Eigenvalues Of Hessian Matrix Research Articles

Structural, topological, vibrational, and electronic analysis, and ADMET study of methyl-2-(4-isobutylphenyl)propanoate

In this work, the methyl ibuprofen ester, named methyl-2-(4-isobutylphenyl)propanoate (C14H20O2, hereinafter MET-IBU).was synthesized and characterized by 1D- and 2D-NMR, ATR-FTIR, FT-Raman, and UV–Vis spectroscopy, while their structural, QTAIM topological and spectroscopic properties were investigated using DFT calculations. Through the analysis of the topological properties of the electron density computed at bonding critical points (BCP's) for MET-IBU molecule were determined the electron density, the Laplacian of electron density, the eigenvalues of Hessian matrix, the ellipticity of electron density, the potential energy density, the kinetic energy density in the Lagrangian and Hamiltonian forms, the total energy density, the Lagrangian density, and the electron delocalization index. Density Functional Theory (DFT) calculations were also used to determine the vibrational normal modes, the frontier molecular orbitals (FMOs), the dipole moment, and the molecular electrostatic potential (MEP) of MET-IBU. Theoretical UV absorption spectrum was also evaluated from time-dependent density functional theory (TD-DFT) providing the electronic transitions, which are expected for this compound. The molecular descriptors of the properties of absorption, distribution, metabolism and excretion, and toxicity (ADMET) were obtained. Empirical models for estimating ADME attributes showed that the MET-IBU has a distribution volume that allows permeability and activity in the Central Nervous System - CNS, with structural contributions from the side chain of isobutyl and methoxy that favor liver metabolism and excretion with a low toxic response. Furthermore, the MET-IBU does not have ionizable centers compared to its analog Ibuprofen constituting a more lipophilic chemical product.

Overcoming Catastrophic Forgetting in Continual Learning by Exploring Eigenvalues of Hessian Matrix.

Neural networks tend to suffer performance deterioration on previous tasks when they are applied to multiple tasks sequentially without access to previous data. The problem is commonly known as catastrophic forgetting, a significant challenge in continual learning (CL). To overcome the catastrophic forgetting, regularization-based CL methods construct a regularization-based term, which can be considered as the approximation loss function of previous tasks, to penalize the update of parameters. However, the rigorous theoretical analysis of regularization-based methods is limited. Therefore, we theoretically analyze the forgetting and the convergence properties of regularization-based methods. The theoretical results demonstrate that the upper bound of the forgetting has a relationship with the maximum eigenvalue of the Hessian matrix. Hence, to decrease the upper bound of the forgetting, we propose eiGenvalues ExplorAtion Regularization-based (GEAR) method, which explores the geometric properties of the approximation loss of prior tasks regarding the maximum eigenvalue. Extensive experimental results demonstrate that our method mitigates catastrophic forgetting and outperforms existing regularization-based methods.

Bounds on eigenvalues of real symmetric interval matrices for αBB method in global optimization

In this paper, we investigate bounds on eigenvalues of real symmetric interval matrices. We present a method that computes bounds on eigenvalues of real symmetric interval matrices. It outperforms many methods developed in the literature and produces as sharp as possible bounds on eigenvalues of real symmetric interval matrices. The aim is to apply the proposed method to compute lower bounds on eigenvalues of a symmetric interval hessian matrix of a nonconvex function in the ?BB method and use them to produce a tighter underestimator that improves the ?BB algorithm for solving global optimization problems. In the end, we illustrate by example, the comparison of various approaches of bounding eigenvalues of real symmetric interval matrices. Moreover, a set of test problems found in the literature are solved efficiently and the performances of the proposed method are compared with those of other methods.

Comparative evaluation of different spinal stability metrics

Direct in vivo measurements of spinal stability are not possible, leaving computational estimations (such as dynamic time series and structural analyses) as the feasible option. However, differences between different stability assessment approaches and metrics remain unclear. To explore this, we asked 32 participants to perform 35 cycles of repetitive lifts with and without load (4/2.6 kg for males/females). EMG signals and 3D kinematics were collected via 12 surface electrodes and 17 inertial sensors, and three dynamical stability measures were computed: short and long temporal and conventional maximum Lyapunov exponents (LyE) and maximum Floquet multipliers (FM). A dynamic subject-specific EMG-assisted musculoskeletal model computed four structural stability measures (critical muscle stiffness coefficient at which spine becomes unstable, average spine stiffness, minimum and geometric average of Hessian matrix eigenvalues). Across cycles, dynamical and structural stability outcomes varied noticeably. Temporal short-term LyE and all structural stability measures were more influenced by the cycle percentage (posture factor) than by phase (lifting, lowering) or load factor. The effect of all factors were non-significant for FM and long LyE, except for the posture on LyE-L with a small effect size. Pearson's correlations revealed a weak to moderate, or non-existent, correlation between structural and dynamical stability metrics, with small shared variances, underscoring their distinct and independent nature and theoretical foundations. Moreover, the low sensitivity of dynamic measures to posture and load factors, found in this study, calls for further examination. Considering the limitations and shortcomings of both dynamical and structural stability assessment approaches, there is a need for the development of improved musculoskeletal stability evaluation techniques.

Infrared Small Target Detection Based on Isolation Constraint Under Complex Background

In the development of infrared search and track (IRST) system, small target detection in complex background is a challenging task due to the low signal-to-noise ratio (SNR) of small targets and interference of irregular clutter. In this paper, a detection method based on isolation constraint is presented. Firstly, the suspected region with certain contrast is obtained by multilayer gray difference (MGD). Then we calculate the isolation index of the suspected region using the eigenvalues of Hessian matrix of the raw image to suppress the irregular clutter. In order to get accurate size of the target, a local scale estimation method is proposed. Experiment results demonstrate that the proposed method is accurate and robust, and superior to baseline methods in signal-to-clutter gain (SCRG) and receiver operating characteristic (ROC) curve.

DGDNet: Deep Gradient Descent Network for Remotely Sensed Image Denoising

Gradient descent strategy, viewed as an important model optimization method, has been widely used for various tasks (such as model-based image denoising) of computer vision. In the gradient descent denoising model, the learning rate (LR) and residual component are two important parts to be adaptively estimated for its stable point. This letter proposes a deep gradient descent network (DGDNet), including two key points: one is that the LR is designed with eigenvalues of Hessian matrix of remotely sensed images (RSIs) and their local weighted factor (LWF), which can recognize structures from RSIs degraded by additive white Gaussian noise (AWGN). The other is that the residual part is calculated by an U-shaped network (USNet) to speed up the DGDNet convergent to a fixed point. Finally, the two components are plugged into the gradient descent scheme and contribute to an enjoyable result with a few iterations. Quantitatively and qualitatively experimental results demonstrate that the proposed DGDNet can obtain a stable solution efficiently, and produce competitive denoising performance which is even better than that yielded by the state-of-the-art noise reduction methods.

A comparison of Quasi-Newton methods considering line search conditions in unconstrained minimization

Optimization algorithms are essential tools in all fields such as engineering, business, science and even in nature. Their performance and efficiency may differ from problem-to-problem. In this respect, the current paper aims to provide an understanding of the three well-known Quasi-Newton methods relation with various line search conditions on a performance basis. To this end, the fifteen Quasi-Newton method-line search condition combinations, which are composed of Symmetric-Rank-1 (SR-1), Broyden-Fletcher-Goldfarb-Shanno (BFGS) and Davidon-Fletcher-Powell (DFP) Quasi-Newton methods and Backtracking (BC), Armijo-Backtracking (ABC), Goldstein (GC), Weak Wolfe (WWC) and Strong Wolfe (SWC) conditions, are subjected to totally 195 computational experiments using thirteen test functions including smooth and non-smooth ones. During the experiments, the number of function evaluations at every iteration for all the combinations are kept track and the total number of function evaluations, when each combination converges, are set as a first performance metric. In addition to that, the eigenvalues of Hessian approximation matrix are checked if the updated matrix is positive definite or not. In case of having a negative definite Hessian approximation, the eigenvalue modification procedure is employed to guarantee that the updated matrix is positive definite, which in turn progress along the descent direction. Besides, for purpose of using in the performance evaluations, the number of negative definite matrix generations, as a second performance metric, are recorded for all the combinations. To conduct a reliable and an efficient performance analysis on the combinations, the performance and data profiles are used along with the number of negative definite Hessian matrix update generations. Based on the mathematical analysis through those data, the BFGS-GC combination is the fastest one whereas the slowest one is the DFP-SWC combination. For an optimal choice, it is determined that the BFGS-WWC combination is a great candidate. It is also observed that the BFGS and DFP methods operate very well as long as the curvature condition is satisfied by any line search conditions. However, this statement is not valid for the SR-1 method.

Design and Implementation of Obstetric Central Monitoring System Based on Medical Image Segmentation Algorithm.

At present, the incidence of emergencies in obstetric care environment is gradually increasing, and different obstetric wards often have a variety of situations. Therefore, it can provide great help in clinical medicine to give early warning and plan coping plans according to different situations. This paper studied an obstetrics central surveillance system based on a medical image segmentation algorithm. Images obtained by central obstetrics monitoring are segmented, magnified in detail, and image features are extracted, collated, and trained. The normal distribution rule is used to classify the features, which are included in the feature library of the obstetric central monitoring system. In the gray space of the medical image, the statistical distribution of gray features of the medical image is described by the mixture model of Rayleigh distribution and Gaussian distribution. In the gray space of the medical image, Taylor series expansion is used to describe the linear geometric structure of medicine. The eigenvalues of Hessian matrix are introduced to obtain high-order multiscale features of medicine. The multiscale feature energy function is introduced into Markov random energy objective function to realize medical image segmentation. Compared with other segmentation algorithms, the accuracy and sensitivity of the proposed algorithm are 87.98% and 86.58%, respectively, which can clearly segment small medical features.

Lymph vessels visualization from optical coherence tomography data using depth-resolved attenuation coefficient calculation.

Multimodal optical coherent tomography grows popularity with researchers and clinicians over the past decade. One of the modalities is lymphangiography, which allows visualization of the lymphatic vessel networks within optical coherence tomography (OCT) imaging volume. In the present study, it is shown that lymphatic vessel visualization obtained from the depth-resolved attenuation coefficient distributions, corrected for the noise, shows improved contrast and detail in comparison with previously proposed approaches. We also argue that the two most popular approaches for lymphatic vessel visualization, namely simple intensity thresholding and vesselness calculation based on local Hessian matrix eigenvalues, imply different definitions of the lymphatic vessel's appearance in the OCT volume and lead to the different networks.

Detection of microaneurysms and hemorrhages based on improved Hessian matrix.

Knowing the early lesion detection of fundus images is very important to prevent blindness, and accurate lesion segmentation can provide doctors with diagnostic evidence. This study proposes a method based on improved Hessian matrix eigenvalue analysis to detect microaneurysms and hemorrhages in the fundus images of diabetic patients. A two-step method including identification of lesion candidate regions and classification of candidate regions is adopted. In the first step, the method of eigenvalue analysis based on the improved hessian matrix was applied to enhance the image preprocessed. A dual-threshold method was used for segmentation. Then, blood vessels were gradually removed to obtain the lesion candidate regions. In the second step, all candidates were classified into three categories: microaneurysms, hemorrhages and the others. The proposed method has achieved a better performance compared with the existing algorithms on accuracy rates. The classification accuracy rates of microaneurysms and hemorrhages obtained by using our method were 94.4% and 94.0%, respectively, while the classification accuracy rates obtained by using Frangi's filter based on the Hessian matrix to enhance the image were 90.9% and 92.1%. This study demonstrated a methodology for enhancing images by using eigenvalue analysis based on the improved Hessian matrix and segmentation by using double thresholds. The proposed method is beneficial to improve the detection accuracy of microaneurysms and hemorrhages in fundus images.

Single-crystal X-ray structural characterization, Hirshfeld surface analysis, electronic properties, NBO, and NLO calculations and vibrational analysis of the monomeric and dimeric forms of 5-nitro-2-oxindole

The information of interactions is given by RDG versus sign(λ2)ρ product of the sign of the second largest eigenvalue of electron density Hessian matrix and electron density) investigated by RDG surface analysis.

X-ray charge density study of the 6-methyluracil derivative in the crystal: Revealing, consequences, and multipole refinement of minor static disorder

The accurate X-ray diffraction experiment was performed on the crystal of 1,6-dimethyl-3-propargyl-2,4-pyrimidinedione at 100 K. The static electron density (ED) was obtained via multipole refinement against these data. The presence of low-intense but nonrandom positive residual density peaks revealed that the structure was complicated by the minor conformational static disorder. Further analysis of the number and positions of critical points (CPs) (3, +3) of Laplacian of ED ∇2ρ(r) and the ratio of eigenvalues of its Hessian matrix unambiguously proved that the multipole-modeled ED of the main disorder component was contaminated by the second one. A method of visualizing the Laplacian minima as CP-ellipsoids with semiaxes inversely proportional to the eigenvalues of Hessian matrix of ∇2ρ(r) was applied to evaluate the correctness of modeled ED. Extra Laplacian CPs (3, +3) were attributed to the incorrect multipole populations, while the elongated shape of the corresponding discoid CP-ellipsoids was mainly considered to be the effect of troublesome kappa-parameters. A number of different multipole models were constructed in order to minimize the undesirable effects of disorder on the multipole ED. The two-component multipole model showed that the heterocyclic moiety of the minor component with an occupancy of 2% underwent the 180° rotation about the N3–C7 bond axis. Furthermore, the partial transfer of multipole parameters from the model refined against theoretical structure factors was utilized on the most problematic atoms, which massively contributed to disorder treatment. This approach allowed us to restore the ED of the main component in the crystal environment, which quality was gauged by the quantum-topological analysis as well as by its conformity to the data obtained from ab initio periodic calculations. Attempts to speculate on reasons for the limited disordering observed were made: theoretical calculations suggest that moderate hydrogen bonds support the disordering in the structure, while multiple weak noncovalent contacts, e.g., pi interactions, may provide the restrictions on the 50:50 disorder.

Automatic detection of intracranial aneurysms in 3D-DSA based on a Bayesian optimized filter

BackgroundIntracranial aneurysm is a common type of cerebrovascular disease with a risk of devastating subarachnoid hemorrhage if it is ruptured. Accurate computer-aided detection of aneurysms can help doctors improve the diagnostic accuracy, and it is very helpful in reducing the risk of subarachnoid hemorrhage. Aneurysms are detected in 2D or 3D images from different modalities. 3D images can provide more vascular information than 2D images, and it is more difficult to detect. The detection performance of 2D images is related to the angle of view; it may take several angles to determine the aneurysm. As the gold standard for the diagnosis of vascular diseases, the detection on digital subtraction angiography (DSA) has more clinical value than other modalities. In this study, we proposed an adaptive multiscale filter to detect intracranial aneurysms on 3D-DSA.MethodsAdaptive aneurysm detection consists of three parts. The first part is a filter based on Hessian matrix eigenvalues, whose parameters are automatically obtained by Bayesian optimization. The second part is aneurysm extraction based on region growth and adaptive thresholding. The third part is the iterative detection strategy for multiple aneurysms.ResultsThe proposed method was quantitatively evaluated on data sets of 145 patients. The results showed a detection precision of 94.6%, and a sensitivity of 96.4% with a false-positive rate of 6.2%. Among aneurysms smaller than 5 mm, 93.9% were found. Compared with aneurysm detection on 2D-DSA, automatic detection on 3D-DSA can effectively reduce the misdiagnosis rate and obtain more accurate detection results. Compared with other modalities detection, we also get similar or better detection performance.ConclusionsThe experimental results show that the proposed method is stable and reliable for aneurysm detection, which provides an option for doctors to accurately diagnose aneurysms.

Deep Learning and Adaptive Graph-Based Growing Contours for Agricultural Field Extraction

Field mapping and information on agricultural landscapes is of increasing importance for many applications. Monitoring schemes and national cadasters provide a rich source of information but their maintenance and regular updating is costly and labor-intensive. Automatized mapping of fields based on remote sensing imagery may aid in this task and allow for a faster and more regular observation. Although remote sensing has seen extensive use in agricultural research topics, such as plant health monitoring, crop type classification, yield prediction, and irrigation, field delineation and extraction has seen comparatively little research interest. In this study, we present a field boundary detection technique based on deep learning and a variety of image features, and combine it with the graph-based growing contours (GGC) method to extract agricultural fields in a study area in northern Germany. The boundary detection step only requires red, green, and blue (RGB) data and is therefore largely independent of the sensor used. We compare different image features based on color and luminosity information and evaluate their usefulness for the task of field boundary detection. A model based on texture metrics, gradient information, Hessian matrix eigenvalues, and local statistics showed good results with accuracies up to 88.2%, an area under the ROC curve (AUC) of up to 0.94, and F1 score of up to 0.88. The exclusive use of these universal image features may also facilitate transferability to other regions. We further present modifications to the GGC method intended to aid in upscaling of the method through process acceleration with a minimal effect on results. We combined the boundary detection results with the GGC method for field polygon extraction. Results were promising, with the new GGC version performing similarly or better than the original version while experiencing an acceleration of 1.3× to 2.3× on different subsets and input complexities. Further research may explore other applications of the GGC method outside agricultural remote sensing and field extraction.

Microaneurysms detection in color fundus images using machine learning based on directional local contrast

BackgroundAs one of the majorcomplications of diabetes, diabetic retinopathy (DR) is a leadingcause of visual impairment and blindness due to delayed diagnosisand intervention. Microaneurysms appear as the earliest symptom ofDR. Accurate and reliable detection of microaneurysms in colorfundus images has great importance for DR screening.MethodsA microaneurysms' detection methodusing machine learning based on directional local contrast (DLC) isproposed for the early diagnosis of DR. First, blood vessels wereenhanced and segmented using improved enhancement function based onanalyzing eigenvalues of Hessian matrix. Next, with blood vesselsexcluded, microaneurysm candidate regions were obtained using shapecharacteristics and connected components analysis. After imagesegmented to patches, the features of each microaneurysm candidatepatch were extracted, and each candidate patch was classified intomicroaneurysm or non-microaneurysm. The main contributions of ourstudy are (1) making use of directional local contrast inmicroaneurysms' detection for the first time, which does make sensefor better microaneurysms' classification. (2) Applying threedifferent machine learning techniques for classification andcomparing their performance for microaneurysms' detection. Theproposed algorithm was trained and tested on e-ophtha MA database,and further tested on another independent DIARETDB1 database.Results of microaneurysms' detection on the two databases wereevaluated on lesion level and compared with existing algorithms.ResultsThe proposed method has achieved better performance compared with existing algorithms on accuracy and computation time. On e-ophtha MA and DIARETDB1 databases, the area under curve (AUC) of receiver operating characteristic (ROC) curve was 0.87 and 0.86, respectively. The free-response ROC (FROC) score on the two databases was 0.374 and 0.210, respectively. The computation time per image with resolution of 2544×1969, 1400×960 and 1500×1152 is 29 s, 3 s and 2.6 s, respectively.ConclusionsThe proposed methodusing machine learning based on directional local contrast of imagepatches can effectively detect microaneurysms in color fundus imagesand provide an effective scientific basis for early clinical DRdiagnosis.

Microaneurysms Detection using Blob Analysis for Diabetic Retinopathy

Blob analysis is a mathematical method to find the region of interest (ROI) by focusing on the characteristics like brightness or colour. In this work, the process to segment Microaneurysms (MAs) involves two stages, which are pre-processing and segmentation. Pre-processing is a phase for noise removal and illumination correction. In this work, several methods were utilized namely Contrast Limited Adaptive Histogram Equalization (CLAHE), Normalization for contrast enhancement and median filter for noise removal. Then, continue with segmentation phase to segment the MAs from the image. In segmentation phase, several methods were used namely morphological opening, thresholding, Hessian Matrix 2D and Eigenvalue of Hessian Matrix. Finally all the resulting images were compared with the benchmark image to measure the accuracy and grading the stage of Diabetic Retinopathy (DR) by comparing the number of detected MAs. The segmentation accuracy of this project is 68% and 55% accuracy for stage grading

Two-Steps Coronary Artery Segmentation Algorithm Based on Improved Level Set Model in Combination with Weighted Shape-Prior Constraints

Due to the complex topological structure of the coronary artery and the uneven distribution of the contrast agent, the angiography images are inevitably blurred and has low contrast, which causes great difficulty in process of segmentation. For this problem, a two-steps segmentation algorithm based on Hessian matrix and level set is proposed in this paper. Firstly, potential blood vessels of coronary images are preliminary extracted via Hessian matrix eigenvalues feature vectors of the geometric features and the response function. Then a novel regularization and area constraint is introduced into the local data energy fitting functional. Finally, the precision of Coronary Artery image is obtained in the evolution of the level set function. Experiments show that our proposed algorithm has better performance to these comparison segmentation algorithms.

Reduction of bubble-like frames using a RSS filter in wireless capsule endoscopy video

Wireless capsule endoscopy (WCE) is an advanced technique for inner visualization of the digestive tract. However, its large amount of video data collected continuously for several hours by wireless image sensors usually results in tiresome and tedious reading for physicians. To develop this technique in practice, the automatic reduction of large amounts of video data arises as a helpful alternative, which is partly implemented by detecting the non-useful frames, such as those filled with intestinal juices accompanying large bubble-like regions. Based on the bubbles’ morphology properties, a novel automatic approach for detecting the bubble-like frames in capsule video endoscopy that is based on a new ring shape selective (RSS) filter is presented. According to the shape of the bubbles’ bright ring boundary, a group of the shape probability functions and the response intensity functions produced by Hessian matrix eigenvalues are used to construct the RSS filters to enhance the boundary areas of the bubbles. Then, the bubble-like frames can be distinguished by in the bright areas after binary and morphological processing in the filtered images. The experimental results show that the uninformative bubble-like frames can be detected effectively by this approach even under non-uniform illumination conditions.

Hessian matrix-based fourth-order anisotropic diffusion filter for image denoising

Image denoising is one of important tasks in image processing. Diffusion filter-based methods have been widely used for image denosing. In order to solve the staircase effect introduced by second-order diffusion filter, different fourth-order diffusion filters were proposed, which can achieve good performance on image denoising. However, fourth-order diffusion filter often suffers over-smoothness. In this paper, we propose an anisotropic fourth-order diffusion filter for astronomical image denoising, in which the eigenvalue of Hessian matrix is introduced for preserving edge information. The experimental results of denoising on several astronomical images show that the proposed method can achieve better performance than several other methods.

A detailed theoretical study on the excited‐state hydrogen‐bonding dynamics and the proton transfer mechanism for a novel white‐light fluorophore

In this work, density functional theory (DFT) and time‐dependent DFT (TDDFT) methods were used to investigate the excited‐state dynamics of the excited‐state hydrogen‐bonding variations and proton transfer mechanism for a novel white‐light fluorophore 2‐(4‐[dimethylamino]phenyl)‐7‐hyroxy‐6‐(3‐phenylpropanoyl)‐4H‐chromen‐4‐one (1). The methods we adopted could successfully reproduce the experimental electronic spectra, which shows the appropriateness of the theoretical level in this work. Using molecular electrostatic potential (MEP) as well as the reduced density gradient (RDG) versus the product of the sign of the second largest eigenvalue of the electron density Hessian matrix and electron density (sign[λ2]ρ), we demonstrate that an intramolecular hydrogen bond O1–H2···O3 should be formed spontaneously in the S0 state. By analyzing the chemical structures, infrared vibrational spectra, and hydrogen‐bonding energies, we confirm that O1–H2·O3 should be strengthened in the S1 state, which reveals the possibility of an excited‐state intramolecular proton transfer (ESIPT) process. On investigating the excitation process, we find the S0 → S1 transition corresponding to the charge transfer, which provides the driving force for ESIPT. By constructing the potential energy curves, we show that the ESIPT reaction results in a dynamic equilibrium in the S1 state between the forward and backward processes, which facilitates the emission of white light.