Fluid registration of diffusion tensor images using information theory

We apply an information-theoretic cost metric, the symmetrized Kullback-Leibler (sKL) divergence, or J-divergence, to fluid registration of diffusion tensor images. The difference between diffusion tensors is quantified based on the sKL-divergence of their associated probability density functions (PDFs). Three-dimensional DTI data from 34 subjects were fluidly registered to an optimized target image. To allow large image deformations but preserve image topology, we regularized the flow with a large-deformation diffeomorphic mapping based on the kinematics of a Navier-Stokes fluid. A driving force was developed to minimize the J-divergence between the deforming source and target diffusion functions, while reorienting the flowing tensors to preserve fiber topography. In initial experiments, we showed that the sKL-divergence based on full diffusion PDFs is adaptable to higher-order diffusion models, such as high angular resolution diffusion imaging (HARDI). The sKL-divergence was sensitive to subtle differences between two diffusivity profiles, showing promise for nonlinear registration applications and multisubject statistical analysis of HARDI data.     

On analyzing diffusion tensor images by identifying manifold structure using isomaps

This paper addresses the problem of statistical analysis of diffusion tensor magnetic resonance images (DT-MRI). DT-MRI cannot be analyzed by commonly used linear methods, due to the inherent nonlinearity of tensors, which are restricted to lie on a nonlinear submanifold of the space in which they are defined, namely R6. We estimate this submanifold using the Isomap manifold learning technique and perform tensor calculations using geodesic distances along this manifold. Multivariate statistics used in group analyses also use geodesic distances between tensors, thereby warranting that proper estimates of means and covariances are obtained via calculations restricted to the proper subspace of R6. Experimental results on data with known ground truth show that the proposed statistical analysis method properly captures statistical relationships among tensor image data, and it identifies group differences. Comparisons with standard statistical analyses that rely on Euclidean, rather than geodesic distances, are also discussed.     

Nonrigid point set matching of white matter tracts for diffusion tensor image analysis

Patient studies based on diffusion tensor images (DTI) require spatial correspondence between subjects. We propose to obtain the correspondence from white matter tracts, by introducing a new method for nonrigid matching of white matter fiber tracts in DTI. The method boils down to point set registration that involves simultaneously clustering and matching of the data points. The tracts are implicitly warped to a common frame of reference to avoid the potential bias toward one of the datasets. The algorithm gradually refines from global to local registration, which is implemented through deterministic annealing. Special care was taken to incorporate the spatial relation between fiber points and the uncertainty in principal diffusion orientation. As a result, the computed clusters are oriented along the fiber tracts and discriminate between adjacent but distinct fiber tracts. This is validated on synthetic and clinical data. The root-mean-squared distance with respect to expert-annotated landmarks is low (3 mm). In contrast to a state-of-the-art nonrigid registration technique, the proposed method is more robust to residual misalignments in terms of measured fractional anisotropy values.     

Segmentation of brain MR images using a charged fluid model

In this paper, we developed a new deformable model, the charged fluid model (CFM), that uses the simulation of a charged fluid to segment anatomic structures in magnetic resonance (MR) images of the brain. Conceptually, the charged fluid behaves like a liquid such that it flows through and around different obstacles. The simulation evolves in two steps governed by Poisson's equation. The first step distributes the elements of the charged fluid within the propagating interface until an electrostatic equilibrium is achieved. The second step advances the propagating front of the charged fluid such that it deforms into a new shape in response to the image gradient. This approach required no prior knowledge of anatomic structures, required the use of only one parameter, and provided subpixel precision in the region of interest. We demonstrated the performance of this new algorithm in the segmentation of anatomic structures on simulated and real brain MR images of different subjects. The CFM was compared to the level-set-based methods [Caselles et al. (1993) and Malladi et al (1995)] in segmenting difficult objects in a variety of brain MR images. The experimental results in different types of MR images indicate that the CFM algorithm achieves good segmentation results and is of potential value in brain image processing applications.     

Bilateral filtering of diffusion tensor magnetic resonance images.

We extend the well-known scalar image bilateral filtering technique to diffusion tensor magnetic resonance images (DTMRI). The scalar version of bilateral image filtering is extended to perform edge-preserving smoothing of DT field data. The bilateral DT filtering is performed in the Log-Euclidean framework which guarantees valid output tensors. Smoothing is achieved by weighted averaging of neighboring tensors. Analogous to bilateral filtering of scalar images, the weights are chosen to be inversely proportional to two distance measures: The geometrical Euclidean distance between the spatial locations of tensors and the dissimilarity of tensors. We describe the noniterative DT smoothing equation in closed form and show how interpolation of DT data is treated as a special case of bilateral filtering where only spatial distance is used. We evaluate different recent DT tensor dissimilarity metrics including the Log-Euclidean, the similarity-invariant Log-Euclidean, the square root of the J-divergence, and the distance scaled mutual diffusion coefficient. We present qualitative and quantitative smoothing and interpolation results and show their effect on segmentation, for both synthetic DT field data, as well as real cardiac and brain DTMRI data.     

用熵与互信息探究信息传输原理

根据信息及其传输的实质建立信息传输的物理模型。用熵与互信息研究信息传输的有效性和可靠性，通过编码和编码定理得到一些重要的性能界限。最后建立了一个数学模型，进一步揭示信息传输原理及其核心理论。     

A note on the validity of statistical bootstrapping for estimating the uncertainty of tensor parameters in diffusion tensor images

Diffusion tensors are estimated from magnetic resonance images (MRIs) that are diffusion-weighted, and those images inherently contain noise. Therefore, noise in the diffusion-weighted images produces uncertainty in estimation of the tensors and their derived parameters, which include eigenvalues, eigenvectors, and the trajectories of fiber pathways that are reconstructed from those eigenvalues and eigenvectors. Although repetition and wild bootstrap methods have been widely used to quantify the uncertainty of diffusion tensors and their derived parameters, we currently lack theoretical derivations that would validate the use of these two bootstrap methods for the estimation of statistical parameters of tensors in the presence of noise. The aim of this paper is to examine theoretically and numerically the repetition and wild bootstrap methods for approximating uncertainty in estimation of diffusion tensor parameters under two different schemes for acquiring diffusion weighted images. Whether these bootstrap methods can be used to quantify uncertainty in some diffusion tensor parameters, such as fractional anisotropy (FA), depends critically on the morphology of the diffusion tensor that is being estimated. The wild and repetition bootstrap methods in particular cannot quantify uncertainty in the principal direction (PD) of isotropic (or oblate) tensor. We also examine the use of bootstrap methods in estimating tensors in a voxel containing multiple tensors, demonstrating their limitations when quantifying the uncertainty of tensor parameters in those locations. Simulation studies are also used to understand more thoroughly our theoretical results. Our findings raise serious concerns about the use of bootstrap methods to quantify the uncertainty of fiber pathways when those pathways pass through voxels that contain either isotropic tensors, oblate tensors, or multiple tensors.      

Segmentation of textured images using a multiresolution Gaussianautoregressive model

We present a new algorithm for segmentation of textured images using a multiresolution Bayesian approach. The new algorithm uses a multiresolution Gaussian autoregressive (MGAR) model for the pyramid representation of the observed image, and assumes a multiscale Markov random field model for the class label pyramid. The models used in this paper incorporate correlations between different levels of both the observed image pyramid and the class label pyramid. The criterion used for segmentation is the minimization of the expected value of the number of misclassified nodes in the multiresolution lattice. The estimate which satisfies this criterion is referred to as the "multiresolution maximization of the posterior marginals" (MMPM) estimate, and is a natural extension of the single-resolution "maximization of the posterior marginals" (MPM) estimate. Previous multiresolution segmentation techniques have been based on the maximum a posterior (MAP) estimation criterion, which has been shown to be less appropriate for segmentation than the MPM criterion. It is assumed that the number of distinct textures in the observed image is known. The parameters of the MGAR model-the means, prediction coefficients, and prediction error variances of the different textures-are unknown. A modified version of the expectation-maximization (EM) algorithm is used to estimate these parameters. The parameters of the Gibbs distribution for the label pyramid are assumed to be known. Experimental results demonstrating the performance of the algorithm are presented.     

Estimating distributed anatomical connectivity using fast marching methods and diffusion tensor imaging

A method is presented for determining paths of anatomical connection between regions of the brain using magnetic resonance diffusion tensor information. Level set theory, applied using fast marching methods, is used to generate three-dimensional time of arrival maps, from which connection paths between brain regions may be identified. The method is demonstrated in the normal brain and it is shown that major white matter tracts may be elucidated and that multiple connections and tract branching are allowed. Maps of connectivity between brain regions are also determined. Four options are described for estimating the degree of connectivity between regions.     

Forecasting fluid milk package type with a multigeneration newproduct diffusion model

A recently introduced multigeneration model, developed for high-technology industries and tested on a high-tech product class, is used to forecast use of three generations of packaging technology in the fluid milk market: glass, paperboard cartons, and plastic. Results show that the model can be successfully applied to industries not usually associated with high technology, and to specific markets, rather than across a whole product class. The model is extended by incorporating pricing, which brings about slight improvements in already good forecasts     

A nonrigid registration framework using spatially encoded mutual information and free-form deformations

Mutual information (MI) registration including spatial information has been shown to perform better than the traditional MI measures for certain nonrigid registration tasks. In this work, we first provide new insight to problems of the MI-based registration and propose to use the spatially encoded mutual information (SEMI) to tackle these problems. To encode spatial information, we propose a hierarchical weighting scheme to differentiate the contribution of sample points to a set of entropy measures, which are associated to spatial variable values. By using free-form deformations (FFDs) as the transformation model, we can first define the spatial variable using the set of FFD control points, and then propose a local ascent optimization scheme for nonrigid SEMI registration. The proposed SEMI registration can improve the registration accuracy in the nonrigid cases where the traditional MI is challenged due to intensity distortion, contrast enhancement, or different imaging modalities. It also has a similar computation complexity to the registration using traditional MI measures, improving up to two orders of magnitude of computation time compared to the traditional schemes. We validate our algorithms using phantom brain MRI, simulated dynamic contrast enhanced mangetic resonance imaging (MRI) of the liver, and in vivo cardiac MRI. The results show that the SEMI registration significantly outperforms the traditional MI registration.     

Multiresolution registration of remote sensing imagery by optimization of mutual information using a stochastic gradient

Image registration is the process by which we determine a transformation that provides the most accurate match between two images. The search for the matching transformation can be automated with the use of a suitable metric, but it can be very time-consuming and tedious. We introduce a registration algorithm that combines a simple yet powerful search strategy based on a stochastic gradient with two similarity measures, correlation and mutual information, together with a wavelet-based multiresolution pyramid. We limit our study to pairs of images, which are misaligned by rotation and/or translation, and present two main results. First, we demonstrate that, in our application, mutual information may be better suited for sub-pixel registration as it produces consistently sharper optimum peaks than correlation. Then, we show that the stochastic gradient search combined with either measure produces accurate results when applied to synthetic data, as well as to multitemporal or multisensor collections of satellite data. Mutual information is generally found to optimize with one-third the number of iterations required by correlation. Results also show that a multiresolution implementation of the algorithm yields significant improvements in terms of both speed and robustness over a single-resolution implementation.     

BSP模型下最大互信息医学图像配准研究

文中研究了在医学图像处理中基于最大互信息的图像配准的理论和实现的算法,并在此基础上给出了并行模型BSP下的实现算法。通过实验数据可以分析得出,文中提出的算法可以很好地解决医学图像处理中的图像配准的速度。     

Two-stage mutual causal filtration and segmentation of heterogeneous images

Using the mathematical technique of mixed Markovian processes in discrete time optimal and quasi-optimal algorithms that combine results of one-dimensional filtration and segmentation of heterogeneous images are synthesized. Analysis of the quasi-optimal algorithm is conducted on a model example using statistical modeling on PC.     

Smaller feature subset selection for real-world datasets using a new mutual information with Gaussian gain

Multidimensional Systems and Signal Processing - A new filter method is proposed for feature selection and ranking that incorporates a novel mutual information with Gaussian gain for evaluating the...     

Temporal subtraction of thorax CR images using a statistical deformation model

We propose a voxel-based nonrigid registration algorithm for temporal subtraction of two-dimensional thorax X-ray computed radiography images of the same subject. The deformation field is represented by a B-spline with a limited number of degrees of freedom, that allows global rib alignment to minimize subtraction artifacts within the lung field without obliterating interval changes of clinically relevant soft-tissue abnormalities. The spline parameters are constrained by a statistical deformation model that is learned from a training set of manually aligned image pairs using principal component analysis. Optimization proceeds along the transformation components rather then along the individual spline coefficients, using pattern intensity of the subtraction image within the automatically segmented lung field region as the criterion to be minimized and applying a simulated annealing strategy for global optimization in the presence of multiple local optima. The impact of different transformation models with varying number of deformation modes is evaluated on a training set of 26 images using a leave-one-out strategy and compared to the manual registration result in terms of criterion value and deformation error. Registration quality is assessed on a second set of validation images by a human expert rating each subtraction image on screen. In 85% of the cases, the registration is subjectively rated to be adequate for clinical use.     

基于Trie树的词语左右熵和互信息新词发现算法

由于大量新词的出现,使得中文文本分析产生了较大的困难,因此新词发现成为目前中文自然语言处理中的热点和难点问题。为此,文中提出了一种基于Trie树的词语左右熵和互信息新词发现算法。先根据成词规则,筛选掉文本中的停用词和非中文字符,将每个字与其右邻的字组成二元组;然后利用左右信息熵和互信息进行成词概率的计算,根据计算到的成词概率和词频筛选出新词;并且设计了三个实验,验证了算法的有效性和可行性。实验结果表明,该新词发现算法成词准确率较高,比其他新词发现算法时间效率有较大的提高,对于中文分词结果的优化起到重要的作用。     

Unwrapping of MR phase images using a Markov random field model

Phase unwrapping is an important problem in many magnetic resonance imaging applications, such as field mapping and flow imaging. The challenge in two-dimensional phase unwrapping lies in distinguishing jumps due to phase wrapping from those due to noise and/or abrupt variations in the actual function. This paper addresses this problem using a Markov random field to model the true phase function, whose parameters are determined by maximizing the a posteriori probability. To reduce the computational complexity of the optimization procedure, an efficient algorithm is also proposed for parameter estimation using a series of dynamic programming connected by the iterated conditional modes. The proposed method has been tested with both simulated and experimental data, yielding better results than some of the state-of-the-art method (e.g., the popular least-squares method) in handling noisy phase images with rapid phase variations.     

Bayesian reconstruction of functional images using anatomical information as priors

Proposes a Bayesian method whereby maximum a posteriori (MAP) estimates of functional (PET and SPECT) images may be reconstructed with the aid of prior information derived from registered anatomical MR images of the same slice. The prior information consists of significant anatomical boundaries that are likely to correspond to discontinuities in an otherwise spatially smooth radionuclide distribution. The authors' algorithm, like others proposed recently, seeks smooth solutions with occasional discontinuities; the contribution here is the inclusion of a coupling term that influences the creation of discontinuities in the vicinity of the significant anatomical boundaries. Simulations on anatomically derived mathematical phantoms are presented. Although computationally intense in its current implication, the reconstructions are improved (ROI-RMS error) relative to filtered backprojection and EM-ML reconstructions. The simulations show that the inclusion of position-dependent anatomical prior Information leads to further improvement relative to Bayesian reconstructions without the anatomical prior. The algorithm exhibits a certain degree of robustness with respect to errors in the location of anatomical boundaries.