Markov Random Field Approach Research Articles

Microwave imaging: Reconstructions from experimental data using conjugate gradient and enhancement by edge-preserving regularization

A method for reconstructing the complex permittivity profile of lossy dielectric objects from measured scattered far-field data is presented. An iterative reconstruction algorithm based on a conjugate gradient method is derived from an integral representation of the electric field and applying a moment method solution. Results obtained from experimental data are shown for both known and unknown targets. Then, a new regularization procedure is developed to enhance the quality of the reconstruction. This method, based on a Markov random fields approach, models the object to be reconstructed by homogeneous areas separated by borderlike discontinuities. Finally, the enhancement is shown by the reconstruction of a polystyrene square cylinder.

The application of mean field theory to image motion estimation

Previously, Markov random field (MRF) model-based techniques have been proposed for image motion estimation. Since motion estimation is usually an ill-posed problem, various constraints are needed to obtain a unique and stable solution. The main advantage of the MRF approach is its capacity to incorporate such constraints, for instance, motion continuity within an object and motion discontinuity at the boundaries between objects. In the MRF approach, motion estimation is often formulated as an optimization problem, and two frequently used optimization methods are simulated annealing (SA) and iterative-conditional mode (ICM). Although the SA is theoretically optimal in the sense of finding the global optimum, it usually takes many iterations to converge. The ICM, on the other hand, converges quickly, but its results are often unsatisfactory due to its "hard decision" nature. Previously, the authors have applied the mean field theory to image segmentation and image restoration problems. It provides results nearly as good as SA but with much faster convergence. The present paper shows how the mean field theory can be applied to MRF model-based motion estimation. This approach is demonstrated on both synthetic and real-world images, where it produced good motion estimates.

Modeling protein cores with Markov random fields

A mathematical formalism is introduced that has general applicability to many protein structure models used in the various approaches to the “inverse protein folding problem.” The inverse nature of the problem arises from the fact that one begins with a set of assumed tertiary structures and searches for those most compatible with a new sequence, rather than attempting to predict the structure directly from the new sequence. The formalism is based on the well-known theory of Markov random fields (MRFs). Our MRF formulation provides explicit representations for the relevant amino acid position environments and the physical topologies of the structural contacts. In particular, MRF models can readily be constructed for the secondary structure packing topologies found in protein domain cores, or other structural motifs, that are anticipated to be common among large sets of both homologous and nonhomologous proteins. MRF models are probabilistic and can exploit the statistical data from the limited number of proteins having known domain structures. The MRF approach leads to a new scoring function for comparing different threadings (placements) of a sequence through different structure models. The scoring function is very important, because comparing alternative structure models with each other is a key step in the inverse folding problem. Unlike previously published scoring functions, the one derived in this paper is based on a comprehensive probabilistic formulation of the threading problem.

Electromagnetic inverse-scattering solutions for inhomogeneous cross-sections of cylindrical biological bodies by a modified Born approximation and a stochastic Markov random fields approach

Two novel methods of microwave imaging for biomedical applications are presented and discussed. The first is a deterministic method based on a modified Born approximation; it extends the validity of the usual Born approximation to strongly scattering bodies. The second is a stochastic method that leads to a Bayesian solution to the nonlinear problem of inverse scattering by modelling the dielectric properties of a scatterer and the electric field as suitable Markov random fields. Both methods exhibit the major feature of easily exploiting a priori knowledge, which can be available in many biomedical applications. Numerical results are reported to show the effectivenesses of the two methods.

A combined Markov random field and wave-packet transform-based approach for image segmentation

The author formulates a novel segmentation algorithm which combines the use of Markov random field models for image-modeling with the use of the discrete wavepacket transform for image analysis. Image segmentations are derived and refined at a sequence of resolution levels, using as data selected wave-packet transform images or "channels". The segmentation algorithm is compared with nonmultiresolution Markov random field-based image segmentation algorithms in the context of synthetic image example problems, and found to be both significantly more efficient and effective.

A Markov random field approach to data fusion and colour segmentation

A Markoman model is described which enables the data fusion and segmentation of multi-sensed images. The model is used to detect the boundaries and label the regions of a simple colour image. This is achieved by maximizing the conditional probability of all region labels and boundaries given an image. The assumption is made that the boundaries within a colour plane are related to those in other planes.