty of the half-life