A note on the primal-dual method for the semi-metric labeling problem

Recently, Komodakis et al. [6] developed the FastPD algorithm for the semi-metric labeling problem, which extends the expansion move algorithm of Boykov et al. [2]. We present a slightly different derivation of the FastPD method

New algorithms for the dual of the convex cost network flow problem with application to computer vision

Motivated by various applications to computer vision, we consider an integer convex optimization problem which is the dual of the convex cost network flow problem. In this paper, we first propose a new primal algorithm for computing an optimal solution of the problem. Our primal algorithm iteratively updates primal variables by solving associated minimum cut problems. The main contribution in this paper is to provide a tight bound for the number of the iterations. We show that the time complexity of the primal algorithm is K ¢ T(n;m) where K is the range of primal variables and T(n;m) is the time needed to compute a minimum cut in a graph with n nodes and m edges. We then propose a primal-dual algorithm for the dual of the convex cost network flow problem. The primal-dual algorithm can be seen as a refined version of the primal algorithm by maintaining dual variables (flow) in addition to primal variables. Although its time complexity is the same as that for the primal algorithm, we can expect a better performance practically. We finally consider an application to a computer vision problem called the panoramic stitching problem. We apply several implementations of our primal-dual algorithm to some instances of the panoramic stitching problem and test their practical performance. We also show that our primal algorithm as well as the proofs can be applied to the L\-convex function minimization problem which is a more general problem than the dual of the convex cost network flow problem

ClassCut for Unsupervised Class Segmentation

Abstract. We propose a novel method for unsupervised class segmentation on a set of images. It alternates between segmenting object instances and learning a class model. The method is based on a segmentation energy defined over all images at the same time, which can be optimized efficiently by techniques used before in interactive segmentation. Over iterations, our method progressively learns a class model by integrating observations over all images. In addition to appearance, this model captures the location and shape of the class with respect to an automatically determined coordinate frame common across images. This frame allows us to build stronger shape and location models, similar to those used in object class detection. Our method is inspired by interactive segmentation methods [1], but it is fully automatic and learns models characteristic for the object class rather than specific to one particular object/image. We experimentally demonstrate on the Caltech4, Caltech101, and Weizmann horses datasets that our method (a) transfers class knowledge across images and this improves results compared to segmenting every image independently; (b) outperforms Grabcut [1] for the task of unsupervised segmentation; (c) offers competitive performance compared to the state-of-the-art in unsupervised segmentation and in particular it outperforms the topic model [2].

The Kelvin-wave cascade in the vortex filament model

The energy transfer mechanism in zero temperature superfluid turbulence of helium-4 is still a widely debated topic. Currently, the main hypothesis is that weakly nonlinear interacting Kelvin waves transfer energy to sufficiently small scales such that energy is dissipated as heat via phonon excitations. Theoretically, there are at least two proposed theories for Kelvin-wave interactions. We perform the most comprehensive numerical simulation of weakly nonlinear interacting Kelvin-waves to date and show, using a specially designed numerical algorithm incorporating the full Biot-Savart equation, that our results are consistent with nonlocal six-wave Kelvin wave interactions as proposed by L'vov and Nazarenko.Comment: 6 pages, 6 figure

Geometric scaling in ultrahigh energy neutrinos and nonlinear perturbative QCD

It is shown that in ultrahigh energy inelastic neutrino-nucleon(nucleus) scattering the cross sections for the boson-hadron(nucleus) reactions should exhibit geometric scaling on the single variable tau_A =Q2/Q2_{sat,A}. The dependence on energy and atomic number of the charged/neutral current cross sections are encoded in the saturation momentum Q_{sat,A}. This fact allows an analytical computation of the neutrino scattering on nucleon/nucleus at high energies, providing a theoretical parameterization based on the scaling property.Comment: 5 pages, 4 figure

Using strong shape priors for stereo

Abstract. This paper addresses the problem of obtaining an accurate 3D reconstruction from multiple views. Taking inspiration from the recent successes of using strong prior knowledge for image segmentation, we propose a framework for 3D reconstruction which uses such priors to overcome the ambiguity inherent in this problem. Our framework is based on an object-specific Markov Random Field (MRF)[10]. It uses a volumetric scene representation and integrates conventional reconstruction measures such as photo-consistency, surface smoothness and visual hull membership with a strong object-specific prior. Simple parametric models of objects will be used as strong priors in our framework. We will show how parameters of these models can be efficiently estimated by performing inference on the MRF using dynamic graph cuts [7]. This procedure not only gives an accurate object reconstruction, but also provides us with information regarding the pose or state of the object being reconstructed. We will show the results of our method in reconstructing deformable and articulated objects.

Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves

We study the long-time evolution of gravity waves on deep water exited by the stochastic external force concentrated in moderately small wave numbers. We numerically implement the primitive Euler equations for the potential flow of an ideal fluid with free surface written in canonical variables, using expansion of the Hamiltonian in powers of nonlinearity of up to fourth order terms. We show that due to nonlinear interaction processes a stationary energy spectrum close to $|k| \sim k^{-7/2}$ is formed. The observed spectrum can be interpreted as a weak-turbulent Kolmogorov spectrum for a direct cascade of energy.Comment: 4 pages, 5 figure

Degree of randomness: numerical experiments for astrophysical signals

Astrophysical and cosmological signals such as the cosmic microwave background radiation, as observed, typically contain contributions of different components, and their statistical properties can be used to distinguish one from the other. A method developed originally by Kolmogorov is involved for the study of astrophysical signals of randomness of various degrees. Numerical performed experiments based on the universality of Kolmogorov distribution and using a single scaling of the ratio of stochastic to regular components, reveal basic features in the behavior of generated signals also in terms of a critical value for that ratio, thus enable the application of this technique for various observational datasetsComment: 6 pages, 9 figures; Europhys.Letters; to match the published versio

Constraining the neutrino magnetic moment with anti-neutrinos from the Sun

We discuss the impact of different solar neutrino data on the spin-flavor-precession (SFP) mechanism of neutrino conversion. We find that, although detailed solar rates and spectra allow the SFP solution as a sub-leading effect, the recent KamLAND constraint on the solar antineutrino flux places stronger constraints to this mechanism. Moreover, we show that for the case of random magnetic fields inside the Sun, one obtains a more stringent constraint on the neutrino magnetic moment down to the level of \mu_\nu \lsim few \times 10^{-12}\mu_B, similar to bounds obtained from star cooling.Comment: 4 pages, 3 figures. Final version to appear in Phys. Rev. Let

Locality and stability of the cascades of two-dimensional turbulence

We investigate and clarify the notion of locality as it pertains to the cascades of two-dimensional turbulence. The mathematical framework underlying our analysis is the infinite system of balance equations that govern the generalized unfused structure functions, first introduced by L'vov and Procaccia. As a point of departure we use a revised version of the system of hypotheses that was proposed by Frisch for three-dimensional turbulence. We show that both the enstrophy cascade and the inverse energy cascade are local in the sense of non-perturbative statistical locality. We also investigate the stability conditions for both cascades. We have shown that statistical stability with respect to forcing applies unconditionally for the inverse energy cascade. For the enstrophy cascade, statistical stability requires large-scale dissipation and a vanishing downscale energy dissipation. A careful discussion of the subtle notion of locality is given at the end of the paper.Comment: v2: 23 pages; 4 figures; minor revisions; resubmitted to Phys. Rev.