Using mathematical morphology methods in the process of generalization in spatial databases

Edge detection is an important work for object recognition and is also an essential pre-processing step in image segmentation and visual analysis. This paper deeply studies the edge detection methods of the noisy images and concentrates on the mathematical morphology methods. By analyzing and studying the theory of mathematical morphology, the paper constructs edge detection operations and analyzes the specialties of the operator and the structure elements. Based on this, the paper proposes a new method of edge detection using mathematical morphology and image fusion. The operations can obtain clear and exact edge of the noisy images. By simulation and comparing with the traditional edge detection operations, the proposed method is more effective on noise restraining and retaining the image details.

This thesis aims at developing efficient mathematical methods for solving hierarchical dynamic optimization problems. The main motivation is to model processes in nature, for which there is evidence to assume that they run optimally. We describe models of such processes by optimal control problems (called optimal control models (OCMs)). However, an OCM typically includes unknown parameters that cannot be derived entirely on a theoretical basis, which is in particular the case for the cost function. Therefore, we develop parameter estimation techniques to estimate the unknowns in an OCM from observation data of the process. Mathematically, this leads to a hierarchical dynamic optimization problem with a parameter estimation problem on the upper level and an optimal control problem on the lower level. We focus on multi-stage equality and inequality constrained optimal control problems based on nonlinear ordinary differential equations. The main goal of this thesis is to derive numerically efficient mathematical methods for solving hierarchical dynamic optimization problems, and to use these methods to estimate parameters in high-dimensional OCMs from real-world measurement data. We develop parameter-dependent OCMs for the gait of cerebral palsy patients and able-bodied subjects. The unknown parameters in the OCMs are then estimated from real-world motion capture data provided by the Heidelberg MotionLab of the Orthopedic University Clinic Heidelberg by using the mathematical methods developed within this work. The main novelties and contributions of this thesis to the field of hierarchical dynamic optimization are summarized herein. - We establish a novel mathematical method, a so-called direct all-at-once approach, for solving hierarchical dynamic optimization problems based on the direct multiple shooting method and first-order optimality conditions. - Furthermore, we propose an efficient numerical algorithm for large-scale hierarchical dynamic optimization problems, which fully exploits the structures inherited from both the hierarchical setting and the discretization. - Pontryagin's maximum principle is used to analyze solution properties of hierarchical dynamic optimization problems like second-order optimality conditions of the lower-level problem. - In addition, we propose and discuss alternative methods for hierarchical dynamic optimization that are based on derivative-free optimization and a bundle approach. These methods keep the hierarchical problem setting and do not reformulate the lower-level problem using first-order optimality conditions. - We establish a novel lifting method for regularizing mathematical programs with complementarity constraints, which is discussed and numerically investigated by means of a well-known collection of benchmark problems. - Proofs of regularity and convergence results for sequential quadratic programming methods applied to lifted mathematical programs with complementarity constraints are provided. - Efficient state-of-the-art implementations of all mathematical methods derived in this thesis, as well as a benchmark collection of hierarchical dynamic optimization problems are presented. - High-dimensional optimal control gait models for cerebral palsy patients and able-bodied subjects are developed. The mathematical methods derived in this thesis are used to estimate the unknown model parameters from real-world motion capture data provided by the Heidelberg MotionLab of the Orthopedic University Clinic Heidelberg. The theoretical and practical results presented in this thesis can be considered an initial motivating step towards answering open questions in current medical research in fields like treatment planning, classification of gaits, or the evaluation of surgeries by means of hierarchical dynamic optimization.

Machine vision based online detection of PCB defect

In computer vision, geometric processing and image analysis, the notation of a shape of a 3-D object has been studied either by an embedded manifold for the continuous stetting or as a collection of a discrete set of marker positions on the manifold. Within the last years, there have been many rapid developments in the field of shape representation, shape correspondence and shape manipulation with technical applications ranging from laser-range scanners to 3-D printing. Classic shape analysis tools from differential geometry have a fresh influence in the field, often powered by modern methods from optimization and numerical computing. At the same time, discrete geometric methods and related techniques such as from mathematical morphology have evolved significantly. Moreover, techniques like deep learning gained a significant influence in the development of corresponding methods and tools. New developments from tropical geometry have a high potential for use in shape analysis. The topics in our seminar addressed the sketched challenges and developments that will be useful for shape analysis. Especially we aimed to discuss the possibilities of combining fields like tropical geometry with more classical techniques as for instance from mathematical morphology. We discussed possibilities of applying machine learning methods in this context and considered recent advances from more classical fields like differential geometry and partial differential equations that can be useful for setting up and understanding shape analysis methods in all of these approaches. This seminar brought together 26 researchers from North America and Europe engaged in recent and upcoming developments in shape analysis who view these challenges from different perspectives and who together discussed the pressing open problems and novel solutions to them.

In the process of nano-electronic circuit design, there are defects inevitably. Due to the variety of defects and nets on circuits, the extraction of the critical area leading to the short circuit fault has become the bottleneck of layout optimization and of integrated circuit yield estimation. This paper proposes a new model of short critical area and extraction algorithm based on short circuit faults caused by redundant defects, combining the redundant defect features and mathematical morphology theory. Firstly, defect feature sizes and the nets ranges of the circuit are extracted. Secondly, according to the definition of short critical area and utilizing the expansion operation of mathematical morphology a new model of short critical area of regular nets is derived. Finally, extraction algorithm of short critical area is designed and implemented in accordance with the new model. The new model and extraction algorithm have the characteristics of being more generic and being independent of the shape features of defects and nets. Compared with the existing models, the new model has the similar performance however the extraction algorithm has significantly raised time efficiency. Furthermore, the extraction algorithm is more efficient than the previous algorithm which is based on mathematical morphology and non-model method. The experimental results on the real layouts of synthesized OpenSparc circuit and MUSB L70 show that the proposed method is accurate and effective.

Modern imaging such as diffusion tensor magnetic resonance imaging (DT-MRI) is consists of matrix valued data. The processing for DT-MRI tractography is a method to determine the architecture of axonal fibers in the central nervous system by computing the direction of the principal eigenvectors that obtained from tensor matrix. This tensor matrix is usually sensitive to noise. Hence adequate image processing methods for regularization are in demand. Our goal of this paper is extend the morphological operation to the matrix-valued data and applies it to noise reduction. We proposed three Mathematical Morphology methods for regularization and compared to matrix medians which are the Simple Median Method. Results The results of the Mathematical Morphology Method are faster and the performance is similar to those of the Simple Median. Mathematical Morphology methods are effective algorithm for the tensor regularization.

Edge detection is one of the fundamental issues of digital image, in this paper, mathematical morphology method and several classical edge detection operators are reviewed. This paper provides two methods: Canny operator and mathematical morphology, which summaries relatively good image edge detection methods, and provides a reference for some detection occasions where requires smaller edge width in practical application.

The alpha-tree, also known as the quasi-flat zone hierarchy is a widely used representation of images in Mathematical Morphology. This structure organizes the regions according to a similarity criterion into a tree, that eases the multiscale analysis of images. Many alpha-tree algorithms exist and computing this structure efficiently is still an active field of research. Indeed, the alpha-tree is commonly used in remote sensing where there is an urge for fast processing of large terabytes images. In this paper, we propose the first massively parallel alpha-tree algorithm that leverages concurrent union-find data structures to exploit the SIMT (Single Instruction Multiple Threads) programming model of GPUs. Our algorithm outperforms the State-of-the-Art parallel CPU algorithms by a factor of 10 on average on desktop computers and servers. It also opens new perspectives for using Mathematical Morphology methods on GPU pipelines.

ABSTACT Image segmentation has been an important and challenging issue in the field of computer vision over decades. It plays a critical role for most image analysis tasks, such as object detection and recognition. The aim of this paper is to obtain segmented image of Printed Circuit Board (PCB)’s track using mathematical morphological operation. Morphological image analysis is based on the idea that images represent a collection of spatial patterns that can be analyzed based on some predefined patterns called structuring elements. Most basic morphological operation, dilation and erosion have been employed in this research. Detail elaboration on this method will be discussed and experimental results are presented.

Background Currently, gas control stations use the gas cleaning systems based on filter net, which is the most cost effective for cleaning purposes. Aims and Objectives Development of a mathematical model to substantiate the value of pressure drop in the mesh-type filter element, at which the filter must be cleaned from mechanical impurities Results In this paper it is proved that the value of the pressure drop at the gas net-type filter element inversely impact on the capital investment into the filter, on the one hand, and on the operating costs associated with the removal of solid particles, on the other hand. On this basis a mathematical model was developed to substantiate the maximum allowed pressure drop in the filter element, caused by gradual clogging of the filter net. The model includes a block diagram, the efficiency function of the integral costs, equations of the balance of expenditure, and limitations of the control parameter. Minimal integral cost of the filter is the taken as a criterion to determine optimum of the efficiency function of the mathematical model. The adopted efficiency function is featured by fractional powers, which makes necessary to solve a complex transcendental equation, and this is a rather time-consuming process of successive iterations. Therefore, to determine the optimal pressure drop across the filter element the numerical method of solving the problem was used, that is, a set of values of the pressure drop with known geometric filter parameters being given, we determine the integral costs. The optimal pressure drop on filter element corresponds to the option with minimal costs. The proposed mathematical model determines the optimal value of the maximum allowable pressure drop on the gas filter.

Nowadays, Remote sensing is widely applied into flood monitoring. In order to obtain the accurate flooded area, water body need be well segmented, however, image segmentation is still a hard problem. In fact, each image segmentation method has its advantages and disadvantages, single method is hard to acquire satisfactory results, so two or more methods combination are applied. In this paper, the algorithm of combination watershed transformation and region merging based on morphologic gradient is introduced and applied in a typical flooded region, Quyuan town of Hunan province of China to extract the area of target water bodies, at the same time, other segmentation methods: ISODATA and the combination segmentation methods of optimal threshold and mathematical morphology, are also applied. Finally, compared with actually measurement area of the target water body by Differential GPS, some suggestive conclusions are drawn.

The authors introduce the concept of free angle to locate boundaries of textured regions in grey-level images. Using this with methods of mathematical morphology, the authors demonstrate that boundaries of all textured regions in remotely sensed images ran be located accurately.

A computer-aided quantitative method for a complex analysis of gel electrophoretograms is presented. The analysis consists of several steps: (i) determination of the background image by methods of mathematical morphology and its subtraction from the gel image, (ii) selection of an appropriate part of the gel lane including curved lanes and lanes with a nonuniform width, (iii) computation of the lane densitogram by averaging several lane-parallel scans, (iv) decomposition of the lane densitogram into component bands using a data selecting algorithm and Marquardt's minimizer. Several different functions for component bands are utilized. It is shown that the densitogram can be decomposed into component bands with reasonable accuracy only if an appropriate model function is chosen. The algorithms are tested on several different gel electrophoretograms which show typical features as a nonuniform background, curved lanes, an asymmetrical band shape and a superposition of small bands on the shoulders of big ones. It is shown that overlapped bands are best approximated by an asymmetrical Gausian curve and an asymmetrical Gauss-Cauchy function. Linear response to the serial dilution of the protein sample is tested.

Metal/dielectric composite films — particle shapes and transport properties

It is argued that the mathematical morphology method seems to be more reasonable and powerful in studying certain multiscaling vision problems than the approach that uses derivatives of Gaussian-shaped filters of different sizes. To show the validity of this method, the authors concentrated on an application that involves forming scale-space image of a 2-D shape using morphological opening filtering. A proof is given to show that morphological opening filtering has a property of not introducing additional zero-crossings as one moves to a coarser scale. This is a different result from the conclusion by A.L. Yuille and T.A. Poggio (ibid., vol.PAMI-8, Jan. 1986) that the Gaussian filter is the only filter with this property. In addition, opening filtering is computationaly simpler than the Gaussian filter.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>