Recent advances of variational model in medical imaging and applications to computer aided surgery

In this paper, we review some mathematical models in medical image processing. Due to the superiority in modeling and computation, variational methods have been proven to be powerful techniques, which have been extremely popular and dramatically improved in the past two decades. On one hand, many models have been proposed for nearly all kinds of applications. On the other hand, a lot of models can be globally optimized and also many computation tools have been introduced. Under the variational framework, we focus on two basic problems in medical imaging： image restoration and segmentation, which are core components for kinds of specific tasks. For image restoration, we discuss some models on both additive and multiplicative noises. For image segmentation, we review some models on both whole image segmentation and specific target delineation, with the later being a key step in computer aided surgery. Additionally, we present some models on liver delineation and give their applications to living donor liver transplantation.

Variational Modeling of Free-form Curve and Surface Using Wavelet Basis Functions

Variational modeling approach is often used to interactively design free-form curves and surfaces. Traditionally, a variational problem can be transformed to the optimization of control points. Unfortunately, as the number of basis functions grows, the local support property of B-spline often makes the computation of an optimization system time-consuming. To solve this problem, wavelet basis instead of B-spline basis is used to represent the curves or surfaces. Because the wavelet basis is a hierarchical basis with multiresolution property, the coarse wavelet basis can be used to describe the overall shape of the curves/surfaces, while the finer wavelet basis used to describe the details of the curves/surfaces. Thus, the computing speed of the optimization system can be raised greatly.

An Efficient Variational Model for Multiplicative Noise Removal

In this paper,an efficient variational model for multiplicative noise removal is proposed.By using a MAP estimator,Aubert and Aujol[SIAM J.Appl.Math.,68(2008),pp.925-946]derived a nonconvex cost functional.With logarithmic transformation,we transform the image into a logarithmic domain which makes the fidelity convex in the transform domain.Considering the TV regularization term in logarithmic domain may cause oversmoothness numerically,we propose the TV regularization directly in the original image domain,which preserves more details of images.An alternative minimization algorithm is applied to solve the optimization problem.The z-subproblem can be solved by a closed formula,which makes the method very efficient.The convergence of the algorithm is discussed.The numerical experiments show the efficiency of the proposed model and algorithm.

Evaluation and Control of Cyclic Variation in Spark Ignited Engines by a Thermodynamic Model

An evaluation method of engine cyclic variation is proposed based on fuzzy mathematics concept. The degree of engine cyclic variation is divided into 4 levels: stable, slight variation, moderate variation and serious variation based on the statistic standard deviation of residual gas temperatures within the specified simulation cycles and the function of cyclic variation is also inducted for the cyclic variation control. Because the degree of engine cyclic variation can be estimated qualitatively, the effective control means can be applied to appease the undesired cyclic variation. Simulation result shows that for a very serious cyclic variation through the proper adjustment of the spark angle and the cyclic variation will disappear.

Statistical Modeling of Gate Capacitance Variations Induced by Random Dopants in Nanometer MOSFETs Reserving Correlations

We consider intrinsic gate capacitance variations due to random dopants in the nanometer metal oxide semi- conductor field effect transistor （MOSFET） channel. The variations of total gate capacitance and gate transcapacitances are investigated and the strong correlations between the trans-capacitance variations are discovered. A simple statistical model is proposed for accurately capturing total gate capacitance variability based on the correlations. The model fits very well with the Monte Carlo simulations and the average errors are -0.033% for n-type metal-oxide semiconductor and -0.012% for p-type metal-oxide semiconductor, respectively. Our simulation studies also indicate that, owing to these correlations, the total gate capacitance variability will not dominate in gate capacitance variations.

Numerical modelling of the depth variation and the fluctuation of the thermocline under the effects of wind in the Bohai Sea

-In this paper, numerical modelling of the fluctuation of the thermocline in the Bohai Sea has been made using a two-dimensional nonlinear model in stratified ocean and the model for the depth of the thermocline under the effects of wind stirring. The computed results depict the variations of the fluctuation of the thermocline driven by different kinds of wind fields. The fluctuation of the thermocline in the Bohai Sea varies somewhat with different directions, paths and locations of typhoon (cyclone). Under the effects of strong wind, the thermoclines both sink due to mixing and fluctuate. Furthermore, the fluctuation of the thermocline speeds up mixing. At last, the thermoclines disappear after 12-15 h when the strong wind increases from Force 6 to Force 9.

Pressure dissociation of dense hydrogen

The self-consistent fluid variational model （SFVM） has been used to describe the pressure dissociation of dense hydrogen at high temperatures. This paper focuses on a mixture of hydrogen atoms and molecules and is devoted to the study of the phenomenon of pressure dissociation at finite temperatures. The equation of state and dissociation degree have been calculated from the free energy functions in the range of temperature 2000-10,000K and density 0.02-1.0g/cm^3, which can be compared with other approaches and experiments. The pressure dissociation is found to occur in higher density range, while temperature dissociation is a more gradual effect.

Stochastic Variational Inference-Based Parallel and Online Supervised Topic Model for Large-Scale Text Processing

Topic modeling is a mainstream and effective technology to deal with text data, with wide applications in text analysis, natural language, personalized recommendation, computer vision, etc. Among all the known topic models, supervised Latent Dirichlet Allocation （sLDA） is acknowledged as a popular and competitive supervised topic model. How- ever, the gradual increase of the scale of datasets makes sLDA more and more inefficient and time-consuming, and limits its applications in a very narrow range. To solve it, a parallel online sLDA, named PO-sLDA （Parallel and Online sLDA）, is proposed in this study. It uses the stochastic variational inference as the learning method to make the training procedure more rapid and efficient, and a parallel computing mechanism implemented via the MapReduce framework is proposed to promote the capacity of cloud computing and big data processing. The online training capacity supported by PO-sLDA expands the application scope of this approach, making it instrumental for real-life applications with high real-time demand. The validation using two datasets with different sizes shows that the proposed approach has the comparative accuracy as the sLDA and can efficiently accelerate the training procedure. Moreover, its good convergence and online training capacity make it lucrative for the large-scale text data analyzing and processing.

An Effective Strip Noise Removal Method for Remote Sensing Image

In this paper,an efficient technique for removing strip noise from remote sensing images is proposed in order to better retain image details.Firstly,the remote sensing image with strip noise is decomposed by wavelet technology;Secondly,two variational models are constructed,stripe preserve variation model and a destriping variation model.In order to efficiently separate the detail information in the low level high-frequency component,the stripe preserve variation model eliminates the detail information from the low level high-frequency component(including strip noise)while maintaining the strip noise(including strip noise).In order to successfully save the details in the high level high-frequency component,the destriping variation model eliminates the strip noise in the high level high-frequency component(including the strip noise).Finally,wavelet reconstruction is used to get the denoised image.It is clear from a comparison with previous approaches that the suggested method not only successfully removes strip noise but also preserves image details.

Reliability analysis of stochastic park-and-ride network

Park-and-ride （P＆R） facilities can alleviate the traffic burden in central urban areas by enabling car drivers to park at the perimeter of congested areas and continue their journeys with public transportation （e.g., metro and bus rapid transit）. Whether a P＆R scheme is successful depends on its attractiveness to car users. This paper presents anevaluation method for the reliability analysis of P＆R mode. Two indices, P＆R reliability and mode reliability, are in- troduced to represent the reliabilities of a transfer point and an entire trip, respectively. Then, a systematic reliability analysis is conducted for a stochastic P＆R network, where travelers can complete their journeys via two options： auto mode or P＆R mode. A variational inequality （VI） model is proposed and solved by a heuristic solution algorithm. Nu- merical results show that the P＆R facility reliability is significantly influenced by the capacity of parking facilities, the dispatching frequency of the connecting metro, and the metro fare. In addition, a higher level of total demand in the network has significant negative impacts on P＆R mode＇s attractiveness compared to auto mode.

IMAGE SUPER-RESOLUTION RECONSTRUCTION BY HUBER REGULARIZATION AND TAILORED FINITE POINT METHOD

In this paper,we propose using the tailored finite point method(TFPM)to solve the resulting parabolic or elliptic equations when minimizing the Huber regularization based image super-resolution model using the augmented Lagrangian method(ALM).The Hu-ber regularization based image super-resolution model can ameliorate the staircase for restored images.TFPM employs the method of weighted residuals with collocation tech-nique,which helps get more accurate approximate solutions to the equations and reserve more details in restored images.We compare the new schemes with the Marquina-Osher model,the image super-resolution convolutional neural network(SRCNN)and the classical interpolation methods:bilinear interpolation,nearest-neighbor interpolation and bicubic interpolation.Numerical experiments are presented to demonstrate that with the new schemes the quality of the super-resolution images has been improved.Besides these,the existence of the minimizer of the Huber regularization based image super-resolution model and the convergence of the proposed algorithm are also established in this paper.

MULTIGRID METHOD FOR A MODIFIED CURVATURE DRIVEN DIFFUSION MODEL FOR IMAGE INPAINTING

Digital inpainting is a fundamental problem in image processing and many variational models for this problem have appeared recently in the literature. Among them are the very successfully Total Variation （TV） model [11] designed for local inpainting and its improved version for large scale inpainting： the Curvature-Driven Diffusion （CDD） model [10]. For the above two models, their associated Euler Lagrange equations are highly nonlinear partial differential equations. For the TV model there exists a relatively fast and easy to implement fixed point method, so adapting the multigrid method of [24] to here is immediate. For the CDD model however, so far only the well known but usually very slow explicit time marching method has been reported and we explain why the implementation of a fixed point method for the CDD model is not straightforward. Consequently the multigrid method as in [Savage and Chen, Int. J. Comput. Math., 82 （2005）, pp. 1001-1015] will not work here. This fact represents a strong limitation to the range of applications of this model since usually fast solutions are expected. In this paper, we introduce a modification designed to enable a fixed point method to work and to preserve the features of the original CDD model. As a result, a fast and efficient multigrid method is developed for the modified model. Numerical experiments are presented to show the very good performance of the fast algorithm.

Variational reconstruction using subdivision surfaces with continuous sharpness control

We present a variational method for subdivision surface reconstruction from a noisy dense mesh. A new set of subdivision rules with continuous sharpness control is introduced into Loop subdivision for better modeling subdivision surface features such as semi-sharp creases, creases, and corners. The key idea is to assign a sharpness value to each edge of the control mesh to continuously control the surface features.Based on the new subdivision rules, a variational model with L_1 norm is formulated to find the control mesh and the corresponding sharpness values of the subdivision surface that best fits the input mesh. An iterative solver based on the augmented Lagrangian method and particle swarm optimization is used to solve the resulting non-linear, non-differentiable optimization problem. Our experimental results show that our method can handle meshes well with sharp/semi-sharp features and noise.

Efficient Dual Algorithms for Image Segmentation Using TV-Allen-Cahn Type Models

Variational image segmentation based on the Mumford and Shah model[31],together with implementation by the piecewise constant level-set method(PCLSM)[26],leads to fully nonlinear Total Variation(TV)-Allen-Cahn equations.The commonlyused numerical approaches usually suffer from the difficulties not only with the nondifferentiability of the TV-term,but also with directly evolving the discontinuous piecewise constant-structured solutions.In this paper,we propose efficient dual algorithms to overcome these drawbacks.The use of a splitting-penalty method results in TVAllen-Cahn type models associated with different"double-well"potentials,which allow for the implementation of the dual algorithm of Chambolle[8].Moreover,we present a new dual algorithm based on an edge-featured penalty of the dual variable,which only requires to solve a vectorial Allen-Cahn type equation with linear∇(div)-diffusion rather than fully nonlinear diffusion in the Chambolle’s approach.Consequently,more efficient numerical algorithms such as time-splitting method and Fast Fourier Transform(FFT)can be implemented.Various numerical tests show that two dual algorithms are much faster and more stable than the primal gradient descent approach,and the new dual algorithm is at least as efficient as the Chambolle’s algorithm but is more accurate.We demonstrate that the new method also provides a viable alternative for image restoration.

Evolution Model Based on Prior Information for Narrow Joint Segmentation

Automated segmentation of hip joint computed tomography images is significantly important in the diagnosis and treatment of hip joint disease.In this paper,we propose an automatic hip joint segmentation method based on a variational model guided by prior information.In particular,we obtain prior features by automatic sample selection,get a discriminative function by training these selected samples and then integrate this prior information into our variational model.Numerical results demonstrate that the proposed method has high accuracy in segmenting narrow joint regions.

A Mean Curvature Regularized Based Model for Demodulating Phase Maps from Fringe Patterns

We introduce a variationalmethod for demodulating phasemaps fromfringe patterns.This newmethod is based on themean curvature of the level sets of the phase surface that is used for regularization.The performance of the method is illustrated with both synthetic and real data.

Truncated Fractional-Order Total Variation Model for Image Restoration

Fractional-order derivative is attracting more and more interest from researchers working on image processing because it helps to preserve more texture than total variation when noise is removed.In the existing works,the Grunwald–Letnikov fractional-order derivative is usually used,where the Dirichlet homogeneous boundary condition can only be considered and therefore the full lower triangular Toeplitz matrix is generated as the discrete partial fractional-order derivative operator.In this paper,a modified truncation is considered in generating the discrete fractional-order partial derivative operator and a truncated fractional-order total variation(tFoTV)model is proposed for image restoration.Hopefully,first any boundary condition can be used in the numerical experiments.Second,the accuracy of the reconstructed images by the tFoTV model can be improved.The alternating directional method of multiplier is applied to solve the tFoTV model.Its convergence is also analyzed briefly.In the numerical experiments,we apply the tFoTV model to recover images that are corrupted by blur and noise.The numerical results show that the tFoTV model provides better reconstruction in peak signal-to-noise ratio(PSNR)than the full fractional-order variation and total variation models.From the numerical results,we can also see that the tFoTV model is comparable with the total generalized variation(TGV)model in accuracy.In addition,we can roughly fix a fractional order according to the structure of the image,and therefore,there is only one parameter left to determine in the tFoTV model,while there are always two parameters to be fixed in TGV model.

A MODEL FOR THE VARIATIONS OF THE CRITICAL FREQUENCY OF F_2 LAYER DURING THE NEGATIVE PHASES OF IONOSPHERIC STORMS

A model for the negative phase of ionospheric storms in middle latitudes is presented. It is assumed that there will be molecule enriched air in the thermosphere above the auroral oval during the period of the main phase of a magnetic storm. The molecule enriched air is carried to the middle latitudes by thermospheric neutral wind, and at the same time it diffuses away. When the molecule enriched air arrives at the F2 layer above a station, the electron loss rate in the F2 layer increases, the electron density decreases and then the negative phase at the station begins. We have calculated the variations of the fo F2 following magnetic storms for Manzhouli （29.5°N, 117.5°E）, Freiburg （48°N, 07°E） and Billerica （43°N, 71°W） respectively. The results agree very well with typical events observed at the three stations and can be used to explain some average features of negative phase ionospheric storms in middle latitudes.

Research on potential influential scholars in the field of information science and their cooperative characteristics

With the continuous development of social media,the ways and means of academic influence evaluation of scholars are increasing rapidly.The emergence of the Citation Network Structural Variation model method breaks the traditional way of identifying the influence of scholars through scientometrics index,author cooperation or node indicators in author citation network structure.Based on this method,CiteSpace software tool is used to detect scholars with potential influence in the field of Information Science and reveal the cooperative characteristics of scholars with potential influence.The study found that the most potentially influential five-pointed star scholars in the field of Information Science mainly include Leydesdorff L,Bornmann L,Thelwall M,Bar-llan J,Waltman L,Huang MH,Rousseau R and others.Pentagram scholars are usually located at the core of different cooperative groups in the author's cooperative network.Other influential non-pentagram scholars and pentagram scholars maintain a high frequency of cooperation and have a high similarity in research direction.

Machining Error Control by Integrating Multivariate Statistical Process Control and Stream of Variations Methodology

For aircraft manufacturing industries, the analyses and prediction of part machining error during machining process are very important to control and improve part machining quality. In order to effectively control machining error, the method of integrating multivariate statistical process control （MSPC） and stream of variations （SoV） is proposed. Firstly, machining error is modeled by multi-operation approaches for part machining process. SoV is adopted to establish the mathematic model of the relationship between the error of upstream operations and the error of downstream operations. Here error sources not only include the influence of upstream operations but also include many of other error sources. The standard model and the predicted model about SoV are built respectively by whether the operation is done or not to satisfy different requests during part machining process. Secondly, the method of one-step ahead forecast error （OSFE） is used to eliminate autocorrelativity of the sample data from the SoV model, and the T2 control chart in MSPC is built to realize machining error detection according to the data characteristics of the above error model, which can judge whether the operation is out of control or not. If it is, then feedback is sent to the operations. The error model is modified by adjusting the operation out of control, and continually it is used to monitor operations. Finally, a machining instance containing two operations demonstrates the effectiveness of the machining error control method presented in this paper.