Elementary Shapes Research Articles

Identification of femoral head center of bipolar hemiarthroplasy in radiostereometric analysis with elementary geometrical shape models

Elementary geometrical shape (EGS) models are useful in radiostereometric analysis (RSA) on hip stems because tantalum markers attached to the stems can be omitted. In order to create an EGS model of a femoral stem, the center of the femoral head has to be identified. The contour of the femoral head is recommended to be used. However, the contour of the femoral head cannot be detected exclusively by computer if it is combined with a bipolar head or a metal cup. We therefore hypothesized that the contour of the outer head of bipolar hemiarthroplasty can be included in the EGS model as well as the femoral head contour. We calculated the time required for the detection of the contour, the precision of analysis and the stem micromotion at 2 years using the two different methods in the same picture set and compared the results. The detection of the bipolar head contour was 10 times faster than that of the femoral head contour. The precision for subsidence was 0.16mm in EGS RSA with the femoral head contour, and 0.15mm with the bipolar head contour (p=0.68). The precisions were comparable and clinically acceptable. There was no significant difference between the results of the 2-year micromotion with the two different methods. We conclude that this new method is applicable to measure stem micromotion of hemi-arthoplasty with EGS RSA and the method facilitates the Radiostereometric analysis.

On the Geometric Accuracy of RepRap Open-Source Three-Dimensional Printer

In the field of additive manufacturing (AM) processes, there is a significant lack of scientific data on the performance of open-source 3D printers in relation to process parameter values. The purpose of this paper is to assess the impact of the main process parameters on the accuracy of a set of typical geometric features, as obtained with an open-source 3D printer, the RepRap Prusa-Mendel I2. For this purpose, a benchmarking part was set up, composed of elementary shapes, representing a series of different geometric features. By means of a DoE approach, it was possible to assess the effects of two process parameters—layer thickness (Lt) and flow rate (Fr)—on five geometric features: cube, sphere, cylinder, cone, and angled surface. A high resolution Laser Scanner was used to evaluate the variation between the acquired geometric feature and the corresponding 3D computer-aided design (CAD) nominal model. On the basis of experimental results, it was possible to analyze and discuss the main effects of the above-mentioned process parameters on each geometric feature. These results can help RepRap users in the correct selection of process parameters with the aim of improving the quality of prototypes.

Elements of style

The human perception of stylistic similarity transcends structure and function: for instance, a bed and a dresser may share a common style. An algorithmically computed style similarity measure that mimics human perception can benefit a range of computer graphics applications. Previous work in style analysis focused on shapes within the same class, and leveraged structural similarity between these shapes to facilitate analysis. In contrast, we introduce the first structure-transcending style similarity measure and validate it to be well aligned with human perception of stylistic similarity. Our measure is inspired by observations about style similarity in art history literature, which point to the presence of similarly shaped, salient, geometric elements as one of the key indicators of stylistic similarity. We translate these observations into an algorithmic measure by first quantifying the geometric properties that make humans perceive geometric elements as similarly shaped and salient in the context of style, then employing this quantification to detect pairs of matching style related elements on the analyzed models, and finally collating the element-level geometric similarity measurements into an object-level style measure consistent with human perception. To achieve this consistency we employ crowdsourcing to quantify the different components of our measure; we learn the relative perceptual importance of a range of elementary shape distances and other parameters used in our measurement from 50K responses to cross-structure style similarity queries provided by over 2500 participants.We train and validate our method on this dataset, showing it to successfully predict relative style similarity with near 90% accuracy based on 10-fold cross-validation.

Understanding Process Parameter Effects of RepRap Open-Source Three-Dimensional Printers Through a Design of Experiments Approach

With a view to enabling additive manufacturing (AM) processes, today, open-source, low-cost 3D printers are systems with great potential. However there is a significant lack of scientific data on the performance of open-source 3D systems and on the selection of adequate process parameters that can help to improve the quality of the parts. The purpose of this paper is to assess the effects of the main process parameters on the dimensional accuracy of a specific open-source 3D printer, the RepRap Prusa-Mendel I2. This study consisted of a benchmarking part, involving elementary shapes representing a series of different features. By means of a full factorial DoE (Design of Experiments), with three factors (layer thickness, deposition speed, and flow rate), three levels, and three replications, 81 parts were obtained. Subsequently, a laser scanner (D700 Laser Scanner—3Shape, Denmark) was used as high resolution reverse engineering system in order to evaluate the variation between real parts and nominal geometry. The impact of the main process parameters was evaluated and optimal combinations were analyzed. On the basis of the results obtained in the experiments, practical suggestions for the settings of common process parameters were formulated. Test results serve to improve the quality of AM parts through the most appropriate selection of the main process parameters.

Nonagons in the Hagia Sophia and the Selimiye Mosque

One of the classical topics in geometry is the ruler and compass construction of good approximations of the regular nonagon. We propose a method to choose a desired error of approximation, based on new linear third-order recurrence relations. It is related to patterns shown on the balustrade of minbar of Selimiye Mosque in Edirne (Turkey, 1569–1575), where apparently regular nonagons are placed over a net of regular hexagons. This kind of ornament also occurs in Hagia Sophia in the minbar, in freezes stucco carvings and in window grilles. In Medieval Islamic art and architecture the use of the nonagon is not frequent, but it is remarkable that this particular grid of interlocked nonagons and hexagons appears in the decorations of the works of Ottoman architect Mimar Sinan. The pattern is present in his masterpiece, the Selimiye Mosque, in the Hagia Sophia and in other works in the Istanbul city. Looking at practical ways for the construction of the pattern, we provide simple procedures to obtain angles close to 40° that could have been useful for a craftsman to realize the nonagonal geometric designs. In particular, almost regular nonagons are constructed using some elementary shapes that are related with semi-regular tessellations. We compare the patterns obtained through theoretical considerations to those displayed in the examples given above. Several hypotheses are proposed for the practical construction of the interlocked hexagonal patterns for nonagons.

English

2 ABSTRACT: In this paper, we tend to describe hybrid feature extraction for offline written character recognition. The projected technique could be a hybrid of structural, applied math and correlation options. Within the opening, the projected technique identifies the kind and placement of some elementary strokes within the character. The strokes to be hunted for comprise horizontal, vertical, positive slant and negative slant lines-as we tend to observe that the structure of any character are often approximated with the assistance of a mix of straightforward line strokes. The strokes are known by correlating completely different segments of the character with the chosen elementary shapes. These normalized correlation values at completely different segments of the character offer correlation options. For creating feature extraction additional strong, we tend to add within the second step sure structural/statistical options to the correlation options. The additional structural/statistical options are supported projections, profiles, invariant moments, endpoints and junction points. This increased, powerful combination of options leads to a 157-variable feature vector for every character, that we discover adequate enough to unambiguously represent and determine every character. Prior, written character recognition downside has not been self-addressed the means our projected hybrid feature extraction technique deals with it. The extracted feature vector is employed throughout the coaching section for building a support vector machine (SVM) classifier. The trained SVM classifier is after used throughout the testing section for classifying unknown characters. Experiments were performed on written digit characters and uppercase alphabets taken from completely different writers, with none constraint on style. The obtained results were compared with some connected existing approaches. Attributable to the projected technique, the results obtained show higher potency concerning classifier accuracy, memory size and coaching time as compared to those different existing approaches. .

PolSAR Coherency Matrix Decomposition Based on Constrained Sparse Representation

This paper presents a new model-based decomposition method for the polarimetric synthetic aperture radar coherency matrices. We improve the model flexibility from the following two aspects: To reach a compromise between model flexibility and computation complexity, for the volume scattering component, the elementary scatterer shape is allowed to change from sphere/flat plate to dipole, then to dihedral, whereas orientation randomness is simplified by only considering two cases. Different orientation angles are considered for each component. Since the models become more complex, new decomposition procedures are developed. The three-component decomposition is first reformulated as a constrained sparse representation problem. Then, inspired by the orthogonal matching pursuit variant developed by Bruckstein et al. in 2008, new decomposition procedures are designed. The effectiveness of the proposed method is verified using a synthetic data set and two real SAR data sets, including a RADARSAT-2 data set and the NASA/JPL AIRSAR data set over San Francisco Bay.

Calculation of electric and magnetic induced fields in humans subjected to electric power lines

In this work, analysis of the human body exposed to high voltage electric and magnetic fields is presented. The distribution of the electric field is obtained by using Laplace's equation. This relates the surface charge induced on the body to the potential in a reciprocal Laplace problem, which is then calculated by charge simulation method coupled with genetic algorithms to determine the appropriate arrangement of simulating charges inside the human body. The magnetic field intensity along the vertical center line of the human is calculated. Exposure to external electric and magnetic fields at power frequency induces electric field, magnetic field and currents inside the human body. The presented model for simulating electric and magnetic fields are a three dimensional field problem and introduced different types of charges to simulate the different elementary geometrical shapes of human body. The particular strength of the charge simulation method in this application is its ability to allow a detailed representation of the shape and posture of the human body. The results have been assessed through comparison induced current, electric field, magnetic field and there distribution over the body surface, as estimated in other experimental and computational work.

Comparison of two different Radiostereometric analysis (RSA) systems with markerless elementary geometrical shape modeling for the measurement of stem migration

Radiostereometric analysis (RSA) is the gold standard of measurement for in vivo 3D implants migration. BackgroundThe aim of this study was to evaluate the in vivo precision of 2 RSA marker-based systems compared with that of marker-free, elementary geometrical shape modeling RSA. MethodsStem migration was measured in 50 patients recruited from an on-going Randomized Controlled Trial. We performed marker-based analysis with the Um RSA and RSAcore systems and compared these results with those of the elementary geometrical shape RSA. FindingsThe precision for subsidence was 0.118mm for Um RSA, 0.141mm for RSAcore, and 0.136mm for elementary geometrical shape RSA. The precision for retroversion was 1.3° for elementary geometrical shape RSA, approximately 2-fold greater than that for the other methods. The intraclass correlation coefficient between the marker-based systems and elementary geometrical shape RSA was approximately 0.5 for retroversion. All 3 methods yielded ICCs for subsidence and varus–valgus rotation above 0.9. DiscussionWe found an excellent correlation between marker-based RSA and elementary geometrical shape RSA for subsidence and varus–valgus rotation, independent of the system used. The precisions for out-of-plane migration were inferior for elementary geometrical shape RSA. Therefore, as a mechanism of failure, retroversion may be more difficult to detect early. This is to our knowledge the first study to compare different RSA systems with or without markers on the implant. InterpretationMarker-based RSA has high precision in all planes, independent of the system used. Elementary geometrical shape RSA is inferior in out-of-plane migration.

Vectorising the detector geometry to optimise particle transport

Among the components contributing to particle transport, geometry navigation is an important consumer of CPU cycles. The tasks performed to get answers to "basic" queries such as locating a point within a geometry hierarchy or computing accurately the distance to the next boundary can become very computing intensive for complex detector setups. So far, the existing geometry algorithms employ mainly scalar optimisation strategies (voxelisation, caching) to reduce their CPU consumption. In this paper, we would like to take a different approach and investigate how geometry navigation can benefit from the vector instruction set extensions that are one of the primary source of performance enhancements on current and future hardware. While on paper, this form of microparallelism promises increasing performance opportunities, applying this technology to the highly hierarchical and multiply branched geometry code is a difficult challenge. We refer to the current work done to vectorise an important part of the critical navigation algorithms in the ROOT geometry library. Starting from a short critical discussion about the programming model, we present the current status and first benchmark results of the vectorisation of some elementary geometry shape algorithms. On the path towards a full vector-based geometry navigator, we also investigate the performance benefits in connecting these elementary functions together to develop algorithms which are entirely based on the flow of vector-data. To this end, we discuss core components of a simple vector navigator that is tested and evaluated on a toy detector setup.

A fast algorithm for the energy space boson Boltzmann collision operator

This paper introduces a fast algorithm for the energy space boson Boltzmann collision operator. Compared to the direct O ( N 3 ) O(N^3) calculation and the previous O ( N 2 log ⁡ N ) O(N^2\log N) method [Markowich and Pareschi, 2005], the new algorithm runs in complexity O ( N log 2 ⁡ N ) O(N\log ^2N) , which is optimal up to a logarithmic factor ( N N is the number of grid points in energy space). The basic idea is to partition the 3-D summation domain recursively into elementary shapes so that the summation within each shape becomes a special double convolution that can be computed efficiently by the fast Fourier transform. Numerical examples are presented to illustrate the efficiency and accuracy of the proposed algorithm.

Calculation of electrostatically induced field in humans subjected to high voltage transmission lines

A new approach is described for calculating the induced current and field in the human body by high-voltage alternating electric fields. The distribution of the electric field is obtained by using Laplace's equation. This relates the surface charge induced on the body to the potential in a reciprocal Laplace problem, which is then calculated by charge simulation method coupled with genetic algorithms to determine the appropriate arrangement of simulating charges inside the human body. The presented model for simulating electrical field is a three dimensional field problem and introduced different types of charges to simulate the different elementary geometrical shapes of human body. The particular strength of the charge simulation method in this application is its ability to allow a detailed representation of the shape and posture of the human body. The results have been assessed through comparison induced current and its distribution over the body surface, as estimated in other experimental and computational work. The accuracy of the simulated electric field is satisfied for the potential error (less than 0.1%), and the field deviation angle (less than 1°) over the human body.

Microfluidic flow-free generation of chemical concentration gradients

This paper presents a class of novel microfluidic concentration gradient generation (CGG) devices that create temporally stable chemical concentration gradients with complex shapes in a flow-free environment. The devices feature a two-layer channel design and the incorporation of a semipermeable membrane, which effectively segregates the concentration gradient region in the lower layer from the flow of reagent sample (simply “sample” onward) and buffer in the upper layer. In the mean time, free diffusion across the membrane constantly replenishes sample and buffer to maintain a stable concentration. The shapes of the concentration gradients are controlled by the geometries of the micro-channels and chambers. Concentration gradients with complex shapes can be achieved by piecewise combining constituent gradients with elementary shapes. Capable of generating concentration gradients in a flow-free environment, our devices eliminate undesirable flow stimulation on biological cells under investigation, while maintaining a stable chemical environment for cell studies.

Influence of granular packing on porosity and tortuosity

In a granular porous medium the packing configuration and the shape of the grains influence how fluid flows through it. This is directly related to the porosity and tortuosity of the pore space. In this paper we present an analytical function relating the porosity φ and the tortuosity τ of a granular pore medium by means of a packing parameter B. A general expression to estimate B for different representative elementary volumes and grain shapes is presented; in particular, for polyhedral packings. Exploring the packing parameter properties, we discuss the nonuniqueness of the packing-shape combination in relation to B and the porosity behavior for the special cases 0<B<1, B=1, and B>1.

Condensed exciton polaritons in a two-dimensional trap: Elementary excitations and shaping by a Gaussian pump beam

An exciton-polariton condensate (EPC) confined in a parabolic two-dimensional trap is considered theoretically. In the realistic limit of weakly interacting polaritons, the nonlinear term in the Gross-Pitaevskii equation describing the properties of the condensate can be considered as a perturbation with respect to the trapping potential, which allows for a convenient analytical description of the EPC ground state and Bogolyubov-type elementary excitations around it. The excitation modes with the energies and wave functions depending on the polariton-polariton coupling strength are derived for the condensate, neglecting interaction with uncondensed polaritons can be neglected. The energies of these modes are shown to be almost equidistant, even for a rather strong polariton-polariton interaction inside the condensate. This makes lateral parabolic traps promising candidates for realization of bosonic cascade lasers based on exciton polaritons. Another physical scenario is also considered where the interaction with a reservoir of uncondensed polaritons is more important than that inside the EPC. In this case, it is shown that the condensate is ``reshaped'' by the repulsive interaction with the reservoir, namely, pushed out from the center of the trap in real space and blue-shifted in energy, in agreement with the results obtained in a number of recent experiments.

A systematic approach for an accuracy level using rapid prototyping technologies

Nowadays there has emerged a series of rapid prototyping processes with great potential, and designers and engineers need to know the accuracy performance of these processes to compare and select the best solution. There is a significant lack of published data related to rapid prototyping processes and feature accuracy. This research was conducted to minimize this gap and provide much needed accuracy in terms of dimensional and geometric information. The methodology includes the summarization of previous studies and definition of a benchmarking part that is composed of elementary shapes representative of different features most likely to be found in a final product. The benchmarking part was controlled in terms of dimensional accuracy, geometric precision and freeform deviation. The sources of errors controlled by the final user were analysed, like Standard Tessellation Language (STL) file format resolution and build direction. Four custom rapid prototyping processes have been used and compared: stereolithography, selective laser sintering, fused deposition modelling and three-dimensional printer. Computer numerically controlled machining has been used as an alternative prototyping process in this study as a standard to compare costs and accuracy. This work assessed measures that can be used to quantify the accuracy performance for a given part so that the choices for prototyping can be made based on scientific knowledge and best working practices. These results are very useful for designing products to be prototyped or manufactured through direct methods. The results can be used to improve the functionality of prototypes and the decision process through the best systematic approach.

Incremental Fourier transform of triangular closed 2-manifolds

In this paper we present a technique for the calculation of the Fourier transform for functions defined on oriented closed 2-manifolds. The objects are given as oriented triangular meshes. Our focus in this paper is on the characteristic function of the model, that is, the function that is equal to one inside the model and zero outside. The advantage of our approach is that it provides an automatic, simple, and efficient method for computing the Fourier coefficients directly from the mesh representation. This avoids the approximation of the mesh by a grid of voxels which leads to a loss of details and error prone in calculation. The main idea is to distribute the calculation of the Fourier coefficients over the elementary shapes composing the mesh. Then we use the divergence theorem to simplify the computation by calculating the coefficients using integrations on simpler domains. The algorithm is simple and efficient, with many potential applications. Some examples are given to demonstrate the effectiveness of our approach. Key words: Fourier coefficients, partial calculation, voxelization, triangular mesh, divergence theorem.

Shape‐Up: Shaping Discrete Geometry with Projections

AbstractWe introduce a unified optimization framework for geometry processing based on shape constraints. These constraints preserve or prescribe the shape of subsets of the points of a geometric data set, such as polygons, one‐ring cells, volume elements, or feature curves. Our method is based on two key concepts: a shape proximity function and shape projection operators. The proximity function encodes the distance of a desired least‐squares fitted elementary target shape to the corresponding vertices of the 3D model. Projection operators are employed to minimize the proximity function by relocating vertices in a minimal way to match the imposed shape constraints. We demonstrate that this approach leads to a simple, robust, and efficient algorithm that allows implementing a variety of geometry processing applications, simply by combining suitable projection operators. We show examples for computing planar and circular meshes, shape space exploration, mesh quality improvement, shape‐preserving deformation, and conformal parametrization. Our optimization framework provides a systematic way of building new solvers for geometry processing and produces similar or better results than state‐of‐the‐art methods.

Superior accuracy of model-based radiostereometric analysis for measurement of polyethylene wear

ObjectivesThe accuracy and precision of two new methods of model-based radiostereometric analysis (RSA) were hypothesised to be superior to a plain radiograph method in the assessment of polyethylene (PE) wear.MethodsA phantom device was constructed to simulate three-dimensional (3D) PE wear. Images were obtained consecutively for each simulated wear position for each modality. Three commercially available packages were evaluated: model-based RSA using laser-scanned cup models (MB-RSA), model-based RSA using computer-generated elementary geometrical shape models (EGS-RSA), and PolyWare. Precision (95% repeatability limits) and accuracy (Root Mean Square Errors) for two-dimensional (2D) and 3D wear measurements were assessed.ResultsThe precision for 2D wear measures was 0.078 mm, 0.102 mm, and 0.076 mm for EGS-RSA, MB-RSA, and PolyWare, respectively. For the 3D wear measures the precision was 0.185 mm, 0.189 mm, and 0.244 mm for EGS-RSA, MB-RSA, and PolyWare respectively. Repeatability was similar for all methods within the same dimension, when compared between 2D and 3D (all p > 0.28). For the 2D RSA methods, accuracy was below 0.055 mm and at least 0.335 mm for PolyWare. For 3D measurements, accuracy was 0.1 mm, 0.2 mm, and 0.3 mm for EGS-RSA, MB-RSA and PolyWare respectively. PolyWare was less accurate compared with RSA methods (p = 0.036). No difference was observed between the RSA methods (p = 0.10).ConclusionsFor all methods, precision and accuracy were better in 2D, with RSA methods being superior in accuracy. Although less accurate and precise, 3D RSA defines the clinically relevant wear pattern (multidirectional). PolyWare is a good and low-cost alternative to RSA, despite being less accurate and requiring a larger sample size.

EVALUATION OF ELEVATION, SLOPE AND STREAM NETWORK QUALITY OF SPOT DEMS

Abstract. Digital elevation models are considered the most useful data for dealing with geomorphology. The quality of these models is an important issue for users. This quality concerns position and shape. Vertical accuracy is the most assessed in many studies and shape quality is often neglected. However, both of them have an impact on the quality of the final results for a particular application. For instance, the elevation accuracy is required for orthorectification and the shape quality for geomorphology and hydrology. In this study, we deal with photogrammetric DEMs and show the importance of the quality assessment of both elevation and shape. For this purpose, we produce several SPOT HRV DEMs with the same dataset but with different template size, that is one of the production parameters from optical images. Then, we evaluate both elevation and shape quality. The shape quality is assessed with in situ measurements and analysis of slopes as an elementary shape and stream networks as a complex shape. We use the fractal dimension and sinuosity to evaluate the stream network shape. The results show that the elevation accuracy as well as the slope accuracy are affected by the template size. Indeed, an improvement of 1 m in the elevation accuracy and of 5 degrees in the slope accuracy has been obtained while changing this parameter. The elevation RMSE ranges from 7.6 to 8.6 m, which is smaller than the pixel size (10 m). For slope, the RMSE depends on the sampling distance. With a distance of 10 m, the minimum slope RMSE is 11.4 degrees. The stream networks extracted from these DEMs present a higher fractal dimension than the reference river. Moreover, the fractal dimension of the extracted networks has a negligible change according to the template size. Finally, the sinuosity of the stream networks is slightly affected by the change of the template size.