Markov random field

About: Markov random field is a research topic. Over the lifetime, 5669 publications have been published within this topic receiving 179568 citations. The topic is also known as: MRF.

Deformed Lattice Detection in Real-World Images Using Mean-Shift Belief Propagation

Abstract: We propose a novel and robust computational framework for automatic detection of deformed 2D wallpaper patterns in real-world images. The theory of 2D crystallographic groups provides a sound and natural correspondence between the underlying lattice of a deformed wallpaper pattern and a degree-4 graphical model. We start the discovery process with unsupervised clustering of interest points and voting for consistent lattice unit proposals. The proposed lattice basis vectors and pattern element contribute to the pairwise compatibility and joint compatibility (observation model) functions in a Markov random field (MRF). Thus, we formulate the 2D lattice detection as a spatial, multitarget tracking problem, solved within an MRF framework using a novel and efficient mean-shift belief propagation (MSBP) method. Iterative detection and growth of the deformed lattice are interleaved with regularized thin-plate spline (TPS) warping, which rectifies the current deformed lattice into a regular one to ensure stability of the MRF model in the next round of lattice recovery. We provide quantitative comparisons of our proposed method with existing algorithms on a diverse set of 261 real-world photos to demonstrate significant advances in accuracy and speed over the state of the art in automatic discovery of regularity in real images.

Monocular Object Instance Segmentation and Depth Ordering with CNNs

Abstract: In this paper we tackle the problem of instance-level segmentation and depth ordering from a single monocular image. Towards this goal, we take advantage of convolutional neural nets and train them to directly predict instance-level segmentations where the instance ID encodes the depth ordering within image patches. To provide a coherent single explanation of an image we develop a Markov random field which takes as input the predictions of convolutional neural nets applied at overlapping patches of different resolutions, as well as the output of a connected component algorithm. It aims to predict accurate instance-level segmentation and depth ordering. We demonstrate the effectiveness of our approach on the challenging KITTI benchmark and show good performance on both tasks.

Incorporation of Anatomical MR Data for Improved Dunctional Imaging with PET

Abstract: A statistical approach to PET image reconstruction offers several potential advantages over the filtered backprojection method currently employed in most clinical PET systems: (1) the true data formation process may be modeled accurately to include the Poisson nature of the observation process and factors such as attenuation, scatter, detector efficiency and randoms; and (2) an a priori statistical model for the image may be employed to model the generally smooth nature of the desired spatial distribution and to include information such as the presence of anatomical boundaries, and hence potential discontinuities, in the image. In this paper we develop a Bayesian algorithm for PET image reconstruction in which a magnetic resonance image is used to provide information about the location of potential discontinuities in the PET image. This is achieved through the use of a Markov random field model for the image which incorporates a “line process” to model the presence of discontinuities. In the case where no a priori edge information is available, this line process may be estimated directly from the data. When edges are available from MR images, this information is introduced as a set of known a priori line sites in the image. It is demonstrated through computer simulation, that the use of a line process in the reconstruction process has the potential for significant improvements in reconstructed image quality, particularly when prior MR edge information is available.

A new look at survey propagation and its generalizations

Abstract: This article provides a new conceptual perspective on survey propagation, which is an iterative algorithm recently introduced by the statistical physics community that is very effective in solving random k-SAT problems even with densities close to the satisfiability threshold. We first describe how any SAT formula can be associated with a novel family of Markov random fields (MRFs), parameterized by a real number ρ ∈ [0, 1]. We then show that applying belief propagation---a well-known “message-passing” technique for estimating marginal probabilities---to this family of MRFs recovers a known family of algorithms, ranging from pure survey propagation at one extreme (ρ = 1) to standard belief propagation on the uniform distribution over SAT assignments at the other extreme (ρ = 0). Configurations in these MRFs have a natural interpretation as partial satisfiability assignments, on which a partial order can be defined. We isolate cores as minimal elements in this partial ordering, which are also fixed points of survey propagation and the only assignments with positive probability in the MRF for ρ = 1. Our experimental results for k = 3 suggest that solutions of random formulas typically do not possess non-trivial cores. This makes it necessary to study the structure of the space of partial assignments for ρ 0 can be viewed as a “smoothed” version of the uniform distribution over satisfying assignments (ρ = 0). Finally, we isolate properties of Gibbs sampling and message-passing algorithms that are typical for an ensemble of k-SAT problems.