This paper addresses the problems of disparity and optical flow partitioning based on the brightness invariance assumption. We investigate new variational approaches to these problems with Potts priors and possibly box constraints. For the optical flow partitioning, our model includes vectorvalued data and an adapted Potts regularizer. Using the notation of asymptotically level stable functions...

The process by which one may take a discrete model of a biophysical process and construct a continuous model based upon it is of mathematical interest as well as being of practical use. In this work, we take the extended Potts model applied to biological cell movement to its continuous limit. Beginning with a single cell moving in one dimension on a lattice and obeying Potts model rules of move...

Efforts to develop better and more efficient algorithms for Monte Carlo simulations have a long history, in which the Fortuin-Kasteleyn (FK) transformation [1] for Potts models has played a pivotal role. The most common use of this transformation has been to create algorithms in which clusters of spins in the Potts model are flipped simultaneously [2, 3]. In this paper, we present a new algorit...

We introduce and discuss a real-space renormalization group (RSRG) procedure on very small lattices, which in principle does not require any of the usual approximations, e.g., a cut-off in the expansion of the Hamiltonian in powers of the field. The procedure is carried out numerically on very small lattices (4×4 to 2×2) and implemented for the Ising Model and the q = 3,4,5-state Potts Models. ...

We perform Monte Carlo simulations using the Wolff cluster algorithm of the q=2 (Ising), 3, 4 and q=10 Potts models on dynamical phi-cubed graphs of spherical topology with up to 5000 nodes. We find that the measured critical exponents are in reasonable agreement with those from the exact solution of the Ising model and with those calculated from KPZ scaling for q=3,4 where no exact solution is...

We study the antiferromagnetic q-state Potts model on the square lattice for q = 3 and q = 4, using the Wang-Swendsen-Kotecký (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q = 3 we obtain good control up to correlation length ξ ∼ 5000; the data are consistent with ξ(β) = Ae2ββp(1 + a1e −β + . . .) as β → ∞, with p ≈ 1. The staggered susceptibility beha...

We perform extensive Monte Carlo simulations of the 10-state Potts model on quenched two-dimensional Φ3 gravity graphs to study the effect of quenched coordination number randomness on the nature of the phase transition, which is strongly first order on regular lattices. The numerical data provides strong evidence that, due to the quenched randomness, the discontinuous first-order phase transit...

We present a segmentation method for live cell images, using graph cuts and learning methods. The images used here are particularly challenging because of the shared grey-level distributions of cells and background, which only differ by their textures, and the local imprecision around cell borders. We use the P Potts model recently presented by Kohli et al. [9]: functions on higher-order clique...

We present a segmentation method for live cell images, using graph cuts and learning methods. The images used here are particularly challenging because of the shared grey-level distributions of cells and background, which only differ by their textures, and the local imprecision around cell borders. We use the Pn Potts model recently presented by Kohli et al. [9]: functions on higher-order cliqu...

Potts model is a powerful tool to uncover community structure in complex networks. Here, we propose a new framework to reveal the optimal number of communities and stability of network structure by quantitatively analyzing the dynamics of Potts model. Specifically we model the community structure detection Potts procedure by a Markov process, which has a clear mathematical explanation. Then we ...