Geometric Transformation Method Research Articles

Regularization of heptahedra using geometric element transformation method

By Geometric element transformation method (GETMe) always we get a new element. In this paper, we investigate the regularization of heptahedra using GETMe. Energy function is a cost function for heptahedra which is also applicable for octahedra, decahedra, hexahedra etc. is defined by a particular process, which we call base diagonal apex method (BDAMe). We also try to find the characterization of different cost function using BDAMe when we transform a heptahedra by GETMe.

Robust moving mesh algorithms for hybrid stretched meshes: Application to moving boundaries problems

A robust Mesh-Mover Algorithm (MMA) approach is designed to adapt meshes of moving boundaries problems. A new methodology is developed from the best combination of well-known algorithms in order to preserve the quality of initial meshes. In most situations, MMAs distribute mesh deformation while preserving a good mesh quality. However, invalid meshes are generated when the motion is complex and/or involves multiple bodies. After studying a few MMA limitations, we propose the following approach: use the Inverse Distance Weighting (IDW) function to produce the displacement field, then apply the Geometric Element Transformation Method (GETMe) smoothing algorithms to improve the resulting mesh quality, and use an untangler to revert negative elements. The proposed approach has been proven efficient to adapt meshes for various realistic aerodynamic motions: a symmetric wing that has suffered large tip bending and twisting and the high-lift components of a swept wing that has moved to different flight stages. Finally, the fluid flow problem has been solved on meshes that have moved and they have produced results close to experimental ones. However, for situations where moving boundaries are too close to each other, more improvements need to be made or other approaches should be taken, such as an overset grid method.

CAD for Lung Nodule Detection in Chest Radiography using Complex Wavelet Transform and Shearlet Transform Features

Background and Objectives: The main objective of this paper is to extract the lung nodules in Chest Radiography (CR) for identifying and locating the presence of small lesion or nodules. Methods and Statistical Analysis: Four stages of works are carried out such as: 1). Image Registration using geometrical transformation method, 2). Lung Segmentation using thresholding method, 3). Feature Extraction using Complex Wavelet Transformation method and Shearlet transformation method and finally 4). Image Classification using Random Forest method and classify the images are normal or abnormal. To confirm the abnormality of the segmented output the results are compared with the labeled ground truth images given by medical experts. Findings: The entire proposed approach is implemented in MATLAB software and the performance is verified by comparing the results obtained from CWT results with the ST results. The proposed experiment is carried out on JSRT dataset and obtained the accuracy 96% which is better than the existing approach’s obtained accuracy is 95.4%. Conclusion and Improvements: The proposed approach in this paper is better than the existing approaches for lung nodule detection and identification through segmentation in chest radiography. In future work the performance of the proposed work is evaluated by comparing the obtained results with the other existing transformation methods.

Customized Encryption of Computer Aided Design Models for Collaboration in Cloud Manufacturing Environment

Computer aided design (CAD) models reflect design goals, intentions, and functions so that they are the key intellectual properties of companies. In a Cloud manufacturing environment, how to effectively protect the sensitive feature information for a model owner while enabling the owner to flexibly share the rest of the CAD model with collaborators is an important yet challenging research issue. In this paper, an innovative partial encryption approach, which is able to represent a CAD model into the granularity of sharing information in order to address various collaboration scenarios and customized requirements from the model owner and collaborators, is presented. The approach is composed of a customized encryption algorithm for a CAD model, a key based customized authorization algorithm for collaborators to decrypt shared features in the model, and a customized geometric transformation method to support the effective protection model-based visualization of the model for collaboration. With this approach, a CAD model can be flexibly encrypted to realize partial sharing of features and safe protection of the rest of the model according to collaboration requirements. Meanwhile, during encryption and decryption, the CAD model is always manifold no matter which feature is encrypted or decrypted to ensure user friendliness, model validity, and robustness of the approach. A case study is used to verify and illustrate the effectiveness of the approach. This research is a new attempt to design a content-based and customized encryption approach applicable to CAD model-based collaboration in a Cloud manufacturing environment.

Research on Face Recognition Based on Three Layer Image Generation

In face recognition with single training sample cases the question of the low recognition rate, proposed a method of a kind of three layer virtual image. Using singular perturbation method to highlight the facial features, increase the quantity, scale change and sample attitude through the geometric transformation method, the spatial distribution of the improved method based on sample distribution. The experimental results on ORL face database show that this method can effectively on the single sample problem in the training sample pretreatment.

Efficient Mesh Optimization Using the Gradient Flow of the Mean Volume

The signed volume function for polyhedra can be generalized to a mean volume function for volume elements by averaging over the triangulations of the underlying polyhedron. If we consider these up to translation and scaling, the resulting quotient space is diffeomorphic to a sphere. The mean volume function restricted to this sphere is a quality measure for volume elements. We show that the gradient ascent of this map regularizes the building blocks of hybrid meshes consisting of tetrahedra, hexahedra, prisms, pyramids, and octahedra, that is, the optimization process converges to regular polyhedra. We show that the (normalized) gradient flow of the mean volume yields a fast and efficient optimization scheme for the finite element method known as the geometric element transformation method. Furthermore, we shed some light on the dynamics of this method and the resulting smoothing procedure both theoretically and experimentally.

Efficient Bistatic SAR Raw Signal Simulator of Extended Scenes

Bistatic SAR system is a new mode that allocates the radar transmitter and receiver on different platforms and has more advantages compared to the monostatic case. However, the existing bistatic SAR raw data simulator in the frequency domain can only handle the case of translation invariant system. In this paper, an efficient 2D frequency-domain raw data simulator of extended scenes for bistatic SAR of translation variant system is proposed by a geometric transformation method for the first time, where inverse STOLT interpolation is used to formulate the range migration terms. The presented simulator can accommodate the translation variant bistatic SAR system compared with existing bistatic SAR simulator. And it is more efficient than the time domain one by making use of Fast Fourier Transform (FFT). Simulation results for point targets and a real SAR image demonstrate its validity and effectiveness.

AN IMPROVED TECHNIQUE FOR PRIVACY PRESERVING CLUSTERING BASED ON DAUBECHIES-2 WAVELET TRANSFORM

Having high accuracy results in data clustering and preserving the privacy of data are among the main challenges in privacy preserving clustering (PPC) techniques. High dimensionality of data is another challenge in PPC, which reduces the efficiency of the data mining algorithms. Therefore, PPC algorithms are divided into two categories. The algorithms in the first category protect the data privacy and do not reduce the data dimensionality whereas the algorithms in the second category not only preserve the data privacy but also reduce the data dimensionality. The techniques based on geometric data transformation methods (GTDMs) are related to the first category whereas the techniques based on random projection (RP), discrete cosine transform (DCT) and Haar wavelet transform (HWT) are related to the second category. The GTDMs algorithms do not reduce the data dimensionality. This is the main drawback of this algorithm which causes reduction in the performance of data mining algorithm in large datasets. The technique based on Haar wavelet transform automatically recognizes the dimensionality of the transformed data by using data energy. However, the main problem is the nature of Haar wavelet, which has one vanishing point. In this paper, we show that using Daubechies-2 wavelet, which has two vanishing points, increases the clustering quality. Therefore, to fix the drawback of the PPC algorithm based on Haar wavelet, we introduce a new algorithm to improve both the clustering quality and the privacy measure of data by using Daubechies-2 wavelet transform (D2WT). The results of experiments using several datasets, comparing the new algorithm with other existing techniques, are also presented in this paper.

PRIVACY PRESERVING CLUSTERING BASED ON SINGULAR VALUE DECOMPOSITION AND GEOMETRIC DATA PERTURBATION

Privacy preservation is a major concern when the application of data mining techniques to large repositories of data consists of personal, sensitive and confidential information. Singular Value Decomposition (SVD) is a matrix factorization method, which can produces perturbed data by efficiently removing unnecessary information for data mining. In this paper two hybrid methods are proposed which takes the advantage of existing techniques SVD and geometric data transformations in order to provide better privacy preservation. Reflection data perturbation and scaling data perturbation are familiar geometric data transformation methods which retains the statistical properties in the dataset. In hybrid method one, SVD and scaling data perturbation are used as a combination to obtain the distorted dataset. In hybrid method two, SVD and reflection data perturbation methods are used as a combination to obtain the distorted dataset. The experimental results demonstrated that the proposed hybrid methods are providing higher utility without breaching privacy.

Improving mesh quality and finite element solution accuracy by GETMe smoothing in solving the Poisson equation

Mesh quality plays an essential role in finite element applications, since it affects the efficiency of the simulation with respect to solution accuracy and computational effort. Therefore, mesh smoothing techniques are often applied for improving mesh quality while preserving mesh topology. One of these methods is the recently proposed geometric element transformation method (GETMe), which is based on regularizing element transformations. It will be shown numerically that this smoothing method is particularly suitable, from an applicational point of view, since it leads to a significant reduction of discretization errors within the first few smoothing steps requiring only little computational effort. Furthermore, due to reduced condition numbers of the stiffness matrices the performance of iterative solvers of the resulting finite element equations is improved. This is demonstrated for the Poisson equation with a number of meshes of different complexity and type as well as for piecewise linear and quadratic finite element basis functions. Results are compared to those obtained by two variants of Laplacian smoothing and a state of the art global optimization-based approach.

Fast smoothing of mixed volume meshes based on the effective geometric element transformation method

The geometric element transformation method (GETMe) is an efficient geometry driven approach to mesh smoothing. It is based on regularizing element transformations which, if applied iteratively to a single element, improve its regularity and with this its quality. The smoothing method has already successfully been applied in the case of mixed surface meshes as well as all-tetrahedral and all-hexahedral meshes. In this paper, a GETMe-based approach for smoothing mixed volume meshes is presented. For this purpose, dual element-based regularizing transformations for tetrahedral, hexahedral, pyramidal, and prismatic elements are introduced and analyzed. Furthermore, it is shown that the general concept of GETMe smoothing also applies to mixed volume meshes requiring only minor modifications. Numerical results demonstrate that high quality meshes comparable to those obtained by a state of the art global optimization-based approach can be achieved within significantly shorter runtimes.

Preform Design for Large-Sized Frame Forging of Ti-Alloy Based on 3-D Electrostatic Field Simulation and Geometric Transformation

Large-sized frame forging of Ti-alloy is an important forced component of aircraft. The frame forging has complicated shape which leads to great difficulties in deformation. Some defects may be produced during the forming process such as un-filling or overlapping. Preform design is an effective method for producing qualified forging. In this article, a new method based on 3-D electrostatic field simulation is proposed to design preform of a large-sized frame forging of Ti-alloy and a geometric transformation method is introduced to obtain the preform dimension. In order to select more suitable preform of large-sized frame forging, FEM software Deform-3D is employed to simulate the isothermal forming process of designed preform. Deformation uniformity index ψ is introduced as a criterion to judge the forging quality and the most appropriate preform is obtained by virtual orthogonal test design.

A dual element based geometric element transformation method for all-hexahedral mesh smoothing

Due to their increased complexity hexahedral elements are more challenging with respect to mesh generation and mesh improvement techniques than tetrahedral elements. In particular, there is a lack of geometry-based all-hexahedral smoothing methods for mesh quality improvement being easy to implement, practicable, and efficient. The recently introduced geometric element transformation method represents a new promising element oriented smoothing concept to resolve this deficiency. By giving a dual octahedron based regularizing transformation this new approach is adapted in order to smooth all-hexahedral meshes. First numerical tests indicate that the resulting smoothing method yields high quality results at least comparable to those of a state of the art global optimization-based approach while being significantly faster.

Determination of geometric deformations in image registration using geometric and radiometric measurements

This paper presents a unified method based on pixels for identifying the geometric deformations of digital images. This method uses radiometric pixel gray values to represent the geometric deformations over the entire image surface, a test plate with a 38 × 22 grid, along x and y directions. This method uses a test plate to measure the radiometric pixel gray values in images which represent the geometric deformations in the image. For image registration and the detection of the geometric deformations the following six geometric transformation methods were utilized; non-reflective similarity, similarity, affine, projective, polynomial, piecewise linear and three resampling methods; nearest neighbour, bilinear and bicubic were used. The image data were taken by using Olympus E-150 digital SLR camera and the applied geometric transformation and resampling methods were coded in Matlab software. The experimental results of all the methods are presented and evaluated. The results showed that non-reflective similarity, similarity and affine transformations have a better accuracy than the other methods. Furthermore, geometric distortions were calculated by using corresponding grid corners of pixel coordinates in normal and registered images. Among all geometric transformation, projective transformation combined with three resampling methods revealed the best results. Key words: Digital image, transformation, geometric deformations, registration, resampling.

Evaluation of Effect of Beach Nourishment Using Imageries Produced from Photographs Taken from Fixed Point by Geometric Transformation

On the Chigasaki coast, beach nourishment using coarse material has been carried out since 2004 to recover the sandy beach. To investigate the daily changes of the nourished beach, photographs have been taken from a fixed point. The 51 photographs taken at 1 s intervals were selected under the conditions that the tide level is within M.S.L.±0.1 m, the significant wave height is less than 0.5 m, and the photograph was taken between 8 and 12 am. The weighted average of these photographs was obtained to clearly determine the shoreline position. The imageries were produced from these photographs by the geometric transformation method. The change in shoreline position after the beach nourishment was monitored using the imageries

The geometric element transformation method for tetrahedral mesh smoothing

The geometric element transformation method (GETMe) has been introduced as a new element driven approach to mesh smoothing. It is based on simple geometric transformations, which, if applied iteratively, lead to the regularization of mesh elements. Global mesh smoothing can be accomplished by successively improving the worst elements or by averaging node positions obtained by the simultaneous transformation of all elements. GETMe smoothing has been successfully applied in the case of surface meshes. As shown in this paper, this approach also naturally extends to tetrahedral mesh smoothing without major conceptual modifications. A regularizing transformation for tetrahedra is presented and a combined approach of simultaneous and sequential GETMe smoothing is described. First numerical examples yield high quality meshes superior to those obtained by other geometry-based methods. In fact, the presented results are in a majority of cases at least comparable to those obtained by a state of the art global optimization-based method.

The geometric element transformation method for mixed mesh smoothing

The geometric element transformation method (GETMe) is a geometry-based smoothing method for mixed and non-mixed meshes. It is based on a simple geometric transformation applicable to elements bounded by polygons with an arbitrary number of nodes. The transformation, if applied iteratively, leads to a regularization of the polygons. Global mesh smoothing is accomplished by averaging the new node positions obtained by local element transformations. Thereby, the choice of transformation parameters as well as averaging weights can be based on the element quality which leads to high quality results. In this paper, a concept of an enhanced transformation approach is presented and a proof for the regularizing effect of the transformation based on eigenpolygons is given. Numerical examples confirm that the GETMe approach leads to superior mesh quality if compared to other geometry-based methods. In terms of quality it can even compete with optimization-based techniques, despite being conceptually significantly simpler.

Wireless Location Uses Geometrical Transformation Method With Single Propagation Delay: Model and Detection Performance

Inspired by recent promotions of wireless location services and applications, this paper develops a simple model for detecting a mobile caller location with low implementation complexity and promising accuracy. The model that is described in this paper employs the geometrical transformation method with single propagation delay measurement. Depending on the number of available surrounding base transceiver stations (BTSs), a set of the pseudodistances and pseudodistance differences is provided through the geometrical distances between the home and multiple foreign BTSs, which is called the geometrical transformation method. Accordingly, the mobile caller location can be detected using the circular location technique and the hyperbolic location technique. The major benefit of the proposed model is that during a call to detect the mobile caller's location, the use of geometrical transformation allows us to overcome the location handover problem. A forcing handover in a global system for mobile communications (GSM) network or a three-way soft handover in a universal mobile telecommunications system (UMTS) network, for example, occurs when detecting the location when a standard model that is based on the measurement of the propagation delay is utilized. Comparing the standard model with the proposed model, the former needs at least three propagation delays that were simultaneously measured from at least three BTSs, whereas the latter needs only a single propagation delay that was measured from the home BTS. Moreover, in the case where we do not have a priori information of a non-line-of-sight (NLOS) error, a deterministic parameter that is related to the propagation delay is defined. This parameter is shown as limited a priori information for calibrating the coarse resolution in the proposed location model, which is caused by the NLOS error. To have significant findings, we conduct a practical experiment in an urban environment based on a 1.8-GHz commercial cellular network. In the five-BTS case where the location error is less than 300 m, the probability of location error that the proposed model with a bit period of 1/2 achieved is greater than 0.85. Although the performance of the proposed location model does not satisfy the U.S. Federal Communications Commission Enhanced 911 (FCC E-911) requirements, it is a good solution for the deployment of wireless location services and applications.

Mesh smoothing using the Geometric Element Transformation Method

A novel method for smoothing triangular surface meshes is presented. It is based on the Geometric Element Transformation Method (GETMe) representing a simple geometric operation. In contrast to existing smoothing techniques, GETMe transforms single elements thus resulting in a simultaneous movement of all nodes of an element. The effect of this transformation, if applied iteratively, is the asymptotical but rapid regularization of the initial element. Mesh smoothing is achieved by applying this transformation to every poor quality element until overall mesh quality reaches a user defined level. Thereby, a lower bound for the minimal element angle and an upper bound for the maximal element angle serve as natural control variables in order to freely adjust mesh quality with respect to subsequent applications. Descriptions of the basic smoothing algorithm as well as modifications to preserve shape and to incorporate constraints on nodes are given. Numerical experiments on both artificial and real world meshes demonstrate the method’s potential and flexibility.

GeoTran-HC: Geometric transformation of highly coupled variable topology multi-body problems

Manipulating geometry to prepare a CAD design model for mesh generation is an important step in the finite element analysis (FEA) process. However, complex problems such as electronic chip packages often consist of hundreds or even thousands of sub-features with varying materials, complex geometrical shapes and changeable connectivity configurations. We define a subclass of such problems, termed highly coupled variable topology multi-body (HCVTMB) problems, where configuration and relative geometric sizes cause meshing changes in one body to propagate throughout much of the model. Today creating FEA models for HCVTMB problems typically requires manual geometrical manipulation which is labour-intensive and error-prone. In this paper we introduce an automated geometric transformation method–GeoTran-HC–within the context of a knowledge-based modeling method for CAD–FEA integration. Through five steps–geometry extraction, cell decomposition, associativity maintenance, feature recognition and associativity recovery–this transformation method automatically decomposes an HCVTMB analytical model into a meshable model. It also manages mesh quality and attribution of non-geometrical information such as material properties and boundary conditions. A plastic ball grid array chip package thermo-mechanical case study demonstrates the efficacy of GeoTran-HC within the context of our knowledge-based FEA modelling method. This and similar studies show reductions in total FEA modeling time from days/hours (using traditional methods) to hours/minutes (using the presented method), as well as enhanced modularity and reusability.