scholarly journals From 2D to 3D: Construction of a 3D Parametric Model for Detection of Dental Roots Shape and Position from a Panoramic Radiograph—A Preliminary Report

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Laura Mazzotta ◽  
Mauro Cozzani ◽  
Armando Razionale ◽  
Sabrina Mutinelli ◽  
Attilio Castaldo ◽  
...  
Keyword(s):  
Panoramic Radiograph ◽  
Maximum Error ◽  
Parametric Model ◽  
Parametric Models ◽  
Free Form ◽  
Spline Curves ◽  
Accuracy Level ◽  
Root Movement ◽  
Free Form Surfaces ◽  
Movement Simulation

Objectives. To build a 3D parametric model to detect shape and volume of dental roots, from a panoramic radiograph (PAN) of the patient.Materials and Methods. A PAN and a cone beam computed tomography (CBCT) of a patient were acquired. For each tooth, various parameters were considered (coronal and root lengths and widths): these were measured from the CBCT and from the PAN. Measures were compared to evaluate the accuracy level of PAN measurements. By using a CAD software, parametric models of an incisor and of a molar were constructed employing B-spline curves and free-form surfaces. PAN measures of teeth 2.1 and 3.6 were assigned to the parametric models; the same two teeth were segmented from CBCT. The two models were superimposed to assess the accuracy of the parametric model.Results. PAN measures resulted to be accurate and comparable with all other measurements. From model superimposition the maximum error resulted was 1.1 mm on the incisor crown and 2 mm on the molar furcation.Conclusion. This study shows that it is possible to build a 3D parametric model starting from 2D information with a clinically valid accuracy level. This can ultimately lead to a crown-root movement simulation.

scholarly journals Measurement point sampling method for inspection of parts with free-form surfaces

2018 ◽  
Vol 10 (11) ◽  
pp. 168781401880957 ◽  
Author(s):  
Dezhong Zhao ◽  
Wenhu Wang ◽  
Jinhua Zhou ◽  
Ruisong Jiang ◽  
Kang Cui ◽  
...  
Keyword(s):  
Measurement Accuracy ◽  
Sampling Method ◽  
Free Form ◽  
Surface Inspection ◽  
B Spline ◽  
Spline Curves ◽  
Data Points ◽  
Manufacturing Accuracy ◽  
Method Of Measurement ◽  
Free Form Surfaces

Parts must be measured to evaluate the manufacturing accuracy in order to check whether their dimension is in expected tolerance. In engineering, parts with free-form surfaces are generally measured by high-precision coordinate-measuring machines. The measurement accuracy is usually improved by increasing the density of measurement points, which is time-consuming and costly. In this article, a novel sampling method of measurement points for free-form surface inspection is proposed. First, surface inspection is simplified into the inspection of a number of section curves of the surface. Second, B-spline curves constructed with an iterative method are employed to approximate these section curves. Subsequently, data points necessary to construct the B-spline curves are taken as the measurement points. Finally, the proposed method is compared with other two sampling methods. The results indicate that the proposed method greatly reduced the number of measurement points without decreasing the precision of surface modeling.

Monte Carlo simulation and analysis of free-form surface registration

1997 ◽  
Vol 211 (8) ◽  
pp. 605-617 ◽  
Author(s):  
D Brujic ◽  
M Ristic
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Confidence Intervals ◽  
Computer Aided Design ◽  
Maximum Error ◽  
Surface Registration ◽  
Performance Criteria ◽  
Free Form ◽  
Registration Method ◽  
Free Form Surfaces

Accurate dimensional inspection and error analysis of free-form surfaces requires accurate registration of the component in hand. Registration of surfaces defined as non-uniform rational B-splines (NURBS) has been realized through an implementation of the iterative closest point method (ICP). The paper presents performance analysis of the ICP registration method using Monte Carlo simulation. A large number of simulations were performed on an example of a precision engineering component, an aero-engine turbine blade, which was judged to possess a useful combination of geometric characteristics such that the results of the analysis had generic significance. Data sets were obtained through CAD (computer aided design)-based inspection. Confidence intervals for estimated transformation parameters, maximum error between a measured point and the nominal surface (which is extremely important for inspection) mean error and several other performance criteria are presented. The influence of shape, number of measured points, measurement noise and some less obvious, but not less important, factors affecting confidence intervals are identified through statistical analysis.

scholarly journals RESEARCHING FOR THE SAMPLING METHOD ON CMM

2009 ◽  
Vol 12 (16) ◽  
pp. 63-71
Author(s):  
Ha Thi Thu Thai ◽  
Thang Duc Dinh
Keyword(s):  
Confidence Intervals ◽  
Computer Aided Design ◽  
Maximum Error ◽  
Performance Criteria ◽  
Free Form ◽  
Data Sets ◽  
Precision Engineering ◽  
Registration Method ◽  
Factors Affecting ◽  
Free Form Surfaces

Accurate dimensional inspection and error analysis of free-form surfaces requires accurate registration of the component in hand. Registration of surfaces defined as non-uniform rational B-splines (NURBS) has been realized through an implementation of the iterative closest point method (ICP). The paper presents performance analysis of the ICP registration method using Monte Carlo simulation. A large number of simulations were performed on an example of a precision engineering component, an aero-engine turbine blade, which was judged to possess a useful combination of geometric characteristics such that the results of the analysis had generic significance. Data sets were obtained through CAD (computer aided design)-based inspection. Confidence intervals for estimated transformation parameters, maximum error between a measured point and the nominal surface (which is extremely important for inspection) mean error and several other performance criteria are presented. The influence of shape, number of measured points, measurement noise and some less obvious, but not less important, factors affecting confidence intervals are identified through statistical analysis.

Structural-parametric model of an electroelastic actuator for nanomechanics

2020 ◽  
pp. 3-11
Author(s):  
S.M. Afonin
Keyword(s):  
Transfer Function ◽  
Piezoelectric Actuator ◽  
Transfer Functions ◽  
Piezoelectric Effect ◽  
Parametric Model ◽  
Elastic Compliance ◽  
Parametric Models ◽  
Piezo Actuator ◽  
Structural Scheme ◽  
Model Transfer

Structural-parametric models, structural schemes are constructed and the transfer functions of electro-elastic actuators for nanomechanics are determined. The transfer functions of the piezoelectric actuator with the generalized piezoelectric effect are obtained. The changes in the elastic compliance and rigidity of the piezoactuator are determined taking into account the type of control. Keywords electro-elastic actuator, piezo actuator, structural-parametric model, transfer function, parametric structural scheme

scholarly journals Construction and analysis of unified 4-point interpolating nonstationary subdivision surfaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mehwish Bari ◽  
Ghulam Mustafa ◽  
Abdul Ghaffar ◽  
Kottakkaran Sooppy Nisar ◽  
Dumitru Baleanu
Keyword(s):  
Computer Graphics ◽  
Geometric Modeling ◽  
Tension Control ◽  
Free Form ◽  
Subdivision Surfaces ◽  
Smooth Curves ◽  
Practical Applications ◽  
Tension Parameter ◽  
Exact Reproduction ◽  
Free Form Surfaces

AbstractSubdivision schemes (SSs) have been the heart of computer-aided geometric design almost from its origin, and several unifications of SSs have been established. SSs are commonly used in computer graphics, and several ways were discovered to connect smooth curves/surfaces generated by SSs to applied geometry. To construct the link between nonstationary SSs and applied geometry, in this paper, we unify the interpolating nonstationary subdivision scheme (INSS) with a tension control parameter, which is considered as a generalization of 4-point binary nonstationary SSs. The proposed scheme produces a limit surface having $C^{1}$ C 1 smoothness. It generates circular images, spirals, or parts of conics, which are important requirements for practical applications in computer graphics and geometric modeling. We also establish the rules for arbitrary topology for extraordinary vertices (valence ≥3). The well-known subdivision Kobbelt scheme (Kobbelt in Comput. Graph. Forum 15(3):409–420, 1996) is a particular case. We can visualize the performance of the unified scheme by taking different values of the tension parameter. It provides an exact reproduction of parametric surfaces and is used in the processing of free-form surfaces in engineering.

Beyond Deep Learning: An Econometric Example

2020 ◽  
Vol 28 (Supp01) ◽  
pp. 31-38 ◽  
Author(s):  
Ruofan Liao ◽  
Paravee Maneejuk ◽  
Songsak Sriboonchitta
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Prediction Models ◽  
Original Data ◽  
Parametric Model ◽  
Parametric Models ◽  
The Past ◽  
Currency Exchange ◽  
Currency Exchange Rate ◽  
Linear And Nonlinear

In the past, in many areas, the best prediction models were linear and nonlinear parametric models. In the last decade, in many application areas, deep learning has shown to lead to more accurate predictions than the parametric models. Deep learning-based predictions are reasonably accurate, but not perfect. How can we achieve better accuracy? To achieve this objective, we propose to combine neural networks with parametric model: namely, to train neural networks not on the original data, but on the differences between the actual data and the predictions of the parametric model. On the example of predicting currency exchange rate, we show that this idea indeed leads to more accurate predictions.

Automatic Generation of Anisotropic Patterns of Geometric Features for Industrial Design

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Diego Andrade ◽  
Ved Vyas ◽  
Kenji Shimada
Keyword(s):  
Boundary Conditions ◽  
Computer Aided Design ◽  
Industrial Design ◽  
Automatic Generation ◽  
Free Form ◽  
Geometric Features ◽  
Target Domain ◽  
Metric Tensor ◽  
Target Region ◽  
Free Form Surfaces

While modern computer aided design (CAD) systems currently offer tools for generating simple patterns, such as uniformly spaced rectangular or radial patterns, these tools are limited in several ways: (1) They cannot be applied to free-form geometries used in industrial design, (2) patterning of these features happens within a single working plane and is not applicable to highly curved surfaces, and (3) created features lack anisotropy and spatial variations, such as changes in the size and orientation of geometric features within a given region. In this paper, we introduce a novel approach for creating anisotropic patterns of geometric features on free-form surfaces. Complex patterns are generated automatically, such that they conform to the boundary of any specified target region. Furthermore, user input of a small number of geometric features (called “seed features”) of desired size and orientation in preferred locations could be specified within the target domain. These geometric seed features are then transformed into tensors and used as boundary conditions to generate a Riemannian metric tensor field. A form of Laplace's heat equation is used to produce the field over the target domain, subject to specified boundary conditions. The field represents the anisotropic pattern of geometric features. This procedure is implemented as an add-on for a commercial CAD package to add geometric features to a target region of a three-dimensional model using two set operations: union and subtraction. This method facilitates the creation of a complex pattern of hundreds of geometric features in less than 5 min. All the features are accessible from the CAD system, and if required, they are manipulable individually by the user.

scholarly journals Development of Non-contact Profile Sensor for 3-D Free-form Surfaces (1st Report)

1992 ◽  
Vol 58 (11) ◽  
pp. 1886-1892
Author(s):  
Takashi MIYOSHI ◽  
Hiroshi AOKI ◽  
Katsumasa SAITO
Keyword(s):  
Free Form ◽  
Free Form Surfaces
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