Set Of Control Points Research Articles

Predator prey optimization for snake‐based contour detection

PurposeThe purpose of this paper is to describe a work that aims to solve contour detection problem using a planar deformable model and a swarm‐based optimization technique. Contour detection is an important task in image processing as it allows depicting boundaries of objects in an image. The proposed approach uses snakes as active contour model and adapts predator prey optimization (PPO) metaheuristic so that to define a new dynamic for evolving snakes in a way to reduce time complexity while providing good quality results.Design/methodology/approachIn the proposed approach, contour detection has been cast as an optimization problem requiring function minimization. PPO has been used to develop a search strategy to handle the optimization process. PPO is a population‐based method inspired by the phenomenon of predators attack and preys evasion. It has been proposed as an improvement of particle swarm optimization (PSO) where additional particles are introduced to repel the other particles into the swarm. The introduced dynamic is intended to achieve better exploration of the search space. In the design, a representation scheme has been first defined. Each particle either a predator or a prey is represented as a curve (snake) defined by a set of control points. The idea is then to evolve a set of curves using the dynamic governed by PPO model equations. As a result, the curve that optimizes a defined energy function is identified as the contour of the target object.FindingsApplication of the proposed method to a variety of images using a multi agent platform has shown that good quality results have been obtained compared to a PSO‐based method.Originality/valueNature inspired computing is an emergent paradigm that witnesses a growing interest because it suggests a new philosophy to optimization. This work contributes in showing its suitability to solve problems even it is still at infancy. In another hand, despite the amount of work done in image processing, it is still required to define new methods for image segmentation. This work outlines a new way to deal with this problem through the use of PPO.

Efficient mesh motion using radial basis functions with data reduction algorithms

Mesh motion using radial basis functions has been demonstrated previously by the authors to produce high quality meshes suitable for use within unsteady and aeroelastic CFD codes. In the aeroelastic case the structural mesh may be used as the set of control points governing the deformation, which is efficient since the structural mesh is usually small. However, as a stand alone mesh motion tool, where the surface mesh points control the motion, radial basis functions may be restricted by the size of the surface mesh, as an update of a single volume point depends on all surface points. In this paper a method is presented that allows an arbitrary deformation to be represented to within a desired tolerance by using a significantly reduced set of surface points intelligently identified in a fashion that minimises the error in the interpolated surface. This method may be used on much larger cases and is successfully demonstrated here for a 10 6 cell mesh, where the initial solve phase cost reduces by a factor of eight with the new scheme and the mesh update by a factor of 55. It has also been shown that the number of surface points required to represent the surface is only geometry dependent (i.e. grid size independent), and so this reduction factor actually increases for larger meshes.

Extending the Limits of Feature-Based SLAM With B-Splines

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper describes a simultaneous localization and mapping (SLAM) algorithm for use in unstructured environments that is effective regardless of the geometric complexity of the environment. Features are described using B-splines as modeling tool, and the set of control points defining their shape is used to form a complete and compact description of the environment, thus making it feasible to use an extended Kalman-filter (EKF) based SLAM algorithm. This method is the first known EKF-SLAM implementation capable of describing general free-form features in a parametric manner. Efficient strategies for computing the relevant Jacobians, perform data association, initialization, and map enlargement are presented. The algorithms are evaluated for accuracy and consistency using computer simulations, and for effectiveness using experimental data gathered from different real environments. </para>

Feature level fusion of range and intensity images of an object

This paper presents feature level fusion of images of an object obtained from two different imaging techniques. A draft 3-D view of the object is generated by registering range images obtained from scanning the object by a laser beam. For that purpose, the method of optical triangulation is employed for data acquisition and feature matching technique for the registration of the images. Triangle-based linear interpolation is used to obtain a 3-D mesh representing the object surface. Structural features are extracted from the draft 3-D model of the object and subsequently mapped to 2-D plane by perspective transformation. Hough transform technique has been implemented for the extraction of structural features from the intensity image of the object obtained under illumination light. Fusion of both the extracted edge maps is accomplished by affine transformation after identifying a set of control points. This provides a high-level description of the object.

Model Registration Control Point Set Selection for Turbine Blade Shape Inspection

Model Registration Control Point Set Selection for Turbine Blade Shape Inspection

Construction of a sphere by using projective Bézier patches

A projective (rational) rectangular second-order Bezier patch is determined by nine points in 3-space and by positive weights assigned to these points. The shape of the patch can be changed by varying the positions of the control points and the weight values. A procedure for constructing a sphere by using a projective rectangular second-order Bezier patch is suggested. A special set of control points, three of which are multiple, and weights is used.

Fast path planning in virtual colonoscopy

We propose a fast path planning algorithm using multi-resolution path tree propagation and farthest visible point. Initial path points are robustly generated by propagating the path tree, and all internal voxels locally most distant from the colon boundary are connected. The multi-resolution scheme is adopted to increase computational efficiency. Control points representing the navigational path are successively selected from the initial path points by using the farthest visible point. The position of the initial path point in a down-sampled volume is accurately adjusted in the original volume. Using the farthest visible point, the number of control points is adaptively changed according to the curvature of the colon shape so that more control points are assigned to highly curved regions. Furthermore, a smoothing step is unnecessary since our method generates a set of control points to be interpolated with the cubic spline interpolation. We applied our method to 10 computed tomography datasets. Experimental results showed that the path was generated much faster than using conventional methods without sacrificing accuracy, and clinical efficiency. The average processing time was approximately 1 s when down-sampling by a factor of 2, 3, or 4. We concluded that our method is useful in diagnosing colon cancer using virtual colonoscopy.

On symmetrical three-dimensional datum conversion

A 3-D similarity transformation is frequently used to convert GPS-WGS84-based coordinates to those in a local datum using a set of control points with coordinate values in both systems. In this application, the Gauss-Markov (GM) model is often employed to represent the problem, and a least-squares approach is used to compute the parameters within the mathematical model. However, the Gauss–Markov model considers the source coordinates in the data matrix (A) as fixed or error-free; this is an imprecise assumption since these coordinates are also measured quantities and include random errors. The errors-in-variables (EIV) model assumes that all the variables in the mathematical model are contaminated by random errors. This model may be solved using the relatively new total least-squares (TLS) estimation technique, introduced in 1980 by Golub and Van Loan. In this paper, the similarity transformation problem is analyzed with respect to the EIV model, and a novel algorithm is described to obtain the transformation parameters. It is proved that even with the EIV model, a closed form Procrustes approach can be employed to obtain the rotation matrix and translation parameters. The transformation scale may be calculated by solving the proper quadratic equation. A numerical example and a practical case study are presented to test this new algorithm and compare the EIV and the GM models.

Inverse modeling of unsaturated flow parameters using dynamic geological structure conditioned by GPR tomography

A method is presented to estimate flow parameters and geological structure in the vadose zone by combining time‐lapse Ground Penetrating Radar (GPR) traveltime tomography and inverse flow modeling. The traveltime tomography is used to determine the spatial electromagnetic velocity distribution in the vadose zone. These time‐lapse velocity images are converted to time‐lapse volumetric soil water content images using petrophysical relationships. Subsequently, the water content images are used as constraints in the flow inversion. The influence of the tomographic artifacts on the flow inversion is minimized by assigning weights that are proportional to the ray coverage. Our flow inversion algorithm estimates the flow parameters and calibrates the geological structure. The geological structure is defined using a set of control points, the positions of which can be modified during the inversion. After the inversion, the final geological and flow model are used to compute GPR traveltimes to check the consistency between these computed traveltimes and the observed traveltimes.The method is first tested on two synthetic models (a steady state and a transient flow models). Subsequently, the method is applied to characterize a real vadose zone at Oslo Airport Gardermoen, Norway, during the snowmelt in 2005. The flow inversion method is applied to locate and quantify the main geological layers at the site. In particular the inversion method identifies and estimates the location and properties of thin dipping layers with relatively low‐permeability. The flow model is cross validated using an independent infiltration event.

The choice of the spherical radial basis functions in local gravity field modeling

The choice of the optimal spherical radial basis function (SRBF) in local gravity field modelling from terrestrial gravity data is investigated. Various types of SRBFs are considered: the point-mass kernel, radial multipoles, Poisson wavelets, and the Poisson kernel. The analytical expressions for the Poisson kernel, the point-mass kernel and the radial multipoles are well known, while for the Poisson wavelet new closed analytical expressions are derived for arbitrary orders using recursions. The performance of each SRBF in local gravity field modelling is analyzed using real data. A penalized least-squares technique is applied to estimate the gravity field parameters. As follows from the analysis, almost the same accuracy of gravity field modelling can be achieved for different types of the SRBFs, provided that the depth of the SRBFs is chosen properly. Generalized cross validation is shown to be a suitable technique for the choice of the depth. As a good alternative to generalized cross validation, we propose the minimization of the RMS differences between predicted and observed values at a set of control points. The optimal regularization parameter is determined using variance component estimation techniques. The relation between the depth and the correlation length of the SRBFs is established. It is shown that the optimal depth depends on the type of the SRBF. However, the gravity field solution does not change significantly if the depth is changed by several km. The size of the data area (which is always larger than the target area) depends on the type of the SRBF. The point-mass kernel requires the largest data area.

SU-GG-T-13: Fast Seed Localization On MR Images For Post-Prostate Implant Dosimetry

Purpose: Accurate and reliable post-prostate implant dosimetric analysis requires optimal identification of the seeds on CT and optimal description of soft tissues on MRI. We present a fast seed localization technique for MRI that is also robust from motion and other artifacts. The robustness of this technique was further investigated with clinical cases. Method and Materials: CT and 1.5T MR axial images of 4 patients were acquired four weeks post-implant were studied. Seed localization was first performed on CT images using either automatic seed detection or manual identification process. Several seeds in CT and seed voids in MR as well as anatomical landmarks were selected as control points. A thin-plate-spline deformable model was then constructed to map all the seeds from the CT to the MR. The robustness of this technique was further investigated by simulating various control point sets. The test started with the entire identifiable seed collections on both CT and MR images. The seeds forming the convex hull and 2 anatomical landmarks were then used as the control point set for TPS modeling. All seed positions were mapped from CT to MR following the TPS model. Seed position accuracy was examined. The process is repeated by continuously eliminating the control points to the last 3. Results and Discussion: The seeds localized on CT images were successfully mapped to the MRI images with only about 8 control points. The mapping can be accomplished in less than 5 minutes. Most of the mis-alignments were with peripheral seed positions. The slice thickness also contributed to the inaccuracy in SI direction as some of the seed positions were rounded to the closest slice. Increase the number of anatomical landmarks may further improve the accuracy. Conclusion: The fast mapping of seed locations from CT to MR facilitates a reliable post-implant dosimetric analysis.

Analytical solutions for 2D topography-driven flow in stratified and syncline aquifers

Two analytical solution methods are presented for regional steady-state groundwater flow in a two-dimensional stratified aquifer cross section where the water table is approximated by the topographic surface. For the first solution, the surficial aquifer is represented as a set of dipping parallel layers with different, but piecewise constant, anisotropic hydraulic conductivities, where the anisotropy is aligned with the dip of the layered formation. The model may be viewed as a generalization of the solutions developed by [Tóth JA. A theoretical analysis of groundwater flows in small drainage basins. J Geophys Res 1963;68(16):4795–812; Freeze R, Witherspoon P. Theoretical analysis of regional groundwater flow 1) analytical and numerical solution to the mathematical model, water resources research. Water Resour Res 1966;2(4):641–56; Selim HM. Water flow through multilayered stratified hillside. Water Resour Res 1975;11:949–57] to an multi-layer aquifer with general anisotropy, layer orientation, and a topographic surface that may intersect multiple layers. The second solution presumes curved (syncline) layer stratification with layer-dependent anisotropy aligned with the polar coordinate system. Both solutions are exact everywhere in the domain except at the topographic surface, where a Dirichlet condition is met in a least-squared sense at a set of control points; the governing equation and no-flow/continuity conditions are met exactly. The solutions are derived and demonstrated on multiple test cases. The error incurred at the location where the layer boundaries intersect the surface is assessed.

Automatic and Accurate Extraction of Road Intersections from Raster Maps

Since maps are widely available for many areas around the globe, they provide a valuable resource to help understand other geospatial sources such as to identify roads or to annotate buildings in imagery. To utilize the maps for understanding other geospatial sources, one of the most valuable types of information we need from the map is the road network, because the roads are common features used across different geospatial data sets. Specifically, the set of road intersections of the map provides key information about the road network, which includes the location of the road junctions, the number of roads that meet at the intersections (i.e., connectivity), and the orientations of these roads. The set of road intersections helps to identify roads on imagery by serving as initial seed templates to locate road pixels. Moreover, a conflation system can use the road intersections as reference features (i.e., control point set) to align the map with other geospatial sources, such as aerial imagery or vector data. In this paper, we present a framework for automatically and accurately extracting road intersections from raster maps. Identifying the road intersections is difficult because raster maps typically contain much information such as roads, symbols, characters, or even contour lines. We combine a variety of image processing and graphics recognition methods to automatically separate roads from the raster map and then extract the road intersections. The extracted information includes a set of road intersection positions, the road connectivity, and road orientations. For the problem of road intersection extraction, our approach achieves over 95% precision (correctness) with over 75% recall (completeness) on average on a set of 70 raster maps from a variety of sources.

Removal of digitization errors in fingerprint ridgelines using B-splines

Most of the contemporary automatic fingerprint identification systems (AFIS) are based on a dual strategy of combining the minutiae information with the ridge topography in order to improve the overall matching performance. To ensure the efficiency and robustness of such an AFIS, it is necessary, therefore, to rectify the abnormalities or aberrations of the underlying ridge topography, in general, and to smoothen the uneven/noisy ridgelines, in particular. The proposed work deals with one such problem besetting fingerprint analysis—the problem of eliminating digitization errors that usually creep in during fingerprint acquisition or during preprocessing. The method mainly involves fitting of B-splines for a set of control points chosen appropriately for each ridgeline in a fingerprint image. These fitted splines, in turn, can be used to reconstruct the concerned fingerprint, which, after the rectification procedure, becomes almost devoid of such digitization error. With a proper “smoothness parameter” that determines the extent to which a ridgeline is smoothed, the structural information of the corrected ridgelines produces improved results on fingerprint matching. Experimental results on several databases have been reported, which clearly demonstrate the strength and elegance of the proposed algorithm.

Estimation of time-varying pollutant emission rates in a ventilated enclosure: inversion of a reduced model obtained by experimental application of the modal identification method

A method is proposed for the estimation of time-varying emission rates of pollutant sources in a ventilated enclosure, through the resolution of an inverse forced convection problem. Unsteady transport–diffusion of the pollutant is considered, with the assumption of a stationary velocity field remaining unchanged during emission (passive contaminant). The pollutant transport equation is therefore linear with respect to concentration. The source's location is also supposed to be known. As the first step, a reduced model (RM) linking concentrations at a set of control points to emission rates of sources is identified from experimental data by using the modal identification method (MIM). This parameter estimation problem uses transient contaminant concentration measurements made at control points inside the ventilated enclosure, corresponding to increasing and decreasing steps of emission rates. Such experimental modelling allows us to avoid dealing with a CFD code involving turbulence modelling and to get rid of uncertainties about sensors position. In a second step, the identified RM is used to solve an inverse forced convection problem: from contaminant concentration measured at the same control points, rates of sources emitting simultaneously are estimated with a sequential in time algorithm using future time steps.

박판성형을 위한 신속한 금형곡면의 수정

In this paper, a novel approach which enables rapid die surface modification for sheet metal forming process is proposed. In this method an implicit surface which interpolates a given set of control points and displacement constraints is generated to compute the displacements at arbitrary points located on die surface. The proposed method does not depend on the underlying surface representation type and is affected neither by its complexity nor by its quality. In addition, the domain decomposition method is introduced in order to treat large surface model. The global domain of interest is divided into smaller domains where the problem can be solved locally. And then the local solutions are combined together to obtain a global solution. In order to verify the validity and effectiveness of the proposed method, various surface modifications are carried out fur three kinds of die surface model including polygonal surface composed of triangular and rectangular meshes, polynomial surface and NURBS surface.

Abstract 1870: A Novel Method of Spatially-Dense 3D Speckle Tracking on 4D Echocardiography for Strain Analysis: with Validation by Sonomicrometry

Background: We have developed a method for spatially-dense 3D speckle tracking that tracks speckle features in myocardium to allow calculation of full 3D displacement and strain from 4D full-volume echo images and have tested its accuracy compared to sonomicrometry in open-chest pigs. Methods: The 4D images were acquired using a Philips iE33 on 6 open-chest piglets. An array of 6 sonomicrometers (sono crystals) was implanted as 2 triangular sets at apex and mid-levels in the LV myocardium. The pair-wise crystal distances were computed offline using Sonometrics® software to yield 3D displacements. For 4D computation of speckle based mechanics, Cartesian coordinate images were entered into an envelope detection program, then a volume-based non-rigid registration was used to obtain optimal displacement between end diastolic (ED) and end systolic (ES) volumes. The displacement field was modeled using B-splines, parameterized by the location of a set of control points. Optimal locations of the control points were obtained by minimizing the sum of squared intensity differences between the ED and ES volumes. Sono crystals were located based on anatomic markers in the ED volume before the adjacent speckle patches were tracked, to ensure that image-derived strains were computed for segments matching the distances between sono crystal pairs. The method was implemented in MATLAB. Results: The comparison of the systolic strains from dense 4D speckle tracking showed a strong correlation (r 2 = 0.82) with sonomicrometry for 44 segmental strains. Conclusions: These studies show that the method we have developed can accurately compute 3D displacement and segmented LV strain from 4D data.

A hybrid immersed boundary and material point method for simulating 3D fluid–structure interaction problems

AbstractA numerical method is developed for solving the 3D, unsteady, incompressible Navier–Stokes equations in curvilinear coordinates containing immersed boundaries (IBs) of arbitrary geometrical complexity moving and deforming under forces acting on the body. Since simulations of flow in complex geometries with deformable surfaces require special treatment, the present approach combines a hybrid immersed boundary method (HIBM) for handling complex moving boundaries and a material point method (MPM) for resolving structural stresses and movement. This combined HIBM &amp; MPM approach is presented as an effective approach for solving fluid–structure interaction (FSI) problems. In the HIBM, a curvilinear grid is defined and the variable values at grid points adjacent to a boundary are forced or interpolated to satisfy the boundary conditions. The MPM is used for solving the equations of solid structure and communicates with the fluid through appropriate interface‐boundary conditions.The governing flow equations are discretized on a non‐staggered grid layout using second‐order accurate finite‐difference formulas. The discrete equations are integrated in time via a second‐order accurate dual time stepping, artificial compressibility scheme. Unstructured, triangular meshes are employed to discretize the complex surface of the IBs. The nodes of the surface mesh constitute a set of Lagrangian control points used for tracking the motion of the flexible body. The equations of the solid body are integrated in time via the MPM. At every instant in time, the influence of the body on the flow is accounted for by applying boundary conditions at stationary curvilinear grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface. The influence of the fluid on the body is defined through pressure and shear stresses acting on the surface of the body.The HIBM &amp; MPM approach is validated for FSI problems by solving for a falling rigid and flexible sphere in a fluid‐filled channel. The behavior of a capsule in a shear flow was also examined. Agreement with the published results is excellent. Copyright © 2007 John Wiley &amp; Sons, Ltd.

A novel generalization of Bézier curve and surface

A new formulation for the representation and designing of curves and surfaces is presented. It is a novel generalization of Bézier curves and surfaces. Firstly, a class of polynomial basis functions with n adjustable shape parameters is present. It is a natural extension to classical Bernstein basis functions. The corresponding Bézier curves and surfaces, the so-called Quasi-Bézier (i.e., Q-Bézier, for short) curves and surfaces, are also constructed and their properties studied. It has been shown that the main advantage compared to the ordinary Bézier curves and surfaces is that after inputting a set of control points and values of newly introduced n shape parameters, the desired curve or surface can be flexibly chosen from a set of curves or surfaces which differ either locally or globally by suitably modifying the values of the shape parameters, when the control polygon is maintained. The Q-Bézier curve and surface inherit the most properties of Bézier curve and surface and can be more approximated to the control polygon. It is visible that the properties of end-points on Q-Bézier curve and surface can be locally controlled by these shape parameters. Some examples are given by figures.

Mesh deformation using radial basis functions for gradient-based aerodynamic shape optimization

Gradient-based aerodynamic shape optimization using computational fluid dynamics (CFD), and time dependent problems in aeroelasticity, that is, coupled calculations between computational structural mechanics (CSM) and CFD, require repeated deformations of the CFD mesh. An interpolation scheme, based on radial basis functions (RBF), is devised in order to propagate the deformations from the boundaries to the interior of the CFD mesh. This method can lower the computational costs due to the deformation of the mesh, in comparison with the usual Laplace smoothing. Moreover, the algorithm is independent of the mesh connectivities. Therefore, structured and unstructured meshes are equally treated as well as hybrid meshes. The application of this interpolation scheme in problems of aerodynamic shape optimization is also carefully investigated. When the optimization is executed by a gradient-based algorithm the cost function is differentiated with respect to the design parameters in order to obtain the gradient. The gradient is most efficiently and accurately calculated by solving a certain adjoint equation derived from the discretized flow equations. The calculation of the gradient, which is detailed in this presentation, involves the Jacobian matrix of the mesh deformation. Finally, we present the results of an optimization of the ONERA M6 wing at transonic speed using the interpolation algorithm. The results are used for comparison with another technique of mesh deformation. The quality of the mesh obtained by the new algorithm, and the interpolation error, are analyzed with respect to the parameters of the interpolation scheme: the type of RBF, the RBF’s shape parameter, and the sets of control points.