Minor Eigenvalues Research Articles

Approach of spectral information-based image registration similarity

For local intensity-based image registration methods, a template of a predefined size is adopted. Some measure of similarity between the images is used to determine when the optimal alignment has occurred. Most intensity-based similarity utilizes the statistical and spatial information of an image. However, there are significant nonlinear radiometric differences between infrared and visible data. Images of natural scenes usually do not have enough spatial features within the template. Hence, many similarities will be useless when dealing with infrared and visible data. Minor eigenvalues (ME) image registration similarity is presented with the exploitation the spectral properties of remote sensing images. ME similarity is based on the linear spectral mixture model and detects control points through searching the minimum of ME of the covariance matrix. Experiments on Landsat-7 satellite Enhanced Thematic Mapper Plus data are performed to verify and evaluate the effectiveness. Transformation performance curves, correct match ratio (CMR), and registration accuracy are also discussed. According to the data, root-mean-square error of phase correlations is 0.0722 pixels and the CMR of ME similarity is nearly 100%. The results on the basis of TM1, TM2, TM3, and TM4 band images indicate that the proposed similarity holds promise for infrared and color image registration in natural scenes, with advantages over previous normal mutual information and gradient mutual information similarities.

Semi-Supervised Multi-Modal Learning with Balanced Spectral Decomposition

Cross-modal retrieval aims to retrieve the relevant samples across different modalities, of which the key problem is how to model the correlations among different modalities while narrowing the large heterogeneous gap. In this paper, we propose a Semi-supervised Multimodal Learning Network method (SMLN) which correlates different modalities by capturing the intrinsic structure and discriminative correlation of the multimedia data. To be specific, the labeled and unlabeled data are used to construct a similarity matrix which integrates the cross-modal correlation, discrimination, and intra-modal graph information existing in the multimedia data. What is more important is that we propose a novel optimization approach to optimize our loss within a neural network which involves a spectral decomposition problem derived from a ratio trace criterion. Our optimization enjoys two advantages given below. On the one hand, the proposed approach is not limited to our loss, which could be applied to any case that is a neural network with the ratio trace criterion. On the other hand, the proposed optimization is different from existing ones which alternatively maximize the minor eigenvalues, thus overemphasizing the minor eigenvalues and ignore the dominant ones. In contrast, our method will exactly balance all eigenvalues, thus being more competitive to existing methods. Thanks to our loss and optimization strategy, our method could well preserve the discriminative and instinct information into the common space and embrace the scalability in handling large-scale multimedia data. To verify the effectiveness of the proposed method, extensive experiments are carried out on three widely-used multimodal datasets comparing with 13 state-of-the-art approaches.

Ternary diffusion path in terms of eigenvalues and eigenvectors

Based on the transfer matrix methodology, a new analysis is presented for the description of slopes of the ternary diffusion path for a solid–solid diffusion couple. Concentration profiles and diffusion paths for isothermal, ternary diffusion couples are examined in the context of eigenvalues and eigenvectors obtained from the diagonalisation of the ternary interdiffusion coefficients employed for their representation. New relations are derived relating the decoupled interdiffusion fluxes to combinations of concentration gradients through the major and minor eigenvalues, and the diffusion path becomes parallel to the major eigenvector at each path end. General expressions for the slope of the ternary diffusion path at any section of the couple are also derived in terms of eigenvalue and eigenvector parameters. Expressions for the path slope at the Matano plane involve only concentrations, major and minor eigenvalues and eigenvector parameters. New constraints relating the eigenvalues and the concentration gradients of the individual components are also presented at selected sections, where the diffusion path is parallel to the straight line joining the terminal composition points on an isotherm. Applications of the various relations are illustrated with the aid of a hypothetical couple and an experimental Cu–Ni–Zn diffusion couple.

4.7-T diffusion tensor imaging of acute traumatic peripheral nerve injury.

Diagnosis and management of peripheral nerve injury is complicated by the inability to assess microstructural features of injured nerve fibers via clinical examination and electrophysiology. Diffusion tensor imaging (DTI) has been shown to accurately detect nerve injury and regeneration in crush models of peripheral nerve injury, but no prior studies have been conducted on nerve transection, a surgical emergency that can lead to permanent weakness or paralysis. Acute sciatic nerve injuries were performed microsurgically to produce multiple grades of nerve transection in rats that were harvested 1 hour after surgery. High-resolution diffusion tensor images from ex vivo sciatic nerves were obtained using diffusion-weighted spin-echo acquisitions at 4.7 T. Fractional anisotropy was significantly reduced at the injury sites of transected rats compared with sham rats. Additionally, minor eigenvalues and radial diffusivity were profoundly elevated at all injury sites and were negatively correlated to the degree of injury. Diffusion tensor tractography showed discontinuities at all injury sites and significantly reduced continuous tract counts. These findings demonstrate that high-resolution DTI is a promising tool for acute diagnosis and grading of traumatic peripheral nerve injuries.

Diffusion Tensor Imaging of the Spondylotic Cervical Spinal Cord: A Preliminary Study of Quantifiable Markers in the Evaluation for Surgical Decompression

Objective: Conventional MRI for the evaluation of cervical spondylotic myelopathy (CSM) may be poorly correlated with a patient’s symptoms and prognosis. Interpretation of canal stenosis, contour deformities, and the presence or absence of T2 signal change, can make it difficult to decide who needs decompressive surgery. Diffusion tensor imaging (DTI) provides quantitative measurements that could help clarify the degree and chronicity of spinal cord disease as a result of compression from degenerative spondylosis. DTI can also detect diffusion abnormalities in areas of acute spondylotic compression occurring without T2 signal change. The purpose of this study is to compare these quantitative DTI measures (i.e. metrics) in patients with severe clinical and radiographic evidence of CSM with controls. Methods: DTI of the cervical spine was performed in 11 patients with severe radiographic and clinical multilevel spondylosis who were planned for surgical decompression versus 10 healthy volunteers (as determined by 2 neurosurgeons A.F.B. and P.R.C., and a neuroradiologist M.L.), using pulsed gradient, double spin echo, echo planar imaging. At the C2-3, C3-4 and C4-5 levels, average FA, MD, E1 (longitudinal diffusion), E2 and E3 (transverse diffusion) were calculated within regions of interest at bilateral anterior, lateral, and posterior regions of the cord. Levels caudal to C4-5 were not analyzed due to artifact on DTI. The average age of the spondylosis patients was 67.2±9.8 years vs. 33.4±15.2 years in the control group (p<.001). Results: Fractional anisotropy (FA) and the minor transverse eigenvalues (E2 and E3) most consistently demonstrated significant differences in values between patients with radiographic and clinical CSM versus controls at C4-5. FA was the most specific in correlating with compression seen on conventional T2 imaging at C4-5; however, the minor eigenvalues showed the greatest degree of significant difference in DTI metrics when compared to controls. At C2-3, significant differences in mean diffusivity (MD) were found at the lateral and central regions as well as minor eigenvalue differences in the posterior, lateral, and central regions. There were no significant differences in the major longitudinal eigenvalue (E1) between patients with CSM versus controls. Conclusion: Minor eigenvalues and fractional anisotropy are significantly different in clinically significant spondylosis with conventional imaging evidence of compression versus controls, with preservation of the major eigenvalue. These values show promise as biomarkers of microscopic injury to the cord, which may help in the early identification of patients who would likely benefit from decompressive therapy. DTI can also provide information on the duration of cord compression in helping to distinguish reversible versus irreversible disease. Supported by: Grants RO1CA093992 and RO1111996 from the National Cancer Institute/National Institute of Health.

Broadband Source Localization From an Eigenanalysis Perspective

Broadband source localization has several applications ranging from automatic video camera steering to target signal tracking and enhancement through beamforming. Consequently, there has been a considerable amount of effort to develop reliable methods for accurate localization over the last few decades. Essentially, the localization process consists in finding the candidate source location that maximizes the synchrony between the properly time-shifted microphone outputs. In addition to using well known cross-correlation-based criteria such as the steered response power (SRP), minimum variance (MV), and multichannel cross-correlation (MCCC), this synchrony can also be measured using the averaged magnitude difference function (AMDF) and the averaged magnitude sum function (AMSF) whose calculations involve low computational cost. In earlier related works, the latter techniques have been used for time delay estimation (TDE) of a target source observed by only one pair of microphones. Their generalization to the multiple microphone case and application to source localization have not been studied yet. In this paper, we consider both categories, i.e., cross-correlation and AMDF (with AMSF)-based approaches, using an arbitrary number of microphones, and analyze their performance. Specifically, we first provide a unifying study of the most popular cross-correlation-based techniques, such as the SRP, MV, and MCCC. In this paper, we use the eigenanalysis of the parameterized spatial correlation matrix (PSCM) to classify these methods and gain some insight into their performance. We demonstrate, for instance, that the MV and SRP consist in searching the major eigenvalue of the PSCM, while the MCCC, essentially, combines its minor eigenvalues when scanning for the source location. Inspired by this analysis, we show, in the second part of this work, the efficiency of the AMDF and AMSF in localizing an acoustic source using multiple microphones. Indeed, we propose two new parameterized matrices named as the parameterized averaged magnitude difference matrix (PAMDM) and the parameterized averaged magnitude sum matrix (PAMSM). The eigenanalysis of these matrices also reveals new criteria for acoustic source localization. Simulation results are provided to illustrate the effectiveness of all the investigated and proposed methods.

A self-stabilizing MSA algorithm in high-dimension data stream

Minor subspace analysis (MSA) is a statistical method for extracting the subspace spanned by all the eigenvectors associated with the minor eigenvalues of the autocorrelation matrix of a high-dimension vector sequence. In this paper, we propose a self-stabilizing neural network learning algorithm for tracking minor subspace in high-dimension data stream. Dynamics of the proposed algorithm are analyzed via a corresponding deterministic continuous time (DCT) system and stochastic discrete time (SDT) system methods. The proposed algorithm provides an efficient online learning for tracking the MS and can track an orthonormal basis of the MS. Computer simulations are carried out to confirm the theoretical results.

Corpus Callosum Morphology and Microstructure Assessed Using Structural MR Imaging and Diffusion Tensor Imaging: Initial Findings in Adults with Neurofibromatosis Type 1

Imaging studies have shown that children with NF-1 have increased brain volumes compared with age-matched controls and the CCs are disproportionately large. The purpose of this study was to determine if the CC in adults with NF-1 differed from that in matched controls by using DTI and volumetric imaging. MR imaging with DTI was performed in 10 adults with NF-1 and in 10 age-, sex-, and handedness-matched controls by using a 3T system. Total brain volumes and the areas and central lengths of the CC were calculated, along with the radial width of callosal subdivisions, in the 2 groups. Our results showed that the total brain volume was not significantly different between adults with NF-1 and matched controls. The length and total cross-sectional area of the CC were statistically larger in adults with NF-1 compared with controls (approximately 10% longer and 20% greater area). On DTI we found a preservation of the primary eigenvalue with increases in the minor eigenvalues at the genu. We have shown that the increased size of the CC found in children with NF-1 is also present in adults with the syndrome, whereas no difference in total brain volume was found.

Characteristics of Abnormal Diffusivity in Normal-Appearing White Matter Investigated with Diffusion Tensor MR Imaging in Tuberous Sclerosis Complex

Although patients with tuberous sclerosis complex (TSC) manifest various structural abnormalities, we hypothesized that white matter (WM) structures that appear normal on conventional MR imaging may be accompanied by microstructural changes, such as gliosis and myelinization defects. Our objective was to determine in vivo whether there was evidence for WM microstructural changes by using diffusion tensor imaging (DTI). We used DTI to evaluate diffusivity and anisotropy in normal-appearing WM (NAWM) of 6 children with TSC and 12 age-matched control subjects. The anterior and posterior limbs of the internal capsule, the external capsule, and the genu and splenium of the corpus callosum were assessed. We hypothesized that previously reported DTI abnormalities of NAWM in patients with TSC may not be equal in all diffusion directions as measured by the major, middle, and minor eigenvalues. When combining NAWM regions in patients with TSC, we observed a significant increase in mean diffusivity (P = .003) and a decrease in anisotropy (P = .03) compared with those of controls. However, the increase in diffusivity was more pronounced in directions orthogonal to the axons measured by the minor and middle eigenvalues (P = .005) than by the major eigenvalue (P = .02). Our findings revealed a decrease in anisotropy and an increase in longitudinal and radial diffusivities in NAWM beyond the location of TSC lesions seen on conventional MR imaging. The axonal microstructural changes suggested by our study may be related to changes in myelin packing due to giant cells accompanied by gliosis and myelination defects known to occur in TSC WM.

Energetics of multicomponent diffusion in molten CaO-Al2O3-SiO2

The energetics of multicomponent diffusion in molten CaO-Al2O3-SiO2 (CAS) were examined experimentally at 1440 to 1650°C and 0.5 to 2 GPa. Two melt compositions were investigated: a haplodacitic melt (25 wt.% CaO, 15% Al2O3, and 60% SiO2) and a haplobasaltic melt (35% CaO, 20% Al2O3, and 45% SiO2). Diffusion matrices were measured in a mass-fixed frame of reference with simple oxides as end-member components and Al2O3 as a dependent variable. Chemical diffusion in molten CAS shows clear evidence of diffusive coupling among the components. The diffusive flux of SiO2 is significantly enhanced whenever there is a large CaO gradient that is oriented in a direction opposite to the SiO2 gradient. This coupling effect is more pronounced in the haplodacitic melt and is likely to be significant in natural magmas of rhyolitic to andesitic compositions. The relative magnitude of coupled chemical diffusion is not very sensitive to changes in temperature and pressure.To a good approximation, the measured diffusion matrices follow well-defined Arrhenius relationships with pressure and reciprocal temperature. Typically, a change in temperature of 100°C results in a relative change in the elements of diffusion matrix of 50 to 100%, whereas a change in pressure of 1 GPa introduces a relative change in elements of diffusion matrix of 4 to 6% for the haplobasalt, and less than 5% for the haplodacite. At a pressure of 1 GPa, the ratios between the major and minor eigenvalues of the diffusion matrix λ1/λ2 are not very sensitive to temperature variations, with an average of 5.5 ± 0.2 for the haplobasalt and 3.7 ± 0.6 for the haplodacite. The activation energies for the major and minor eigenvalues of the diffusion matrix are 215 ± 12 and 240 ± 21 kJ mol−1, respectively, for the haplodacite and 192 ± 8 and 217 ± 14 kJ mol−1 for the haplobasalt. These values are comparable to the activation energies for self-diffusion of calcium and silicon at the same melt compositions and pressure. At a fixed temperature of 1500°C, the ratios λ1/λ2 increase with the increase of pressure, with λ1/λ2 varying from 2.5 to 4.1 (0.5 to 1.3 GPa) for the haplodacite and 4 to 6.5 (0.5 to 2.0 GPa) for the haplobasalt. The activation volumes for the major and minor eigenvalues of the diffusion matrix are 0.31 ± 0.44 and 2.3 ± 0.8 cm3 mol−1, respectively, for the haplodacite and −1.48 ± 0.18 and −0.42 ± 0.24 cm3 mol−1 for the haplobasalt. These values are quite different from the activation volumes for self-diffusion of calcium and silicon at the same melt compositions and temperature. These differences in activation volumes between the two melts likely result from a difference in the structure and thermodynamic properties of the melt between the two compositions (e.g., partial molar volume).Applications of the measured diffusion matrices to quartz crystal dissolution in molten CAS reveal that the activation energy and activation volume for quartz dissolution are almost identical to the activation energy and activation volume for diffusion of the minor or slower eigencomponent of the diffusion matrix. This suggests that the diffusion rate of slow eigencomponent is the rate-limiting factor in isothermal crystal dissolution, a conclusion that is likely to be valid for crystal growth and dissolution in natural magmas when diffusion in liquid is the rate-limiting factor.

Eigenvalues of the inertia tensor and exteroception by the “muscular sense”

Muscle spindles and Golgi tendon organs constitute the receptor foundation to the “muscle sense”. Muscle sensitivity has long been assumed relevant to the non-visual perception of the positions and motions of the body's segments and of the properties of hand-held objects. Dynamic touch is the label given to the particular kind of tactile exteroperception that involves a non-spatial input from muscles and tendons. When a hand-held object is wielded, hefted, carried and so on, the hand movements, together with the physical properties of the object, produce torques and angular motions that change in time with the movement. There is, however, an unchanging quantity that relates the variable torques and angular motions, namely, the object's inertia for rotation about a fixed point in the wrist. Our research revealed that the non-visual perception of the length of a wielded object by dynamic touch is a function of muscular sensitivity to the principal moments or eigenvalues of the inertia tensor. Across four experiments, variations in object length were accompanied by variations in width, spatial and material heterogeneity, the relation of the tensorial components to mass, and geometric shape. Subjects had no foreknowledge of the variations in object dimensions. Perceived lengths of occluded objects were reported by adjusting a visible marker so that its position corresponded to the position of the felt end of the object. In each experiment, perceived length was closely related to actual length and uniquely constrained by the major and minor eigenvalues of the inertia tensor. The present results, in conjunction with previous research, suggest that the inertia tensor provides the domains for two sets of functions realized by the “muscular sense” one consisting of the principal moments of inertia or eigenvalues, which map on to perceived object magnitudes (e.g. length, weight), and one consisting of the principal directions or eigenvectors, which map on to perceived relations between hand and object (e.g. position of grasp). The significance of information-perception specificity over cognitive mechanisms is underlined and perspectives on dynamic touch and its underlying muscular sensitivity, including a general tensorial analysis, are discussed.