On analyzing diffusion tensor images by identifying manifold structure using isomaps

Fault diagnosis for industrial robots based on a combined approach of manifold learning, treelet transform and Naive Bayes

This research introduces a novel fault diagnosis method for an industrial robot based on manifold learning algorithms, Treelet Transform (TT) and Naive Bayes. The vibration signals of an industrial robot working under three working conditions are acquired as the raw data. Three typical manifold learning algorithms, Principal Component Analysis (PCA), Locality Preserving Projections (LPPs), and Isometric Feature Mapping (ISOMAP), are utilized to extract three-dimensional features from the vibration signals. Then, these features were combined into nine-dimensional features and, these nine-dimensional features were reduced to three-dimensional feature vectors by TT. Finally, a Naive Bayes model is trained with these three-dimensional feature vectors. Experimental results show that compared with the three methods, PCA, LPP, and ISOMAP, the accuracy of the proposed combined method is higher than the single method. The fault diagnosis method presented in this paper is easy to implement and can effectively identify the fault types.

On the averaging of cardiac diffusion tensor MRI data: the effect of distance function selection

Diffusion tensor magnetic resonance imaging (DT-MRI) allows a unique insight into the microstructure of highly-directional tissues. The selection of the most proper distance function for the space of diffusion tensors is crucial in enhancing the clinical application of this imaging modality. Both linear and nonlinear metrics have been proposed in the literature over the years. The debate on the most appropriate DT-MRI distance function is still ongoing. In this paper, we presented a framework to compare the Euclidean, affine-invariant Riemannian and log-Euclidean metrics using actual high-resolution DT-MRI rat heart data. We employed temporal averaging at the diffusion tensor level of three consecutive and identically-acquired DT-MRI datasets from each of five rat hearts as a means to rectify the background noise-induced loss of myocyte directional regularity. This procedure is applied here for the first time in the context of tensor distance function selection. When compared with previous studies that used a different concrete application to juxtapose the various DT-MRI distance functions, this work is unique in that it combined the following: (i) metrics were judged by quantitative-rather than qualitative-criteria, (ii) the comparison tools were non-biased, (iii) a longitudinal comparison operation was used on a same-voxel basis. The statistical analyses of the comparison showed that the three DT-MRI distance functions tend to provide equivalent results. Hence, we came to the conclusion that the tensor manifold for cardiac DT-MRI studies is a curved space of almost zero curvature. The signal to noise ratio dependence of the operations was investigated through simulations. Finally, the 'swelling effect' occurrence following Euclidean averaging was found to be too unimportant to be worth consideration.

Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools

The extreme complexity of the brain naturally requires mathematical modeling approaches on a large variety of scales; the spectrum ranges from single neuron dynamics over the behavior of groups of neurons to neuronal network activity. Thus, the connection between the microscopic scale (single neuron activity) to macroscopic behavior (emergent behavior of the collective dynamics) and vice versa is a key to understand the brain in its complexity. In this work, we attempt a review of a wide range of approaches, ranging from the modeling of single neuron dynamics to machine learning. The models include biophysical as well as data-driven phenomenological models. The discussed models include Hodgkin-Huxley, FitzHugh-Nagumo, coupled oscillators (Kuramoto oscillators, Rössler oscillators, and the Hindmarsh-Rose neuron), Integrate and Fire, networks of neurons, and neural field equations. In addition to the mathematical models, important mathematical methods in multiscale modeling and reconstruction of the causal connectivity are sketched. The methods include linear and nonlinear tools from statistics, data analysis, and time series analysis up to differential equations, dynamical systems, and bifurcation theory, including Granger causal connectivity analysis, phase synchronization connectivity analysis, principal component analysis (PCA), independent component analysis (ICA), and manifold learning algorithms such as ISOMAP, and diffusion maps and equation-free techniques. WIREs Syst Biol Med 2016, 8:438-458. doi: 10.1002/wsbm.1348 For further resources related to this article, please visit the WIREs website.

Comparative analysis of nonlinear dimensionality reduction techniques for breast MRI segmentation

PURPOSE

Visualization of anatomical structures using radiological imaging methods is an important tool in medicine to differentiate normal from pathological tissue and can generate large amounts of data for a radiologist to read. Integrating these large data sets is difficult and time-consuming. A new approach uses both supervised and unsupervised advanced machine learning techniques to visualize and segment radiological data. This study describes the application of a novel hybrid scheme, based on combining wavelet transform and nonlinear dimensionality reduction (NLDR) methods, to breast magnetic resonance imaging (MRI) data using three well-established NLDR techniques, namely, ISOMAP, local linear embedding (LLE), and diffusion maps (DfM), to perform a comparative performance analysis.

METHODS

Twenty-five breast lesion subjects were scanned using a 3T scanner. MRI sequences used were T1-weighted, T2-weighted, diffusion-weighted imaging (DWI), and dynamic contrast-enhanced (DCE) imaging. The hybrid scheme consisted of two steps: preprocessing and postprocessing of the data. The preprocessing step was applied for B(1) inhomogeneity correction, image registration, and wavelet-based image compression to match and denoise the data. In the postprocessing step, MRI parameters were considered data dimensions and the NLDR-based hybrid approach was applied to integrate the MRI parameters into a single image, termed the embedded image. This was achieved by mapping all pixel intensities from the higher dimension to a lower dimensional (embedded) space. For validation, the authors compared the hybrid NLDR with linear methods of principal component analysis (PCA) and multidimensional scaling (MDS) using synthetic data. For the clinical application, the authors used breast MRI data, comparison was performed using the postcontrast DCE MRI image and evaluating the congruence of the segmented lesions.

RESULTS

The NLDR-based hybrid approach was able to define and segment both synthetic and clinical data. In the synthetic data, the authors demonstrated the performance of the NLDR method compared with conventional linear DR methods. The NLDR approach enabled successful segmentation of the structures, whereas, in most cases, PCA and MDS failed. The NLDR approach was able to segment different breast tissue types with a high accuracy and the embedded image of the breast MRI data demonstrated fuzzy boundaries between the different types of breast tissue, i.e., fatty, glandular, and tissue with lesions (>86%).

CONCLUSIONS

The proposed hybrid NLDR methods were able to segment clinical breast data with a high accuracy and construct an embedded image that visualized the contribution of different radiological parameters.

BRAIN PATTERN ANALYSIS OF CORTICAL VALUED DISTRIBUTIONS

We introduce a new representation of cortical regions via distribution functions of their features. The distribution functions are estimated non-parametrically from the data and are observed to be non Gaussian. Cortical pattern matching is enabled by using the information-based Jensen-Shannon divergence as a measure between features. Our approach explicitly avoids pairwise registrations between brains, but instead focuses on modeling and discriminating between the cortical structural patterns. We demonstrate our approach on 120 subject brains from an Alzheimer's dataset, and present applications to clustering, classification, and dimension reduction.

Geodesic distance on non-singular coherency matrix space in polarization optics

We define a geodesic distance associated with the polarization space of non-singular coherency matrices. Its introduction on HPD(2) (the manifold of Hermitian positive definite matrices of dimension 2) can be directly related to the Jones calculus. The expression of distance and related notion of mean value in this particular metric space are also presented. We investigate the properties of this geodesic distance and the classical Euclidean one and their appropriateness for interpixel comparisons in a context of imaging polarimetry. Finally, results are presented for a geodesic version of the classical K-means clustering algorithm with simulated data and real data. The results demonstrate the advantages of the geodesic approach.

On approximation of orientation distributions by means of spherical ridgelets

Visualization and analysis of the micro-architecture of brain parenchyma by means of magnetic resonance imaging is nowadays believed to be one of the most powerful tools used for the assessment of various cerebral conditions as well as for understanding the intracerebral connectivity. Unfortunately, the conventional diffusion tensor imaging (DTI) used for estimating the local orientations of neural fibers is incapable of performing reliably in the situations when a voxel of interest accommodates multiple fiber tracts. In this case, a much more accurate analysis is possible using the high angular resolution diffusion imaging (HARDI) that represents local diffusion by its apparent coefficients measured as a discrete function of spatial orientations. In this note, a novel approach to enhancing and modeling the HARDI signals using multiresolution bases of spherical ridgelets is presented. In addition to its desirable properties of being adaptive, sparsifying, and efficiently computable, the proposed modeling leads to analytical computation of the orientation distribution functions associated with the measured diffusion, thereby providing a fast and robust analytical solution for q-ball imaging.

The effect of metric selection on the analysis of diffusion tensor MRI data

The measurement of the distance between diffusion tensors is the foundation on which any subsequent analysis or processing of these quantities, such as registration, regularization, interpolation, or statistical inference is based. In recent years a family of Riemannian tensor metrics based on geometric considerations has been introduced for this purpose. In this work we examine the properties one would use to select metrics for diffusion tensors, diffusion coefficients, and diffusion weighted MR image data. We show that empirical evidence supports the use of a Euclidean metric for diffusion tensors, based upon Monte Carlo simulations. Our findings suggest that affine invariance is not a desirable property for a diffusion tensor metric because it leads to substantial biases in tensor data. Rather, the relationship between distribution and distance is suggested as a novel criterion for metric selection.

A continuous STAPLE for scalar, vector, and tensor images: an application to DTI analysis

The comparison of images of a patient to a reference standard may enable the identification of structural brain changes. These comparisons may involve the use of vector or tensor images (i.e., 3-D images for which each voxel can be represented as an RN vector) such as diffusion tensor images (DTI) or transformations. The recent introduction of the Log-Euclidean framework for diffeomorphisms and tensors has greatly simplified the use of these images by allowing all the computations to be performed on a vector-space. However, many sources can result in a bias in the images, including disease or imaging artifacts. In order to estimate and compensate for these sources of variability, we developed a new algorithm, called continuous STAPLE, that estimates the reference standard underlying a set of vector images. This method, based on an expectation-maximization method similar in principle to the validation method STAPLE, also estimates for each image a set of parameters characterizing their bias and variance with respect to the reference standard. We demonstrate how to use these parameters for the detection of atypical images or outliers in the population under study. We identified significant differences between the tensors of diffusion images of multiple sclerosis patients and those of control subjects in the vicinity of lesions.

Diffusion MRI registration using orientation distribution functions

We propose a linear-elastic registration method to register diffusion-weighted MRI (DW-MRI) data sets by mapping their diffusion orientation distribution functions (ODFs). The ODFs were reconstructed using a q-ball imaging (QBI) technique to resolve intravoxel fiber crossing. The registration method is based on mapping the ODF maps represented by spherical harmonics which yield analytic solutions and reduce the computational complexity. ODF reorientation is required to maintain the consistency with transformed local fiber directions. The reorientation matrices are extracted from the local Jacobian and directly applied to the coefficients of spherical harmonics. The similarity cost of the registration is defined by the ODF shape distance calculated from the spherical harmonic coefficients. The transformation fields are regularized by linear elastic constraints. The proposed method was validated using both synthetic and real data sets. Experimental results show that the elastic registration improved the affine alignment by further reducing the ODF shape difference; reorientation during the registration produced registered ODF maps with more consistent principle directions compared to registrations without reorientation or simultaneous reorientation.

New techniques for cartilage magnetic resonance imaging relaxation time analysis: texture analysis of flattened cartilage and localized intra- and inter-subject comparisons

MR relaxation time measurements of knee cartilage have shown potential to characterize knee osteoarthritis (OA). In this work, techniques that allow localized intra- and inter-subject comparisons of cartilage relaxation times, as well as cartilage flattening for texture analysis parallel and perpendicular to the natural cartilage layers, are presented. The localized comparisons are based on the registration of bone structures and the assignment of relaxation time feature vectors to each point in the bone-cartilage interface. Cartilage flattening was accomplished with Bezier splines and warping, and texture analysis was performed with second-order texture measures using gray-level co-occurrence matrices (GLCM). In a cohort of five normal subjects the performance and reproducibility of the techniques were evaluated using T1rho maps of femoral knee cartilage. The feasibility of creating a mean cartilage relaxation time map is also presented. Successful localized intra- and inter-subject T1rho comparisons were obtained with reproducibility similar to that reported in the literature for regional T2. Improvement of the reproducibility of GLCM features was obtained by flattening the T1rho maps. The results indicate that the presented techniques have potential in longitudinal and population studies of knee OA at different stages of the disease.