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.

Unsupervised Polarimetric SAR Image Segmentation and Classification Using Region Growing With Edge Penalty

Abstract: A region-based unsupervised segmentation and classification algorithm for polarimetric synthetic aperture radar (SAR) imagery that incorporates region growing and a Markov random field edge strength model is designed and implemented. This algorithm is an extension of the successful Iterative Region Growing with Semantics (IRGS) segmentation and classification algorithm, which was designed for amplitude only SAR imagery, to polarimetric data. Polarimetric IRGS (PolarIRGS) extends IRGS by incorporating a polarimetric feature model based on the Wishart distribution and modifying key steps such as initialization, edge strength computation, and the region growing criterion. Like IRGS, PolarIRGS oversegments an image into regions and employs iterative region growing to reduce the size of the solution search space. The incorporation of an edge penalty in the spatial context model improves segmentation performance by preserving segment boundaries that traditional spatial models will smooth over. Evaluation of PolarIRGS with Flevoland fully polarimetric data shows that it improves upon two other recently published techniques in terms of classification accuracy.

Adaptive Markov Random Field Approach for Classification of Hyperspectral Imagery

Abstract: An adaptive Markov random field (MRF) approach is proposed for classification of hyperspectral imagery in this letter. The main feature of the proposed method is the introduction of a relative homogeneity index for each pixel and the use of this index to determine an appropriate weighting coefficient for the spatial contribution in the MRF classification. In this way, overcorrection of spatially high variation areas can be avoided. Support vector machines are implemented for improved class modeling and better estimate of spectral contribution to this approach. Experimental results of a synthetic hyperspectral data set and a real hyperspectral image demonstrate that the proposed method works better on both homogeneous regions and class boundaries with improved classification accuracy.

An efficient algorithm for image segmentation, Markov random fields and related problems

Abstract: Problems of statistical inference involve the adjustment of sample observations so they fit some a priori rank requirements, or order constraints. In such problems, the objective is to minimize the deviation cost function that depends on the distance between the observed value and the modify value. In Markov random field problems, there is also a pairwise relationship between the objects. The objective in Markov random field problem is to minimize the sum of the deviation cost function and a penalty function that grows with the distance between the values of related pairs---separation function.We discuss Markov random fields problems in the context of a representative application---the image segmentation problem. In this problem, the goal is to modify color shades assigned to pixels of an image so that the penalty function consisting of one term due to the deviation from the initial color shade and a second term that penalizes differences in assigned values to neighboring pixels is minimized. We present here an algorithm that solves the problem in polynomial time when the deviation function is convex and separation function is linear; and in strongly polynomial time when the deviation cost function is linear, quadratic or piecewise linear convex with few pieces (where “few” means a number exponential in a polynomial function of the number of variables and constraints). The complexity of the algorithm for a problem on n pixels or variables, m adjacency relations or constraints, and range of variable values (colors) U, is O(T(n,m) + n log U) where T(n,m) is the complexity of solving the minimum s, t cut problem on a graph with n nodes and m arcs. Furthermore, other algorithms are shown to solve the problem with convex deviation and convex separation in running time O(mn log n log nU) and the problem with nonconvex deviation and convex separation in running time O(T(nU, mU). The nonconvex separation problem is NP-hard even for fixed value of U.For the family of problems with convex deviation functions and linear separation function, the algorithm described here runs in polynomial time which is demonstrated to be fastest possible.

Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data

Abstract: Subsequence clustering of multivariate time series is a useful tool for discovering repeated patterns in temporal data. Once these patterns have been discovered, seemingly complicated datasets can be interpreted as a temporal sequence of only a small number of states, or clusters. For example, raw sensor data from a fitness-tracking application can be expressed as a timeline of a select few actions (i.e., walking, sitting, running). However, discovering these patterns is challenging because it requires simultaneous segmentation and clustering of the time series. Furthermore, interpreting the resulting clusters is difficult, especially when the data is high-dimensional. Here we propose a new method of model-based clustering, which we call Toeplitz Inverse Covariance-based Clustering (TICC). Each cluster in the TICC method is defined by a correlation network, or Markov random field (MRF), characterizing the interdependencies between different observations in a typical subsequence of that cluster. Based on this graphical representation, TICC simultaneously segments and clusters the time series data. We solve the TICC problem through alternating minimization, using a variation of the expectation maximization (EM) algorithm. We derive closed-form solutions to efficiently solve the two resulting subproblems in a scalable way, through dynamic programming and the alternating direction method of multipliers (ADMM), respectively. We validate our approach by comparing TICC to several state-of-the-art baselines in a series of synthetic experiments, and we then demonstrate on an automobile sensor dataset how TICC can be used to learn interpretable clusters in real-world scenarios.

Abnormal events detection based on spatio-temporal co-occurences

Abstract: We explore a location based approach for behavior modeling and abnormality detection. In contrast to the conventional object based approach where an object may first be tagged, identified, classified, and tracked, we proceed directly with event characterization and behavior modeling at the pixel(s) level based on motion labels obtained from background subtraction. Since events are temporally and spatially dependent, this calls for techniques that account for statistics of spatiotemporal events. Based on motion labels, we learn co-occurrence statistics for normal events across space-time. For one (or many) key pixel(s), we estimate a co-occurrence matrix that accounts for any two active labels which co-occur simultaneously within the same spatiotemporal volume. This co-occurrence matrix is then used as a potential function in a Markov random field (MRF) model to describe the probability of observations within the same spatiotemporal volume. The MRF distribution implicitly accounts for speed, direction, as well as the average size of the objects passing in front of each key pixel. Furthermore, when the spatiotemporal volume is large enough, the co-occurrence distribution contains the average normal path followed by moving objects. The learned normal co-occurrence distribution can be used for abnormal detection. Our method has been tested on various outdoor videos representing various challenges.