Spatial Smoothness Constraint Research Articles

Hyperspectral Unmixing Network Accounting for Spectral Variability Based on a Modified Scaled and a Perturbed Linear Mixing Model

Spectral unmixing is one of the prime topics in hyperspectral image analysis, as images often contain multiple sources of spectra. Spectral variability is one of the key factors affecting unmixing accuracy, since spectral signatures are affected by variations in environmental conditions. These and other factors interfere with the accurate discrimination of source type. Several spectral mixing models have been proposed for hyperspectral unmixing to address the spectral variability problem. The interpretation for the spectral variability of these models is usually insufficient, and the unmixing algorithms corresponding to these models are usually classic unmixing techniques. Hyperspectral unmixing algorithms based on deep learning have outperformed classic algorithms. In this paper, based on the typical extended linear mixing model and the perturbed linear mixing model, the scaled and perturbed linear mixing model is constructed, and a spectral unmixing network based on this model is constructed using fully connected neural networks and variational autoencoders to update the abundances, scales, and perturbations involved in the variable endmembers. Adding spatial smoothness constraints to the scale and adding regularization constraints to the perturbation improve the robustness of the model, and adding sparseness constraints to the abundance determination prevents overfitting. The proposed approach is evaluated on both synthetic and real data sets. Experimental results show the superior performance of the proposed method against other competitors.

Geometric Prior-Guided Self-Supervised Learning for Multi-View Stereo

Recently, self-supervised multi-view stereo (MVS) methods, which are dependent primarily on optimizing networks using photometric consistency, have made clear progress. However, the difference in lighting between different views and reflective objects in the scene can make photometric consistency unreliable. To address this issue, a geometric prior-guided multi-view stereo (GP-MVS) for self-supervised learning is proposed, which exploits the geometric prior from the input data to obtain high-quality depth pseudo-labels. Specifically, two types of pseudo-labels for self-supervised MVS are proposed, based on the structure-from-motion (SfM) and traditional MVS methods. One converts the sparse points of SfM into sparse depth maps and combines the depth maps with spatial smoothness constraints to obtain a sparse prior loss. The other generates initial depth maps for semi-dense depth pseudo-labels using the traditional MVS, and applies a geometric consistency check to filter the wrong depth in the initial depth maps. We conducted extensive experiments on the DTU and Tanks and Temples datasets, which demonstrate that our method achieves state-of-the-art performance compared to existing unsupervised/self-supervised approaches, and even performs on par with traditional and supervised approaches.

Time-Variant Spectrum Mapping via Reduced Basis Representation and Greedy Sampling Locations Optimization

Spectrum mapping has been increasingly important in various wireless communication applications, such as spectrum management, network planning, power control, dynamic spectrum access etc. In this letter, we consider the problem of time-varying spectrum situation map reconstruction using a small amount of sampled data. In contrast to traditional assumption that the statistical signal propagation model is known, we infer spatial propagation characteristics from the spectrum data. Then, a greedy optimization is applied to calculate the sampling locations with the reduced spatial spectrum situation basis representation, which also converts the original underdetermined problem of spectrum situation recovery into a least squares problem with spatial smoothness constraint, thus greatly reducing the matrix operations. Simulations confirm the superiority of our proposed algorithm in reconstruction performance and computational efficiency in online spectrum mapping tasks.

DiFiR-CT: Distance field representation to resolve motion artifacts in computed tomography.

Motion during data acquisition leads to artifacts in computed tomography (CT) reconstructions. In cases such as cardiac imaging, not only is motion unavoidable, but evaluating the motion of the object is of clinical interest. Reducing motion artifacts has typically been achieved by developing systems with faster gantry rotation or via algorithms which measure and/or estimate the displacement. However, these approaches have had limited success due to both physical constraints as well as the challenge of estimating non-rigid, temporally varying, and patient-specific motionfields. To develop a novel reconstruction method which generates time-resolved, artifact-free images without estimation or explicit modeling of themotion. We describe an analysis-by-synthesis approach which progressively regresses a solution consistent with the acquired sinogram. In our method, we focus on the movement of object boundaries. Not only are the boundaries the source of image artifacts, but object boundaries can simultaneously be used to represent both the object as well as its motion over time without the need for an explicit motion model. We represent the object boundaries via a signed distance function (SDF) which can be efficiently modeled using neural networks. As a result, optimization can be performed under spatial and temporal smoothness constraints without the need for explicit motion estimation. We illustrate the utility of DiFiR-CT in three imaging scenarios with increasing motion complexity: translation of a small circle, heart-like change in an ellipse's diameter, and a complex topological deformation. Compared to filtered backprojection, DiFiR-CT provides high quality image reconstruction for all three motions without hyperparameter tuning or change to the architecture. We also evaluate DiFiR-CT's robustness to noise in the acquired sinogram and found its reconstruction to be accurate across a wide range of noise levels. Lastly, we demonstrate how the approach could be used for multi-intensity scenes and illustrate the importance of the initial segmentation providing a realistic initialization. Code and supplemental movies are available at https://kunalmgupta.github.io/projects/DiFiR-CT.html. Projection data can be used to accurately estimate a temporally-evolving scene without the need for explicit motion estimation using a neural implicit representation and analysis-by-synthesisapproach.

Joint spectral quantification of MR spectroscopic imaging using linear tangent space alignment-based manifold learning.

To develop a manifold learning-based method that leverages the intrinsic low-dimensional structure of MR Spectroscopic Imaging (MRSI) signals for joint spectral quantification. A linear tangent space alignment (LTSA) model was proposed to represent MRSI signals. In the proposed model, the signals of each metabolite were represented using a subspace model and the local coordinates of the subspaces were aligned to the global coordinates of the underlying low-dimensional manifold via linear transform. With the basis functions of the subspaces predetermined via quantum mechanics simulations, the global coordinates and the matrices for the local-to-global coordinate alignment were estimated by fitting the proposed LTSA model to noisy MRSI data with a spatial smoothness constraint on the global coordinates and a sparsity constraint on the matrices. The performance of the proposed method was validated using numerical simulation data and in vivo proton-MRSI experimental data acquired on healthy volunteers at 3T. The results of the proposed method were compared with the QUEST method and the subspace-based method. In all the compared cases, the proposed method achieved superior performance over the QUEST and the subspace-based methods both qualitatively in terms of noise and artifacts in the estimated metabolite concentration maps, and quantitatively in terms of spectral quantification accuracy measured by normalized root mean square errors. Joint spectral quantification using linear tangent space alignment-based manifold learning improves the accuracy of MRSI spectral quantification.

Windowed 4D inversion for near real-time geoelectrical monitoring applications

Many different approaches have been developed to regularise the time-lapse geoelectrical inverse problem. While their advantages and limitations have been demonstrated using synthetic models, there have been few direct comparisons of their performance using field data. We test four time-lapse inversion methods (independent inversion, temporal smoothness-constrained 4D inversion, spatial smoothness constrained inversion of temporal data differences, and sequential inversion with spatial smoothness constraints on the model and its temporal changes). We focus on the applicability of these methods to automated processing of geoelectrical monitoring data in near real-time. In particular, we examine windowed 4D inversion, the use of short sequences of time-lapse data, without which the 4D method would not be suitable in the near real-time context. We develop measures of internal consistency for the different methods so that the effects of the use of short time windows or the choice of baseline data set can be compared. The resulting inverse models are assessed against qualitative and quantitative ground truth information. Our findings are that 4D inversion of the full data set performed best, and that windowed 4D inversion retained the majority of its benefits while also being applicable to applications requiring near real-time inversion.

Evaluation of the 3D Near-Surface Velocity Structure in an Urban Environment from Ambient Noise Array Tomography: The Case of the City of Thessaloniki (Northern Greece)

Abstract We examine the implementation of ambient noise array tomography in an urban environment to assess the 3D near-surface shear wave velocity (VS) structure at an intermediate spatial scale (∼1 km2, depth range 200–300 m). The application employs cross correlation traces of vertical component ambient noise recordings from a local network installed in Thessaloniki city (Northern Greece), allowing the determination of Rayleigh wave travel times for the frequency range of 1.5–14 Hz. The results confirm the presence of a complex subsurface with strong lateral variations in the geology, with travel times varying up to almost one order of magnitude. A surface wave travel time tomography approach was applied for each frequency to determine the spatial variability of the group velocity, involving the use of approximate Fresnel volumes, as well as damping and spatial smoothing constraints to stabilize the results. We also employed an interfrequency smoothing scheme to obtain smooth but data-compatible dispersion curves at the cost of inverting all travel time data simultaneously. Following the application of several quality cutoff criteria, we reconstructed local group slowness dispersion curves for a predefined tomographic grid in the study area. The final 3D velocity model was determined by a modified Monte Carlo inversion of these dispersion curves and the spatial integration of the obtained 1D VS profiles. Different model parameterizations were tested for the inversion to determine the optimal datafit. The final 3D velocity model is in a very good agreement with the local geology, previous larger scale studies, and other geophysical surveys, providing additional structural constraints (such as hidden fault identification) for the complex sedimentary deposits and bedrock formation in Thessaloniki, up to the depth of ∼250–300 m. The introduction of the aforementioned modifications to the ambient noise array tomography suggests that it can be efficiently adjusted and employed as a reliable tool for imaging the 3D seismic structure in urban environments with complex geology.

A Joint Framework for Denoising and Estimating Diffusion Kurtosis Tensors Using Multiple Prior Information.

Diffusion kurtosis imaging (DKI) has been shown to be valuable in a wide range of neuroscientific and clinical applications. However, reliable estimation of DKI tensors is often compromised by noise, especially for the kurtosis tensor (KT). Here, we propose a joint denoising and estimating framework that integrates multiple sources of prior information, including nonlocal structural self-similarity (NSS), local spatial smoothness (LSS), physical relevance (PR) of the DKI model, and noise characteristics of magnitude diffusion MRI (dMRI) images for improved estimation of DKI tensors. The local and nonlocal spatial smoothing constraints are complementary to each other, making the proposed framework highly effective in reducing the noise fluctuations on DKI tensors, especially KT. As an additional refinement, we propose to impose a physically relevant constraint within our joint denoising and estimation framework. We further adopt the first-moment noise-corrected fitting model (M1NCM) to remove the noncentral χ -distribution noise bias. The effectiveness of integrating multiple sources of priors into the joint framework is verified by comparing the proposed M1NCM-NSS-LSS-PR method with various versions of M1NCM-based estimators and two state-of-the-art methods. Results show that the proposed method outperformed the compared methods in simulations and in-vivo dMRI datasets of both spatially stationary and nonstationary noise distributions. The in-vivo experiments also show that the proposed M1NCM-NSS-LSS-PR method was robust to the number of diffusion directions.

Efficient joint model learning, segmentation and model updating for visual tracking

The Tracking-by-segmentation framework is widely used in visual tracking to handle severe appearance change such as deformation and occlusion. Tracking-by-segmentation methods first segment the target object from the background, then use the segmentation result to estimate the target state. In existing methods, target segmentation is formulated as a superpixel labeling problem constrained by a target likelihood constraint, a spatial smoothness constraint and a temporal consistency constraint. The target likelihood is calculated by a discriminative part model trained independently from the superpixel labeling framework and updated online using historical tracking results as pseudo-labels. Due to the lack of spatial and temporal constraints and inaccurate pseudo-labels, the discriminative model is unreliable and may lead to tracking failure. This paper addresses the aforementioned problems by integrating the objective function of model training into the target segmentation optimization framework. Thus, during the optimization process, the discriminative model can be constrained by spatial and temporal constraints and provides more accurate target likelihoods for part labeling, and the results produce more reliable pseudo-labels for model learning. Moreover, we also propose a supervision switch mechanism to detect erroneous pseudo-labels caused by a severe change in data distribution and switch the classifier to a semi-supervised setting in such a case. Evaluation results on OTB2013, OTB2015 and TC-128 benchmarks demonstrate the effectiveness of the proposed tracking algorithm.

A Patch-Wise Deep Learning Approach for Myocardial Blood Flow Quantification with Robustness to Noise and Nonrigid Motion.

Quantitative analysis of dynamic contrast-enhanced cardiovascular MRI (cMRI) datasets enables the assessment of myocardial blood flow (MBF) for objective evaluation of ischemic heart disease in patients with suspected coronary artery disease. State-of-the-art MBF quantification techniques use constrained deconvolution and are highly sensitive to noise and motion-induced errors, which can lead to unreliable outcomes in the setting of high-resolution MBF mapping. To overcome these limitations, recent iterative approaches incorporate spatial-smoothness constraints to tackle pixel-wise MBF mapping. However, such iterative methods require a computational time of up to 30 minutes per acquired myocardial slice, which is a major practical limitation. Furthermore, they cannot enforce robustness to residual nonrigid motion which can occur in clinical stress/rest studies of patients with arrhythmia. We present a non-iterative patch-wise deep learning approach for pixel-wise MBF quantification wherein local spatio-temporal features are learned from a large dataset of myocardial patches acquired in clinical stress/rest cMRI studies. Our approach is scanner-independent, computationally efficient, robust to noise, and has the unique feature of robustness to motion-induced errors. Numerical and experimental results obtained using real patient data demonstrate the effectiveness of our approach.Clinical Relevance- The proposed patch-wise deep learning approach significantly improves the reliability of high-resolution myocardial blood flow quantification in cMRI by improving its robustness to noise and nonrigid myocardial motion and is up to 300-fold faster than state-of-the-art iterative approaches.

Real-Time Monocular Obstacle Detection Based on Horizon Line and Saliency Estimation for Unmanned Surface Vehicles

Recently, real-time obstacle detection by monocular vision exhibits a promising prospect in enhancing the safety of unmanned surface vehicles (USVs). Since the obstacles that may threaten USVs generally appear below the water edge, most existing methods first detect the horizon line and then search for obstacles below the estimated horizon line. However, these methods detect horizon line only using edge or line features, which are susceptible to interference edges from clouds, waves, and land, eventually resulting in poor obstacle detection. To avoid being affected by interference edges, in this paper, we propose a novel horizon line detection method based on semantic segmentation. The method assumes a Gaussian mixture model (GMM) with spatial smoothness constraints to fit the semantic structure of marine images and simultaneously generate a water segmentation mask. The horizon line is estimated from the water boundary points via straight line fitting. Further, inspired by human visual attention mechanisms, an efficient saliency detection method based on background prior and contrast prior is presented to detect obstacles below the estimated horizon line. To reduce false positives caused by sun glitter, waves and foam, the continuity of the adjacent frames is employed to filter the detected obstacles. An extensive evaluation was conducted on a large marine image dataset collected by our ‘Jinghai VIII’ USV. The experimental results show that the proposed method significantly outperformed the recent state-of-the-art marine obstacle method by 22.07% in terms of F-score while running over 24 fps on an NVIDIA GTX1080Ti GPU.

Photometric constraint for absolute phase unwrapping from single-frequency fringe patterns.

As a fundamental step in fringe projection profilometry, absolute phase unwrapping via single-frequency fringe patterns is still a challenging ill-posed problem, which attracts lots of interest in the research area. To solve the problem above, additional constraints were constructed, such as spatial smoothness constraint (SSC) in spatial phase unwrapping algorithm and viewpoint consistency constraint (VCC) in multi-view systems (e.g., stereo and light-field cameras). However, there still exists phase ambiguity in the unwrapping result based on SSC. Moreover, VCC-based methods rely on additional cameras or light-field cameras, which makes the system complicated and expensive. In this paper, we propose to construct a novel constraint directly from photometric information in captured image intensity, which has never been fully exploited in phase unwrapping. The proposed constraint, named photometric constraint (PC), provides a prospective constraint for absolute phase unwrapping from single-frequency fringe patterns without any additional cameras. Extensive experiments have been conducted for the validation of the proposed method, which achieved comparable performance with the state-of-the-art method, given a traditional camera-projector setup and single high-frequency fringe patterns.

Geodynamic tomography: constraining upper-mantle deformation patterns from Bayesian inversion of surface waves

SUMMARY In the Earth’s upper mantle, seismic anisotropy mainly originates from the crystallographic preferred orientation (CPO) of olivine due to mantle deformation. Large-scale observation of anisotropy in surface wave tomography models provides unique constraints on present-day mantle flow. However, surface waves are not sensitive to the 21 coefficients of the elastic tensor, and therefore the complete anisotropic tensor cannot be resolved independently at every location. This large number of parameters may be reduced by imposing spatial smoothness and symmetry constraints to the elastic tensor. In this work, we propose to regularize the tomographic problem by using constraints from geodynamic modelling to reduce the number of model parameters. Instead of inverting for seismic velocities, we parametrize our inverse problem directly in terms of physical quantities governing mantle flow: a temperature field, and a temperature-dependent viscosity. The forward problem consists of three steps: (1) calculation of mantle flow induced by thermal anomalies, (2) calculation of the induced CPO and elastic properties using a micromechanical model, and (3) computation of azimuthally varying surface wave dispersion curves. We demonstrate how a fully nonlinear Bayesian inversion of surface wave dispersion curves can retrieve the temperature and viscosity fields, without having to explicitly parametrize the elastic tensor. Here, we consider simple flow models generated by spherical temperature anomalies. The results show that incorporating geodynamic constraints in surface wave inversion help to retrieve patterns of mantle deformation. The solution to our inversion problem is an ensemble of models (i.e. thermal structures) representing a posterior probability, therefore providing uncertainties for each model parameter.

Robust Feature Matching with Spatial Smoothness Constraints

Feature matching is to detect and match corresponding feature points in stereo pairs, which is one of the key techniques in accurate camera orientations. However, several factors limit the feature matching accuracy, e.g., image textures, viewing angles of stereo cameras, and resolutions of stereo pairs. To improve the feature matching accuracy against these limiting factors, this paper imposes spatial smoothness constraints over the whole feature point sets with the underlying assumption that feature points should have similar matching results with their surrounding high-confidence points and proposes a robust feature matching method with the spatial smoothness constraints (RMSS). The core algorithm constructs a graph structure from the feature point sets and then formulates the feature matching problem as the optimization of a global energy function with first-order, spatial smoothness constraints based on the graph. For computational purposes, the global optimization of the energy function is then broken into sub-optimizations of each feature point, and an approximate solution of the energy function is iteratively derived as the matching results of the whole feature point sets. Experiments on close-range datasets with some above limiting factors show that the proposed method was capable of greatly improving the matching robustness and matching accuracy of some feature descriptors (e.g., scale-invariant feature transform (SIFT) and Speeded Up Robust Features (SURF)). After the optimization of the proposed method, the inlier number of SIFT and SURF was increased by average 131.9% and 113.5%, the inlier percentages between the inlier number and the total matches number of SIFT and SURF were increased by average 259.0% and 307.2%, and the absolute matching accuracy of SIFT and SURF was improved by average 80.6% and 70.2%.

Nonstationary Least-Squares Decomposition With Structural Constraint for Denoising Multi-Channel Seismic Data

The seismic data usually contains strong random noise, which impedes the effective usage of the seismic signals for imaging and inversion. We propose an effective seismic denoising method based on a least-squares decomposition model. We assume that each trace in the multi-channel seismic data can be decomposed into several smoothly variable components. Since the decomposition is basically an inverse problem, we apply the temporal smoothness to constrain the inversion and control the stability. Considering the spatial coherency in a multi-channel seismic data, we also apply the spatial smoothness constraint to the decomposition. The space constraint is applied along the structural direction of the seismic events to preserve the dipping energy. The structural constraint is equivalent to applying a structure-oriented smoothing that requires the estimation of the local slope from the input noisy data. We validate the effectiveness of the proposed algorithm via several synthetic and real seismic data. The proposed method outperforms the state-of-the-art single-channel and multi-channel algorithms even in the case of strong random noise.

Detection of People With Camouflage Pattern Via Dense Deconvolution Network

In this letter, we explore the detection of people with camouflage pattern in cluttered natural scenes. First, considering the lack of open evaluation and training data on camouflaged people detection, a specific dataset of camouflaged people in natural scenes is constructed by us for the first time to the best of our knowledge. Secon, due to the serious corruption of the discrimination of low-level features by the camouflage patterns and cluttered background, we extract the high-level semantic features in deep convolution network and introduce short connections in deconvolution phase, to construct the dense deconvolution network. In training procedure, we augment and shift the images of camouflaged people to generate the proper training data. Attributing to the usage and fusion of semantic information, the proposed network effectively labels the camouflaged people regions as a whole. Finally, we use the superpixel segmentation and spatial smoothness constraint for further improvement of the detection result. Experimental results demonstrate that the proposed method outperforms the classical camouflaged object detection method and typical CNN-based detection methods.

Strain budget of the Ecuador–Colombia subduction zone: A stochastic view

The 2016 Pedernales earthquake (MW=7.8) ruptured a portion of the Colombia–Ecuador subduction interface where several large historical earthquakes have been documented since the great 1906 earthquake (M=8.6). Considering all significant ruptures that occurred in the region, it has been suggested that the cumulative moment generated co-seismically along this part of the subduction over the last century exceeds the moment deficit accumulated inter-seismically since 1906. Such an excess challenges simple models with earthquakes resetting the elastic strain accumulated inter-seismically in locked asperities. These inferences are however associated with large uncertainties that are generally unknown. The impact of spatial smoothing constraints on co-seismic and inter-seismic models also prevents any robust assessment of the strain budget. We propose a Bayesian kinematic slip model of the 2016 Pedernales earthquake using the most comprehensive dataset to date including InSAR and GPS offsets, tsunami waveforms, and kinematic records from high-rate GPS and strong-motions. In addition, we use inter-seismic geodetic velocities to produce a probabilistic inter-seismic coupling model of the subduction interface. Our stochastic co-seismic and inter-seismic solutions include the ensemble of all plausible models consistent with our prior information and that fit the observations within uncertainties. The analysis of these model ensembles indicates that an excess of co-seismic moment during the 1906–2016 period is likely in Central Ecuador only if we assume that 1942 and 2016 earthquakes are colocated. If this assumption is relaxed, we show that this conclusion no longer holds given uncertainties in co- and inter-seismic processes. The comparison of 1942 and 2016 teleseismic records reveals large uncertainties in the location of the 1942 event, hampering our ability to draw strong conclusions on the unbalanced moment budget in the region. Our results also show a heterogeneous coupling of the subduction interface that coincides with two slip asperities in our co-seismic model for the 2016 Pedernales earthquake and with the location of historical ruptures in 1958, 1979 and 1998. The spatial variability in coupling and complexity in earthquake history suggest strong heterogeneities in frictional properties of the subduction megathrust.

Motion Estimation in Echocardiography Using Sparse Representation and Dictionary Learning.

This paper introduces a new method for cardiac motion estimation in 2-D ultrasound images. The motion estimation problem is formulated as an energy minimization, whose data fidelity term is built using the assumption that the images are corrupted by multiplicative Rayleigh noise. In addition to a classical spatial smoothness constraint, the proposed method exploits the sparse properties of the cardiac motion to regularize the solution via an appropriate dictionary learning step. The proposed method is evaluated on one data set with available ground-truth, including four sequences of highly realistic simulations. The approach is also validated on both healthy and pathological sequences of in vivo data. We evaluate the method in terms of motion estimation accuracy and strain errors and compare the performance with state-of-the-art algorithms. The results show that the proposed method gives competitive results for the considered data. Furthermore, the in vivo strain analysis demonstrates that meaningful clinical interpretation can be obtained from the estimated motion vectors.This paper introduces a new method for cardiac motion estimation in 2-D ultrasound images. The motion estimation problem is formulated as an energy minimization, whose data fidelity term is built using the assumption that the images are corrupted by multiplicative Rayleigh noise. In addition to a classical spatial smoothness constraint, the proposed method exploits the sparse properties of the cardiac motion to regularize the solution via an appropriate dictionary learning step. The proposed method is evaluated on one data set with available ground-truth, including four sequences of highly realistic simulations. The approach is also validated on both healthy and pathological sequences of in vivo data. We evaluate the method in terms of motion estimation accuracy and strain errors and compare the performance with state-of-the-art algorithms. The results show that the proposed method gives competitive results for the considered data. Furthermore, the in vivo strain analysis demonstrates that meaningful clinical interpretation can be obtained from the estimated motion vectors.

Model-Based segmentation of image data using spatially constrained mixture models

Abstract In this paper, a novel Bayesian statistical approach is proposed to tackle the problem of natural image segmentation. The proposed approach is based on finite Dirichlet mixture models in which contextual proportions (i.e., the probabilities of class labels) are modeled with spatial smoothness constraints. The major merits of our approach are summarized as follows: Firstly, it exploits the Dirichlet mixture model which can obtain a better statistical performance than commonly used mixture models (such as the Gaussian mixture model), especially for proportional data (i.e, normalized histogram). Secondly, it explicitly models the mixing contextual proportions as probability vectors and simultaneously integrate spatial relationship between pixels into the Dirichlet mixture model, which results in a more robust framework for image segmentation. Finally, we develop a variational Bayes learning method to update the parameters in a closed-form expression. The effectiveness of the proposed approach is compared with other mixture modeling-based image segmentation approaches through extensive experiments that involve both simulated and natural color images.

VBI-MRF model for image segmentation

In statistical image segmentation, the distribution of pixel values is usually assumed to be Gaussian and the optimal result is believed to be the one that has maximum a posteriori (MAP) probability. In spite of its prevalence and computational efficiency, the Gaussian assumption, however, is not always strictly followed, and hence may lead to less accurate results. Although the variational Bayes inference (VBI), in which statistical model parameters are also assumed to be random variables, has been widely used, it can hardly handle the spatial information embedded in pixels. In this paper, we incorporate spatial smoothness constraints on pixels labels interpreted by the Markov random field (MRF) model into the VBI process, and thus propose a novel statistical model called VBI-MRF for image segmentation. We evaluated our algorithm against the variational expectation-maximization (VEM) algorithm and the hidden Markov random field (HMRF) model and MAP-MRF model based algorithms on both noise-corrupted synthetic images and mosaics of natural texture. Our pilot results suggest that the proposed algorithm can segment images more accurately than other three methods and is capable of producing robust image segmentation.