Using the Sharp Operator for edge detection and nonlinear diffusion

In this paper we investigate the use of the sharp function known from functional analysis in image processing. The sharp function gives a measure of the variations of a function and can be used as an edge detector. We extend the classical notion of the sharp function for measuring anisotropic behaviour and give a fast anisotropic edge detection variant inspired by the sharp function. We show that these edge detection results are useful to steer isotropic and anisotropic nonlinear diffusion filters for image enhancement

A proof of convergence of a finite volume scheme for modified steady Richards’ equation describing transport processes in the pressing section of a paper machine

A number of water flow problems in porous media are modelled by Richards’ equation [1]. There exist a lot of different applications of this model. We are concerned with the simulation of the pressing section of a paper machine. This part of the industrial process provides the dewatering of the paper layer by the use of clothings, i.e. press felts, which absorb the water during pressing [2]. A system of nips are formed in the simplest case by rolls, which increase sheet dryness by pressing against each other (see Figure 1). A lot of theoretical studies were done for Richards’ equation (see [3], [4] and references therein). Most articles consider the case of x-independent coefficients. This simplifies the system considerably since, after Kirchhoff’s transformation of the problem, the elliptic operator becomes linear. In our case this condition is not satisfied and we have to consider nonlinear operator of second order. Moreover, all these articles are concerned with the nonstationary problem, while we are interested in the stationary case. Due to complexity of the physical process our problem has a specific feature. An additional convective term appears in our model because the porous media moves with the constant velocity through the pressing rolls. This term is zero in immobile porous media. We are not aware of papers, which deal with such kind of modified steady Richards’ problem. The goal of this paper is to obtain the stability results, to show the existence of a solution to the discrete problem, to prove the convergence of the approximate solution to the weak solution of the modified steady Richards’ equation, which describes the transport processes in the pressing section. In Section 2 we present the model which we consider. In Section 3 a numerical scheme obtained by the finite volume method is given. The main part of this paper is theoretical studies, which are given in Section 4. Section 5 presents a numerical experiment. The conclusion of this work is given in Section 6

Applying multiobjective evolutionary algorithms in industrial projects

During the recent years, multiobjective evolutionary algorithms have matured as a flexible optimization tool which can be used in various areas of reallife applications. Practical experiences showed that typically the algorithms need an essential adaptation to the specific problem for a successful application. Considering these requirements, we discuss various issues of the design and application of multiobjective evolutionary algorithms to real-life optimization problems. In particular, questions on problem-specific data structures and evolutionary operators and the determination of method parameters are treated. As a major issue, the handling of infeasible intermediate solutions is pointed out. Three application examples in the areas of constrained global optimization (electronic circuit design), semi-infinite programming (design centering problems), and discrete optimization (project scheduling) are discussed

PREDICTION OF RESPIRATORY MOTION

Radiation therapy is a cancer treatment method that employs high-energy radiation beams to destroy cancer cells by damaging the ability of these cells to reproduce. Thoracic and abdominal tumors may change their positions during respiration by as much as three centimeters during radiation treatment. The prediction of respiratory motion has become an important research area because respiratory motion severely affects precise radiation dose delivery. This study describes recent radiotherapy technologies including tools for measuring target position during radiotherapy and tracking-based delivery systems. In the first part of our study we review three prediction approaches of respiratory motion, i.e., model-based methods, model-free heuristic learning algorithms, and hybrid methods. In the second part of our work we propose respiratory motion estimation with hybrid implementation of extended Kalman filter. The proposed method uses the recurrent neural network as the role of the predictor and the extended Kalman filter as the role of the corrector. In the third part of our work we further extend our research work to present customized prediction of respiratory motion with clustering from multiple patient interactions. For the customized prediction we construct the clustering based on breathing patterns of multiple patients using the feature selection metrics that are composed of a variety of breathing features. In the fourth part of our work we retrospectively categorize breathing data into several classes and propose a new approach to detect irregular breathing patterns using neural networks. We have evaluated the proposed new algorithm by comparing the prediction overshoot and the tracking estimation value. The experimental results of 448 patients’ breathing patterns validated the proposed irregular breathing classifier

Robustness properties of estimators in generalized Pareto Models

We study global and local robustness properties of several estimators for shape and scale in a generalized Pareto model. The estimators considered in this paper cover maximum likelihood estimators, skipped maximum likelihood estimators, moment-based estimators, Cramér-von-Mises Minimum Distance estimators, and, as a special case of quantile-based estimators, Pickands Estimator as well as variants of the latter tuned for higher finite sample breakdown point (FSBP), and lower variance. We further consider an estimator matching population median and median of absolute deviations to the empirical ones (MedMad); again, in order to improve its FSBP, we propose a variant using a suitable asymmetric Mad as constituent, and which may be tuned to achieve an expected FSBP of 34%. These estimators are compared to one-step estimators distinguished as optimal in the shrinking neighborhood setting, i.e., the most bias-robust estimator minimizing the maximal (asymptotic) bias and the estimator minimizing the maximal (asymptotic) MSE. For each of these estimators, we determine the FSBP, the influence function, as well as statistical accuracy measured by asymptotic bias, variance, and mean squared error—all evaluated uniformly on shrinking convex contamination neighborhoods. Finally, we check these asymptotic theoretical findings against finite sample behavior by an extensive simulation study

Image Guided Respiratory Motion Analysis: Time Series and Image Registration.

The efficacy of Image guided radiation therapy (IGRT) systems relies on accurately extracting, modeling and predicting tumor movement with imaging techniques. This thesis investigates two key problems associated with such systems: motion modeling and image processing. For thoracic and upper abdominal tumors, respiratory motion is the dominant factor for tumor movement. We have studied several special structured time series analysis techniques to incorporate the semi-periodicity characteristics of respiratory motion. The proposed methods are robust towards large variations among fractions and populations; the algorithms perform stably in the presence of sparse radiographic observations with noise. We have proposed a subspace projection method to quantitatively evaluate the semi-periodicity of a given observation trace; a nonparametric local regression approach for real-time prediction of respiratory motion; a state augmentation scheme to model hysteresis; and an ellipse tracking algorithm to estimate the trend of respiratory motion in real time. For image processing, we have focused on designing regularizations to account for prior information in image registration problems. We investigated a penalty function design that accommodates tissue-type-dependent elasticity information. We studied a class of discontinuity preserving regularizers that yield smooth deformation estimates in most regions, yet allow discontinuities supported by data. We have further proposed a discriminate regularizer that preserves shear discontinuity, but discourages folding or vacuum generating flows. In addition, we have initiated a preliminary principled study on the fundamental performance limit of image registration problems. We proposed a statistical generative model to account for noise effect in both source and target images, and investigated the approximate performance of the maximum-likelihood estimator corresponding to the generative model and the commonly adopted M-estimator. A simple example suggests that the approximation is reasonably accurate. Our studies in both time series analysis and image registration constitute essential building-blocks for clinical applications such as adaptive treatment. Besides their theoretical interests, it is our sincere hope that with further justifications, the proposed techniques would realize its clinical value, and improve the quality of life for patients.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/60673/1/druan_1.pd

Inverse Integer Optimization With an Application in Recommender Systems

In typical (forward) optimization, the goal is to obtain optimal values for the decision variables given known values of optimization model parameters. However, in practice, it may be challenging to determine appropriate values for these parameters. Assuming the availability of historical observations that represent past decisions made by an optimizing agent, the goal of inverse optimization is to impute the unknown model parameters that would make these observations optimal (or approximately optimal) solutions to the forward optimization problem. Inverse optimization has many applications, including geology, healthcare, transportation, and production planning. In this dissertation, we study inverse optimization with integer observation(s), focusing on the cost coefficients as the unknown parameters. Furthermore, we demonstrate an application of inverse optimization to recommender systems. First, we address inverse optimization with a single imperfect integer observation. The aim is to identify the unknown cost vector so that it makes the given imperfect observation approximately optimal by minimizing the optimality error. We develop a cutting plane algorithm for this problem. Results show that the proposed cutting plane algorithm works well for small instances. To reduce computational time, we propose an LP relaxation heuristic method. Furthermore, to obtain an optimal solution in a shorter amount of time, we combine both methods into a hybrid approach by initializing the cutting plane algorithm with a solution from the heuristic method. In the second study, we generalize the previous approach to inverse optimization with multiple imperfect integer observations that are all feasible solutions to one optimization problem. A cutting plane algorithm is proposed and then compared with an LP heuristic method. The results show the value of using multiple data points instead of a single observation. Finally, we apply the proposed methods in the setting of recommender systems. By accessing past user preferences, through inverse optimization we identify the unknown model parameters that minimize an aggregate of the optimality errors over multiple points. Once the unknown parameters are imputed, the recommender system can recommend the best items to the users. The advantage of using inverse optimization is that when users are optimizing their decisions, there is no need to have access to a large amount of data for imputing recommender system model parameters. We demonstrate the accuracy of our approach on a real data set for a restaurant recommender system