Automatic segmentation for brain MR images via a convex optimized segmentation and bias field correction coupled model

Accurate segmentation of magnetic resonance (MR) images remains challenging mainly due to the intensity inhomogeneity, which is also commonly known as bias field. Recently active contour models with geometric information constraint have been applied, however, most of them deal with the bias field by using a necessary pre-processing step before segmentation of MR data. This paper presents a novel automatic variational method, which can segment brain MR images meanwhile correcting the bias field when segmenting images with high intensity inhomogeneities. We first define a function for clustering the image pixels in a smaller neighborhood. The cluster centers in this objective function have a multiplicative factor that estimates the bias within the neighborhood. In order to reduce the effect of the noise, the local intensity variations are described by the Gaussian distributions with different means and variances. Then, the objective functions are integrated over the entire domain. In order to obtain the global optimal and make the results independent of the initialization of the algorithm, we reconstructed the energy function to be convex and calculated it by using the Split Bregman theory. A salient advantage of our method is that its result is independent of initialization, which allows robust and fully automated application. Our method is able to estimate the bias of quite general profiles, even in 7T MR images. Moreover, our model can also distinguish regions with similar intensity distribution with different variances. The proposed method has been rigorously validated with images acquired on variety of imaging modalities with promising results.     

A dual image approach for bias field correction in magnetic resonance imaging

In this paper, we propose a dual image approach to correcting intensity inhomogeneities for MR images acquired using surface coils. Previous methods are usually not satisfactory due to restricted application domains, considerable human interactions, or some undesirable artifacts. The proposed algorithm provides nice correction results for a variety of surface-coil MR images. It is accomplished by using an additional body-coil MR image of a smaller size captured at the same position as that of the surface-coil image to facilitate the estimation of the bias field function. The correction algorithm consists of aligning the surface-coil image with the body-coil image and fitting a spline surface from a sparse set of data points for the associated bias field function. Experiments on some real images show satisfactory correction results by using the proposed algorithm.     

Non-locally regularized segmentation of multiple sclerosis lesion from multi-channel MRI data

Segmentation of multiple sclerosis (MS) lesion is important for many neuroimaging studies. In this paper, we propose a novel algorithm for automatic segmentation of MS lesions from multi-channel MR images (T1W, T2W and FLAIR images). The proposed method is an extension of Li et al.'s algorithm in [1], which only segments the normal tissues from T1W images. The proposed method is aimed to segment MS lesions, while normal tissues are also segmented and bias field is estimated to handle intensity inhomogeneities in the images. Another contribution of this paper is the introduction of a nonlocal means technique to achieve spatially regularized segmentation, which overcomes the influence of noise. Experimental results have demonstrated the effectiveness and advantages of the proposed algorithm.     

Image-guided regularization level set evolution for MR image segmentation and bias field correction

Magnetic resonance (MR) image segmentation is a crucial step in surgical and treatment planning. In this paper, we propose a level-set-based segmentation method for MR images with intensity inhomogeneous problem. To tackle the initialization sensitivity problem, we propose a new image-guided regularization to restrict the level set function. The maximum a posteriori inference is adopted to unify segmentation and bias field correction within a single framework. Under this framework, both the contour prior and the bias field prior are fully used. As a result, the image intensity inhomogeneity can be well solved. Extensive experiments are provided to evaluate the proposed method, showing significant improvements in both segmentation and bias field correction accuracies as compared with other state-of-the-art approaches.     

An energy minimization method for MS lesion segmentation from T1-w and FLAIR images

In this paper, we extend the multiplicative intrinsic component optimization (MICO) algorithm to multichannel MR image segmentation, with focus on segmentation of multiple sclerosis (MS) lesions. The MICO algorithm was originally proposed by Li et al. in Ref. [1] for normal brain tissue segmentation and intensity inhomogeneity correction of a single channel MR image, which exhibits desirable advantages over other methods for MR image segmentation and intensity inhomogeneity correction in terms of segmentation accuracy and robustness. In this paper, we extend the MICO algorithm to multi-channel MR image segmentation and enable the segmentation of MS lesions. We assign different weights for different channels to control the impact of each channel. The weighted channels allow the enhancement of the impact of the FLAIR image on the segmentation of MS lesions by assigning a larger weight to the FLAIR image channel than the other channels. With the inherent mechanism of estimation of the bias field, our method is able to deal with the intensity inhomogeneity in the input multi-channel MR images. In the application of our method, we only use T1-w and FLAIR images as the input two channel MR images. Experimental results show promising result of our method.     

Use of a Phase Reference for Field Mapping with Amplitude Images at Low Field

We present a method to obtain MRI amplitude images that can picture the magnetic field due to arbitrary shaped magnetized objects. The method employees the gradient recalled echo sequence and two sets of data obtained in separate experiments, one of which provides a phase reference image making it possible to eliminate the effect of theB₀field inhomogeneities. The final magnitude images have a good signal-to-noise even at low fields, and provide qualitative as well as quantitative information about the magnetic field produced by the ferromagnetic object. As an example the method is applied to study the field produced by a small metal piece in a 500-G scanner, and the experimental results are compared with numerical simulations.     

B(1)(+)/actual flip angle and reception sensitivity mapping methods: simulation and comparison

Knowledge of the spatial distribution of transmission field B₁⁺ and reception sensitivity maps is important in high-field (≥3 T) human magnetic resonance (MR) imaging for several reasons: these include post-acquisition correction of intensity inhomogeneities, which may affect the quality of images; modeling and design of radiofrequency (RF) coils and pulses; validating theoretical models for electromagnetic field calculations; testing the compatibility with MR environment of biomedical implants. Moreover, inhomogeneities in the RF field are an essential source of error for quantitative MR spectroscopy. Recent studies have also shown that B₁⁺ and reception sensitivity maps can be used for direct calculation of tissue electrical parameters and for estimating the local specific absorption rate (SAR) in vivo.Several B₁⁺ mapping techniques have been introduced in the past few years based on actual flip angle (FA) mapping, but, to date, none has emerged as a standard. For reception sensitivity calculation, the signal intensity equation can be used where the nominal FA distribution must be replaced with the actual FA distribution calculated by one of the B₁⁺ mapping techniques.This study introduces a quantitative comparison between two known methods for B₁⁺/actual FA and reception sensitivity mapping: the double-angle method (DAM) and the fitting (FIT) method. Experimental data obtained using DAM and FIT methods are also compared with numerical simulation results.     

Multiplicative intrinsic component optimization (MICO) for MRI bias field estimation and tissue segmentation

This paper proposes a new energy minimization method called multiplicative intrinsic component optimization (MICO) for joint bias field estimation and segmentation of magnetic resonance (MR) images. The proposed method takes full advantage of the decomposition of MR images into two multiplicative components, namely, the true image that characterizes a physical property of the tissues and the bias field that accounts for the intensity inhomogeneity, and their respective spatial properties. Bias field estimation and tissue segmentation are simultaneously achieved by an energy minimization process aimed to optimize the estimates of the two multiplicative components of an MR image. The bias field is iteratively optimized by using efficient matrix computations, which are verified to be numerically stable by matrix analysis. More importantly, the energy in our formulation is convex in each of its variables, which leads to the robustness of the proposed energy minimization algorithm. The MICO formulation can be naturally extended to 3D/4D tissue segmentation with spatial/sptatiotemporal regularization. Quantitative evaluations and comparisons with some popular softwares have demonstrated superior performance of MICO in terms of robustness and accuracy.     

Modulation-spectral method for analyzing the amplitude-phase structure of optical inhomogeneities of objects

An original solution to the phase problem in optics is considered as applied to the problems of recording and analysis of the amplitude-phase structure of optical fields used for studying fine structures and inhomogeneities in steady-state objects producing effects to fractions of the wavelength period. The problem is solved by probing objects using radiation with a known structure. Intensity distributions of the probing field are detected at the exit from the object by using the modulation-spectral method directly for the spatial frequency spectrum and for the spatial frequency spectrum subjected to additional modulation formed in a special way, which is realized in the plane under study and provides visualization of the phase information contained in the light field in some form. The intensity distributions obtained make it possible to calculate the two-dimensional amplitude-phase structure of the field analyzed and, hence, the fine structure of the optical inhomogeneities of the object analyzed for the chosen probing direction. For steady-state objects, probing in a number of directions is possible. Information on the bulk structure of the inhomogeneities under study can be obtained by using the information available on the symmetry of the object. Two variants of action of the medium on probing radiation are considered. In the first one, the action is related to spatial field modulation (described by the multiplication operation); in the second one, the action leads to redistribution of radiation in the plane studied (described by the convolution operation).     

Brain tissue classification based on DTI using an improved Fuzzy C-means algorithm with spatial constraints

We present an effective method for brain tissue classification based on diffusion tensor imaging (DTI) data. The method accounts for two main DTI segmentation obstacles: random noise and magnetic field inhomogeneities. In the proposed method, DTI parametric maps were used to resolve intensity inhomogeneities of brain tissue segmentation because they could provide complementary information for tissues and define accurate tissue maps. An improved fuzzy c-means with spatial constraints proposal was used to enhance the noise and artifact robustness of DTI segmentation. Fuzzy c-means clustering with spatial constraints (FCM_S) could effectively segment images corrupted by noise, outliers, and other imaging artifacts. Its effectiveness contributes not only to the introduction of fuzziness for belongingness of each pixel but also to the exploitation of spatial contextual information. We proposed an improved FCM_S applied on DTI parametric maps, which explores the mean and covariance of the feature spatial information for automated segmentation of DTI. The experiments on synthetic images and real-world datasets showed that our proposed algorithms, especially with new spatial constraints, were more effective.     

A novel, fast entropy-minimization algorithm for bias field correction in MR images

A novel, fast entropy-minimization algorithm for bias field correction in magnetic resonance (MR) images is suggested to correct the intensity inhomogeneity degradation of MR images that has become an increasing problem with the use of phased-array coils. Four important modifications were made to the conventional algorithm: (a) implementation of a modified two-step sampling strategy for stacked 2D image data sets, which included reducing the size of the measured image on each slice with a simple averaging method without changing the number of slices and then using a binary mask generated by a histogram threshold method to define the sampled voxels in the reduced image; (b) improvement of the efficiency of the correction function by using a Legendre polynomial as an orthogonal base function polynomial; (c) use of a nonparametric Parzen window estimator with a Gaussian kernel to calculate the probability density function and Shannon entropy directly from the image data; and (d) performing entropy minimization with a conjugate gradient method. Results showed that this algorithm could correct different types of MR images from different types of coils acquired at different field strengths very efficiently and with decreased computational load.     

A non-iterative multi-scale approach for intensity inhomogeneity correction in MRI

Intensity inhomogeneity is the prime obstacle for MR image processing like automatic segmentation, registration etc. This complication has strong dependence on the associated acquisition hardware and patient anatomy which recommends retrospective correction. In this paper, a new method is developed for correcting the intensity inhomogeneity using a non-iterative multi-scale approach that doesn't necessitate segmentation and any prior knowledge on the scanner or subject. The proposed algorithm extracts bias field at different scales using a Log-Gabor filter bank followed by smoothing operation. Later, they are combined to fit a third degree polynomial to estimate the bias field. Finally, the corrected image is estimated by performing pixel-wise division of original image and bias field. The performance of the same was tested on BrainWeb simulated data, HCP dataset and is found to provide better performance than the state-of-the-art method, N4. A good agreement between the extracted and ground truth bias field is observed through correlation coefficient on different MR modality images that include T1w, T2w and PD. Significant reduction in coefficient variation and coefficient of joint variation ratios in real data indicate an improved inter-class separation and reduced intra-class intensity variations across white and grey matter tissue regions.     

Nonlocal maximum likelihood estimation method for denoising multiple-coil magnetic resonance images

Effective denoising is vital for proper analysis and accurate quantitative measurements from magnetic resonance (MR) images. Even though many methods were proposed to denoise MR images, only few deal with the estimation of true signal from MR images acquired with phased-array coils. If the magnitude data from phased array coils are reconstructed as the root sum of squares, in the absence of noise correlations and subsampling, the data is assumed to follow a non central-χ distribution. However, when the k-space is subsampled to increase the acquisition speed (as in GRAPPA like methods), noise becomes spatially varying. In this note, we propose a method to denoise multiple-coil acquired MR images. Both the non central-χ distribution and the spatially varying nature of the noise is taken into account in the proposed method. Experiments were conducted on both simulated and real data sets to validate and to demonstrate the effectiveness of the proposed method.     

Gaussian mixture model-based gradient field reconstruction for infrared image detail enhancement and denoising

Infrared images are characterized by low signal-to-noise ratio and low contrast. Therefore, the edge details are easily immerged in the background and noise, making it much difficult to achieve infrared image edge detail enhancement and denoising. This article proposes a novel method of Gaussian mixture model-based gradient field reconstruction, which enhances image edge details while suppressing noise. First, by analyzing the gradient histogram of noisy infrared image, Gaussian mixture model is adopted to simulate the distribution of the gradient histogram, and divides the image information into three parts corresponding to faint details, noise and the edges of clear targets, respectively. Then, the piecewise function is constructed based on the characteristics of the image to increase gradients of faint details and suppress gradients of noise. Finally, anisotropic diffusion constraint is added while visualizing enhanced image from the transformed gradient field to further suppress noise. The experimental results show that the method possesses unique advantage of effectively enhancing infrared image edge details and suppressing noise as well, compared with the existing methods. In addition, it can be used to effectively enhance other types of images such as the visible and medical images.     

Analysis of machine-dependent and object-induced geometric distortion in 2DFT MR imaging.

Geometric distortion in MR imaging predominantly arises from the inhomogeneity of the static field and the nonlinearity of the gradients. It is the purpose of this paper to analyse the object and machine related contributions to geometric distortion in order to determine which corrections are necessary for attaining a specified precision. System related imperfections were measured by systematic variation of the strength, direction, and polarity of the read-out gradient in imaging experiments on a grid of cylindrical sample tubes. For the 1.5-T system used in this study, static field related errors up to 7 mm and gradient related errors up to 4 mm were observed (midcoronal plane, FOV 400-mm, G-read between 0.5 and 3.0 mT/m). Field related errors were shown to be inversely proportional to gradient strength, whereas gradient related errors turned out to be virtually independent of gradient strength. It therefore seems recommendable to always apply the strongest available selection and read-out gradients when geometric fidelity is given preference to signal-to-noise considerations. Correction of system related geometric distortions in MR images can readily be performed by table lookup. Object-induced distortions of the gradient fields were studied by experiments on a grid of sample tubes immersed into a cylindrical water bath of variable saline concentration. These experiments revealed a negligible influence of the object on the gradient error distribution, and lead to the conclusion that correction for the nonlinearity of the gradients only requires the application of system dependent correction factors. Object-related distortions of B0 were studied by conventional SE and fat-suppressed IR experiments on phantoms and human subjects. In these experiments the polarity of the read-out gradient was reversed. Subtraction images showed significant object-induced inhomogeneities of the static field at tissue-air interfaces and in the immediate vicinity of the object being imaged. A first attempt to correct for object related B0 inhomogeneities was made by contour analysis of the source images. At present this correction still has to be done manually.     

Hepatic vessel segmentation using variational level set combined with non-local robust statistics

Hepatic vessel segmentation is a challenging step in therapy guided by magnetic resonance imaging (MRI). This paper presents an improved variational level set method, which uses non-local robust statistics to suppress the influence of noise in MR images. The non-local robust statistics, which represent vascular features, are learned adaptively from seeds provided by users. K-means clustering in neighborhoods of seeds is utilized to exclude inappropriate seeds, which are obviously corrupted by noise. The neighborhoods of appropriate seeds are placed in an array to calculate the non-local robust statistics, and the variational level set formulation can be constructed. Bias correction is utilized in the level set formulation to reduce the influence of intensity inhomogeneity of MRI. Experiments were conducted over real MR images, and showed that the proposed method performed better on small hepatic vessel segmentation compared with other segmentation methods.     

A novel content-based active contour model for brain tumor segmentation

Brain tumor segmentation is a crucial step in surgical and treatment planning. Intensity-based active contour models such as gradient vector flow (GVF), magneto static active contour (MAC) and fluid vector flow (FVF) have been proposed to segment homogeneous objects/tumors in medical images. In this study, extensive experiments are done to analyze the performance of intensity-based techniques for homogeneous tumors on brain magnetic resonance (MR) images. The analysis shows that the state-of-art methods fail to segment homogeneous tumors against similar background or when these tumors show partial diversity toward the background. They also have preconvergence problem in case of false edges/saddle points. However, the presence of weak edges and diffused edges (due to edema around the tumor) leads to oversegmentation by intensity-based techniques. Therefore, the proposed method content-based active contour (CBAC) uses both intensity and texture information present within the active contour to overcome above-stated problems capturing large range in an image. It also proposes a novel use of Gray-Level Co-occurrence Matrix to define texture space for tumor segmentation. The effectiveness of this method is tested on two different real data sets (55 patients - more than 600 images) containing five different types of homogeneous, heterogeneous, diffused tumors and synthetic images (non-MR benchmark images). Remarkable results are obtained in segmenting homogeneous tumors of uniform intensity, complex content heterogeneous, diffused tumors on MR images (T1-weighted, postcontrast T1-weighted and T2-weighted) and synthetic images (non-MR benchmark images of varying intensity, texture, noise content and false edges). Further, tumor volume is efficiently extracted from 2-dimensional slices and is named as 2.5-dimensional segmentation.     

基于灰度和空间联合信息最小化的磁共振图像偏差场纠正

在磁共振图像（MR）的偏差场纠正中,针对灰度信息最小化方法没有考虑空间信息问题,提出联合信息最小化方法,该方法把图像的灰度信息和空间信息结合起来.空间信息采用灰度导数信息.被偏差场破坏的图像灰度及其导数值的联合信息（联合熵）大于对应的没被偏差场破坏的图像联合熵.联合熵是通过计算灰度及其导数值的联合概率分布得到.仿真脑部MR数据和临床脑部MR数据的试验结果都表明,灰度及其二阶导数联合信息最小化方法纠正效果良好,大大减少了脑白质和脑灰质的灰度交叠.