Showing papers on "Markov random field published in 2010"

Noise-contrastive estimation: A new estimation principle for unnormalized statistical models

Abstract: We present a new estimation principle for parameterized statistical models. The idea is to perform nonlinear logistic regression to discriminate between the observed data and some artificially generated noise, using the model log-density function in the regression nonlinearity. We show that this leads to a consistent (convergent) estimator of the parameters, and analyze the asymptotic variance. In particular, the method is shown to directly work for unnormalized models, i.e. models where the density function does not integrate to one. The normalization constant can be estimated just like any other parameter. For a tractable ICA model, we compare the method with other estimation methods that can be used to learn unnormalized models, including score matching, contrastive divergence, and maximum-likelihood where the normalization constant is estimated with importance sampling. Simulations show that noise-contrastive estimation offers the best trade-off between computational and statistical efficiency. The method is then applied to the modeling of natural images: We show that the method can successfully estimate a large-scale two-layer model and a Markov random field.

High-dimensional Ising model selection using ${\ell_1}$-regularized logistic regression

Abstract: We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on $\ell_1$-regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an $\ell_1$-constraint. The method is analyzed under high-dimensional scaling in which both the number of nodes $p$ and maximum neighborhood size $d$ are allowed to grow as a function of the number of observations $n$. Our main results provide sufficient conditions on the triple $(n,p,d)$ and the model parameters for the method to succeed in consistently estimating the neighborhood of every node in the graph simultaneously. With coherence conditions imposed on the population Fisher information matrix, we prove that consistent neighborhood selection can be obtained for sample sizes $n=\Omega(d^3\log p)$ with exponentially decaying error. When these same conditions are imposed directly on the sample matrices, we show that a reduced sample size of $n=\Omega(d^2\log p)$ suffices for the method to estimate neighborhoods consistently. Although this paper focuses on the binary graphical models, we indicate how a generalization of the method of the paper would apply to general discrete Markov random fields.

High-dimensional Ising model selection using ℓ1-regularized logistic regression

Abstract: We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on l1-regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an l1-constraint. The method is analyzed under high-dimensional scaling in which both the number of nodes p and maximum neighborhood size d are allowed to grow as a function of the number of observations n. Our main results provide sufficient conditions on the triple (n, p, d) and the model parameters for the method to succeed in consistently estimating the neighborhood of every node in the graph simultaneously. With coherence conditions imposed on the population Fisher information matrix, we prove that consistent neighborhood selection can be obtained for sample sizes n=Ω(d3log p) with exponentially decaying error. When these same conditions are imposed directly on the sample matrices, we show that a reduced sample size of n=Ω(d2log p) suffices for the method to estimate neighborhoods consistently. Although this paper focuses on the binary graphical models, we indicate how a generalization of the method of the paper would apply to general discrete Markov random fields.

SVM- and MRF-Based Method for Accurate Classification of Hyperspectral Images

Abstract: The high number of spectral bands acquired by hyperspectral sensors increases the capability to distinguish physical materials and objects, presenting new challenges to image analysis and classification. This letter presents a novel method for accurate spectral-spatial classification of hyperspectral images. The proposed technique consists of two steps. In the first step, a probabilistic support vector machine pixelwise classification of the hyperspectral image is applied. In the second step, spatial contextual information is used for refining the classification results obtained in the first step. This is achieved by means of a Markov random field regularization. Experimental results are presented for three hyperspectral airborne images and compared with those obtained by recently proposed advanced spectral-spatial classification techniques. The proposed method improves classification accuracies when compared to other classification approaches.

Superparsing: scalable nonparametric image parsing with superpixels

Abstract: This paper presents a simple and effective nonparametric approach to the problem of image parsing, or labeling image regions (in our case, superpixels produced by bottom-up segmentation) with their categories. This approach requires no training, and it can easily scale to datasets with tens of thousands of images and hundreds of labels. It works by scene-level matching with global image descriptors, followed by superpixel-level matching with local features and efficient Markov random field (MRF) optimization for incorporating neighborhood context. Our MRF setup can also compute a simultaneous labeling of image regions into semantic classes (e.g., tree, building, car) and geometric classes (sky, vertical, ground). Our system outperforms the state-of-the-art non-parametric method based on SIFT Flow on a dataset of 2,688 images and 33 labels. In addition, we report per-pixel rates on a larger dataset of 15,150 images and 170 labels. To our knowledge, this is the first complete evaluation of image parsing on a dataset of this size, and it establishes a new benchmark for the problem.

Semisupervised Hyperspectral Image Segmentation Using Multinomial Logistic Regression With Active Learning

Abstract: This paper presents a new semisupervised segmentation algorithm, suited to high-dimensional data, of which remotely sensed hyperspectral image data sets are an example. The algorithm implements two main steps: 1) semisupervised learning of the posterior class distributions followed by 2) segmentation, which infers an image of class labels from a posterior distribution built on the learned class distributions and on a Markov random field. The posterior class distributions are modeled using multinomial logistic regression, where the regressors are learned using both labeled and, through a graph-based technique, unlabeled samples. Such unlabeled samples are actively selected based on the entropy of the corresponding class label. The prior on the image of labels is a multilevel logistic model, which enforces segmentation results in which neighboring labels belong to the same class. The maximum a posteriori segmentation is computed by the α-expansion min-cut-based integer optimization algorithm. Our experimental results, conducted using synthetic and real hyperspectral image data sets collected by the Airborne Visible/Infrared Imaging Spectrometer system of the National Aeronautics and Space Administration Jet Propulsion Laboratory over the regions of Indian Pines, IN, and Salinas Valley, CA, reveal that the proposed approach can provide classification accuracies that are similar or higher than those achieved by other supervised methods for the considered scenes. Our results also indicate that the use of a spatial prior can greatly improve the final results with respect to a case in which only the learned class densities are considered, confirming the importance of jointly considering spatial and spectral information in hyperspectral image segmentation.

Fusion Moves for Markov Random Field Optimization

Abstract: The efficient application of graph cuts to Markov Random Fields (MRFs) with multiple discrete or continuous labels remains an open question. In this paper, we demonstrate one possible way of achieving this by using graph cuts to combine pairs of suboptimal labelings or solutions. We call this combination process the fusion move. By employing recently developed graph-cut-based algorithms (so-called QPBO-graph cut), the fusion move can efficiently combine two proposal labelings in a theoretically sound way, which is in practice often globally optimal. We demonstrate that fusion moves generalize many previous graph-cut approaches, which allows them to be used as building blocks within a broader variety of optimization schemes than were considered before. In particular, we propose new optimization schemes for computer vision MRFs with applications to image restoration, stereo, and optical flow, among others. Within these schemes the fusion moves are used 1) for the parallelization of MRF optimization into several threads, 2) for fast MRF optimization by combining cheap-to-compute solutions, and 3) for the optimization of highly nonconvex continuous-labeled MRFs with 2D labels. Our final example is a nonvision MRF concerned with cartographic label placement, where fusion moves can be used to improve the performance of a standard inference method (loopy belief propagation).

Markov Random Field Image Models and Their Applications to Computer Vision

Abstract: 1. Introduction. Computer vision refers to a variety of applications involving a sensing device, a computer, and software for restoring and possibly interpreting the sensed data. Most commonly, visible light is sensed by a video camera and converted to an array of measured light intensities, each element corresponding to a small patch in the scene (a picture element, or "pixel"). The image is thereby "digitized," and this format is suitable for computer analysis. In some applications, the sensing mechanism responds to other forms of light, such as in infrared imaging where the camera is tuned to the invisible part of the spectrum neighboring the color red. Infrared light is emitted in proportion to temperature, and thus infrared imaging is suitable for detecting and analyzing the temperature profile of a scene. Applications include automated inspection in industrial settings, medical diagnosis, and targeting and tracking of military objects. In single photon emission tomography, as a diagnostic tool, individual photons, emitted from a "radiopharmaceutical" (isotope combined with a suitable pharmaceutical) are detected. The object is to reconstruct the distribution of isotope density inside the body from the externally-collected counts. Depending on the pharmaceutical, the isotope density may correspond to local blood flow ("perfusion") or local metabolic activity. Other applications of computer vision include satellite imaging for weather and crop yield prediction, radar imaging in military applications, ultrasonic imaging for industrial inspection and a host of medical applications, and there is a growing role for video imaging in robotics. The variety of applications has yielded an equal variety of algorithms for restoration and interpretation. Unfortunately, few general principals have emerged and no common foundation has been layed. Algorithms are by and-large-ad=hoet=they=are=typic^^ ically tuned to the particulars of the environment (lighting, weather conditions, magnification, and so on) in which they are implemented. It is likely that a

Semantic segmentation of urban scenes using dense depth maps

Abstract: In this paper we present a framework for semantic scene parsing and object recognition based on dense depth maps. Five view-independent 3D features that vary with object class are extracted from dense depth maps at a superpixel level for training a classifier using randomized decision forest technique. Our formulation integrates multiple features in a Markov Random Field (MRF) framework to segment and recognize different object classes in query street scene images. We evaluate our method both quantitatively and qualitatively on the challenging Cambridge-driving Labeled Video Database (CamVid). The result shows that only using dense depth information, we can achieve overall better accurate segmentation and recognition than that from sparse 3D features or appearance, or even the combination of sparse 3D features and appearance, advancing state-of-the-art performance. Furthermore, by aligning 3D dense depth based features into a unified coordinate frame, our algorithm can handle the special case of view changes between training and testing scenarios. Preliminary evaluation in cross training and testing shows promising results.

Scene Text Extraction with Edge Constraint and Text Collinearity

Abstract: In this paper, we propose a framework for isolating text regions from natural scene images. The main algorithm has two functions: it generates text region candidates, and it verifies of the label of the candidates (text or non-text). The text region candidates are generated through a modified K-means clustering algorithm, which references texture features, edge information and color information. The candidate labels are then verified in a global sense by the Markov Random Field model where collinearity weight is added as long as most texts are aligned. The proposed method achieves reasonable accuracy for text extraction from moderately difficult examples from the ICDAR 2003 database.

Bayesian Markov Random Field analysis for protein function prediction based on network data.

Abstract: Inference of protein functions is one of the most important aims of modern biology. To fully exploit the large volumes of genomic data typically produced in modern-day genomic experiments, automated computational methods for protein function prediction are urgently needed. Established methods use sequence or structure similarity to infer functions but those types of data do not suffice to determine the biological context in which proteins act. Current high-throughput biological experiments produce large amounts of data on the interactions between proteins. Such data can be used to infer interaction networks and to predict the biological process that the protein is involved in. Here, we develop a probabilistic approach for protein function prediction using network data, such as protein-protein interaction measurements. We take a Bayesian approach to an existing Markov Random Field method by performing simultaneous estimation of the model parameters and prediction of protein functions. We use an adaptive Markov Chain Monte Carlo algorithm that leads to more accurate parameter estimates and consequently to improved prediction performance compared to the standard Markov Random Fields method. We tested our method using a high quality S.cereviciae validation network with 1622 proteins against 90 Gene Ontology terms of different levels of abstraction. Compared to three other protein function prediction methods, our approach shows very good prediction performance. Our method can be directly applied to protein-protein interaction or coexpression networks, but also can be extended to use multiple data sources. We apply our method to physical protein interaction data from S. cerevisiae and provide novel predictions, using 340 Gene Ontology terms, for 1170 unannotated proteins and we evaluate the predictions using the available literature.

Spatio-temporal context for codebook-based dynamic background subtraction

Abstract: In background subtraction, it is challenging to detect foreground objects in the presence of dynamic background motions. The paper proposes two new algorithms to this problem by improving the codebook model with the incorporation of the spatial and temporal context of each pixel. The spatial context involves the local spatial dependency between neighboring pixels, and the temporal context involves the preceding detection result. Only the spatial context is incorporated into the first algorithm which makes the background representation more compact than the standard codebook. The second algorithm explicitly models the spatio-temporal context with a Markov random field model, thus achieving more accurate foreground detection. Extensive experiments on several dynamic scenes are conducted to compare the two proposed algorithms with each other and with the standard codebook algorithm. (C) 2009 Elsevier GmbH. All rights reserved.

A Label Field Fusion Bayesian Model and Its Penalized Maximum Rand Estimator for Image Segmentation

Abstract: This paper presents a novel segmentation approach based on a Markov random field (MRF) fusion model which aims at combining several segmentation results associated with simpler clustering models in order to achieve a more reliable and accurate segmentation result. The proposed fusion model is derived from the recently introduced probabilistic Rand measure for comparing one segmentation result to one or more manual segmentations of the same image. This non-parametric measure allows us to easily derive an appealing fusion model of label fields, easily expressed as a Gibbs distribution, or as a nonstationary MRF model defined on a complete graph. Concretely, this Gibbs energy model encodes the set of binary constraints, in terms of pairs of pixel labels, provided by each segmentation results to be fused. Combined with a prior distribution, this energy-based Gibbs model also allows for definition of an interesting penalized maximum probabilistic rand estimator with which the fusion of simple, quickly estimated, segmentation results appears as an interesting alternative to complex segmentation models existing in the literature. This fusion framework has been successfully applied on the Berkeley image database. The experiments reported in this paper demonstrate that the proposed method is efficient in terms of visual evaluation and quantitative performance measures and performs well compared to the best existing state-of-the-art segmentation methods recently proposed in the literature.

Multivariate Image Segmentation Using Semantic Region Growing With Adaptive Edge Penalty

Abstract: Multivariate image segmentation is a challenging task, influenced by large intraclass variation that reduces class distinguishability as well as increased feature space sparseness and solution space complexity that impose computational cost and degrade algorithmic robustness. To deal with these problems, a Markov random field (MRF) based multivariate segmentation algorithm called “multivariate iterative region growing using semantics” (MIRGS) is presented. In MIRGS, the impact of intraclass variation and computational cost are reduced using the MRF spatial context model incorporated with adaptive edge penalty and applied to regions. Semantic region growing starting from watershed over-segmentation and performed alternatively with segmentation gradually reduces the solution space size, which improves segmentation effectiveness. As a multivariate iterative algorithm, MIRGS is highly sensitive to initial conditions. To suppress initialization sensitivity, it employs a region-level k -means (RKM) based initialization method, which consistently provides accurate initial conditions at low computational cost. Experiments show the superiority of RKM relative to two commonly used initialization methods. Segmentation tests on a variety of synthetic and natural multivariate images demonstrate that MIRGS consistently outperforms three other published algorithms.

Information-theoretic bounds on model selection for Gaussian Markov random fields

Abstract: The problem of graphical model selection is to estimate the graph structure of an unknown Markov random field based on observed samples from the graphical model. For Gaussian Markov random fields, this problem is closely related to the problem of estimating the inverse covariance matrix of the underlying Gaussian distribution. This paper focuses on the information-theoretic limitations of Gaussian graphical model selection and inverse covariance estimation in the high-dimensional setting, in which the graph size p and maximum node degree d are allowed to grow as a function of the sample size n. Our first result establishes a set of necessary conditions on n(p, d) for any recovery method to consistently estimate the underlying graph. Our second result provides necessary conditions for any decoder to produce an estimate Θ Θ of the true inverse covariance matrix T satisfying ‖ Θ-Θ ‖ ∞ -norm (which implies analogous results in the Frobenius norm as well). Combined with previously known sufficient conditions for polynomial-time algorithms, these results yield sharp characterizations in several regimes of interest.

Impact of rock-physics depth trends and Markov random fields on hierarchical Bayesian lithology/fluid prediction

Abstract: Early assessments of petroleum reservoirs are usually based on seismic data and observations in a small number of wells. Decision-making concerning the reservoir will be improved if these data can be integrated and converted into a lithology/fluid map of the reservoir. We analyze lithology/fluid prediction in a Bayesian setting, based on prestack seismic data and well observations. The likelihood model contains a convolved linearized Zoeppritz relation and rock-physics models with depth trends caused by compaction and cementation. Well observations are assumed to be exact. The likelihood model contains several global parameters such as depth trend, wavelets, and error parameters; the inference of these is an integral part of the study. The prior model is based on a profile Markov random field parameterized to capture different continuity directions for lithologies and fluids. The posterior model captures prediction and model-parameter uncertainty and is assessed by Markov-chain Monte Carlo simulation-base...

Markov Random Field Surface Reconstruction

Abstract: A method for implicit surface reconstruction is proposed. The novelty in this paper is the adaption of Markov Random Field regularization of a distance field. The Markov Random Field formulation allows us to integrate both knowledge about the type of surface we wish to reconstruct (the prior) and knowledge about data (the observation model) in an orthogonal fashion. Local models that account for both scene-specific knowledge and physical properties of the scanning device are described. Furthermore, how the optimal distance field can be computed is demonstrated using conjugate gradients, sparse Cholesky factorization, and a multiscale iterative optimization scheme. The method is demonstrated on a set of scanned human heads and, both in terms of accuracy and the ability to close holes, the proposed method is shown to have similar or superior performance when compared to current state-of-the-art algorithms.

Document Ink Bleed-Through Removal with Two Hidden Markov Random Fields and a Single Observation Field

Abstract: We present a new method for blind document bleed-through removal based on separate Markov random field (MRF) regularization for the recto and for the verso side, where separate priors are derived from the full graph. The segmentation algorithm is based on Bayesian maximum a posteriori (MAP) estimation. The advantages of this separate approach are the adaptation of the prior to the contents creation process (e.g., superimposing two handwritten pages), and the improvement of the estimation of the recto pixels through an estimation of the verso pixels covered by recto pixels; moreover, the formulation as a binary labeling problem with two hidden labels per pixels naturally leads to an efficient optimization method based on the minimum cut/maximum flow in a graph. The proposed method is evaluated on scanned document images from the 18th century, showing an improvement of character recognition results compared to other restoration methods.

An Extension of the Standard Mixture Model for Image Segmentation

Abstract: Standard Gaussian mixture modeling (GMM) is a well-known method for image segmentation. However, the pixels themselves are considered independent of each other, making the segmentation result sensitive to noise. To reduce the sensitivity of the segmented result with respect to noise, Markov random field (MRF) models provide a powerful way to account for spatial dependences between image pixels. However, their main drawback is that they are computationally expensive to implement, and require large numbers of parameters. Based on these considerations, we propose an extension of the standard GMM for image segmentation, which utilizes a novel approach to incorporate the spatial relationships between neighboring pixels into the standard GMM. The proposed model is easy to implement and compared with MRF models, requires lesser number of parameters. We also propose a new method to estimate the model parameters in order to minimize the higher bound on the data negative log-likelihood, based on the gradient method. Experimental results obtained on noisy synthetic and real world grayscale images demonstrate the robustness, accuracy and effectiveness of the proposed model in image segmentation, as compared to other methods based on standard GMM and MRF models.

Unsupervised classification of digital images using enhanced sensor pattern noise

Abstract: We present in this work an unsupervised image classifier, which is capable of clustering images taken by an unknown number of unknown digital cameras into a number of classes, each corresponding to one camera. The classification system first extracts and enhances a sensor pattern noise (SPN) from each image, which serves as the fingerprint of the camera that has taken the image. Secondly, it applies an unsupervised classifier trainer to a small training set of randomly selected SPNs to cluster the SPNs into classes and uses the centroids of those identified classes as the trained classifier. The classifier trainer treats each SPN as a random variable and uses Markov random field (MRF) approach to iteratively assigns a class label to each SPN (i.e., random variable) based on the class labels assigned to the members of a small set of SPNs, called membership committee, and the similarity values between it and the members of the membership committee until a stop criteria is met. The classifier trainer requires no a priori knowledge about the dataset from the user. Finally the image not included in the small training set are classified using the trained classifier depending on the similarity between their SPNs and the centroids of the trained classifier.

The Value of Information in Spatial Decision Making

Abstract: Experiments performed over spatially correlated domains, if poorly chosen, may not be worth their cost of acquisition. In this paper, we integrate the decision-analytic notion of value of information with spatial statistical models. We formulate methods to evaluate monetary values associated with experiments performed in the spatial decision making context, including the prior value, the value of perfect information, and the value of the experiment, providing imperfect information. The prior for the spatial distinction of interest is assumed to be a categorical Markov random field whereas the likelihood distribution can take any form depending on the experiment under consideration. We demonstrate how to efficiently compute the value of an experiment for Markov random fields of moderate size, with the aid of two examples. The first is a motivating example with presence-absence data, while the second application is inspired by seismic exploration in the petroleum industry. We discuss insights from the two examples, relating the value of an experiment with its accuracy, the cost and revenue from downstream decisions, and the design of the experiment.

The Infinite Hidden Markov Random Field Model

Abstract: Hidden Markov random field (HMRF) models are widely used for image segmentation, as they appear naturally in problems where a spatially constrained clustering scheme is asked for. A major limitation of HMRF models concerns the automatic selection of the proper number of their states, i.e., the number of region clusters derived by the image segmentation procedure. Existing methods, including likelihood- or entropy-based criteria, and reversible Markov chain Monte Carlo methods, usually tend to yield noisy model size estimates while imposing heavy computational requirements. Recently, Dirichlet process (DP, infinite) mixture models have emerged in the cornerstone of nonparametric Bayesian statistics as promising candidates for clustering applications where the number of clusters is unknown a priori; infinite mixture models based on the original DP or spatially constrained variants of it have been applied in unsupervised image segmentation applications showing promising results. Under this motivation, to resolve the aforementioned issues of HMRF models, in this paper, we introduce a nonparametric Bayesian formulation for the HMRF model, the infinite HMRF model, formulated on the basis of a joint Dirichlet process mixture (DPM) and Markov random field (MRF) construction. We derive an efficient variational Bayesian inference algorithm for the proposed model, and we experimentally demonstrate its advantages over competing methodologies.

Markov random field based super-resolution mapping for identification of urban trees in VHR images

Abstract: Extraction of individual tree crown objects from very high resolution imagery is a challenging task given the limited spectral and spatial resolution of space-borne systems and the complexity of the urban space. Besides, traditional pixel based image classification techniques do not fully exploit the spatial and spectral characteristics of tree crowns imaged in remote sensing datasets. In this work, we propose a contextual and probabilistic detection of tree crowns in very high resolution imagery by using super resolution mapping (SRM) based on Markov random fields (MRF). Our method models and objective energy function which considers the conditional probabilities of panchromatic and multispectral values of a Quickbird image and models the prior information as the spatial smoothness of pixels labeled as tree crown. We apply this method for extraction of tree crown objects in a residential area in the Netherlands. We found that the proposed method leads to improvement in tree crown identification compared with a maximum likelihood classification of a pan-sharpened product.

Image segmentation with topic random field

Abstract: Recently, there has been increasing interests in applying aspect models (e.g., PLSA and LDA) in image segmentation. However, these models ignore spatial relationships among local topic labels in an image and suffers from information loss by representing image feature using the index of its closest match in the codebook. In this paper, we propose Topic Random Field (TRF) to tackle these two problems. Specifically, TRF defines a Markov Random Field over hidden labels of an image, to enforce the spatial coherence between topic labels for neighboring regions. Moreover, TRF utilizes a noise channel to model the generation of local image features, and avoids the off-line process of building visual codebook. We provide details of variational inference and parameter learning for TRF. Experimental evaluations on three image data sets show that TRF achieves better segmentation performance.

Handwriting Recognition: Soft Computing and Probabilistic Approaches

Abstract: In this book, we introduce several methods for recognising unconstrained handwritten words and digits using hidden Markov models (HMMs) and Markov random field (MRF) models. Since the hidden Markov model (HMM) is stochastic finite state automation, it is able to represent a sequence of features. we used HMMs to model features that are extracted from outer contours of images to form sequences. To overcome the limitation of HMMs in modelling structural information, we used structural models, which are based on the best sequences of states, to represent structural information and enhance the performance of HMMs. In addition, we presented a procdure to model relationships between spectral components using 2-D HMMs, where the spectral features are extracted by Fourier descriptor. This method can be used to recognise two-dimensional shapes as well as handwritten digits. Markov random field models are appropriate to model two-dimensional features of handwritten words and digits. The most important merit of Markov random field models is that they provide flexible and natural methods for modelling the interaction between spatially related random variables in their neighbourhood systems via designed clique functions. In MRF model, the global optimum can be derived from local information in term of clique functions. This book also describes methods to use MRFs to model structural relationships between line-segments for recognising handwritten words and to model both structural and statistical information for recognising handwritten digits. Relaxation labelling is used to maximise the global compatibility of MRF models. To evaluate the proposed methods, we had conducted experiments on two databases: handwritten word database and handwritten digit database. Both databases are taken from USPS CEDAR CDROM1. The recognition rates for handwritten words are from 69.0% to 96.5% among top 1 to top 5 positions with only 7.5 training images per word on the average. The recognition rates for handwritten digits range from 96.48\% to 98.37% with different methods. These results show our method can achieve recognition rates comparable to that reported in the literature recently.

Joint registration and segmentation of dynamic cardiac perfusion images using MRFs

Abstract: In this paper we propose a Markov random field (MRF) based method for joint registration and segmentation of cardiac perfusion images, specifically the left ventricle (LV). MRFs are suitable for discrete labeling problems and the labels are defined as the joint occurrence of displacement vectors (for registration) and segmentation class. The data penalty is a combination of gradient information and mutual dependency of registration and segmentation information. The smoothness cost is a function of the interaction between the defined labels. Thus, the mutual dependency of registration and segmentation is captured in the objective function. Sub-pixel precision in registration and segmentation and a reduction in computation time are achieved by using a multiscale graph cut technique. The LV is first rigidly registered before applying our method. The method was tested on multiple real patient cardiac perfusion datasets having elastic deformations, intensity change, and poor contrast between LV and the myocardium. Compared to MRF based registration and graph cut segmentation, our method shows superior performance by including mutually beneficial registration and segmentation information.

Occlusion boundary detection using pseudo-depth

Abstract: We address the problem of detecting occlusion boundaries from motion sequences, which is important for motion segmentation, estimating depth order, and related tasks. Previous work by Stein and Hebert has addressed this problem and obtained good results on a benchmarked dataset using two-dimensional image cues, motion estimation, and a global boundary model [1]. In this paper we describe a method for detecting occlusion boundaries which uses depth cues and local segmentation cues. More specifically, we show that crude scaled estimates of depth, which we call pseudo-depth, can be extracted from motion sequences containing a small number of image frames using standard SVD factorization methods followed by weak smoothing using a Markov Random Field defined over super-pixels. We then train a classifier for occlusion boundaries using pseudo-depth and local static boundary cues (adding motion cues only gives slightly better results). We evaluate performance on Stein and Hebert's dataset and obtain results of similar average quality which are better in the low recall/high precision range. Note that our cues and methods are different from [1] - in particular we did not use their sophisticated global boundary model - and so we conjecture that a unified approach would yield even better results.