Geometric Centroid Research Articles

Characterization of Respiration-Induced Motion in Prone Versus Supine Patient Positioning for Thoracic Radiation Therapy

PurposeVariations in the breathing characteristics, both on short term (intrafraction) and long term (interfraction) time scales, may adversely affect the radiation therapy process at all stages when treating lung tumors. Prone position has been shown to improve consistency (ie, reduced intrafraction variability) and reproducibility (ie, reduced interfraction variability) of the respiratory pattern with respect to breathing amplitude and period as a result of natural abdominal compression, with no active involvement required from the patient. The next natural step in investigating breathing-induced changes is to evaluate motion amplitude changes between prone and supine targets or organs at risk, which is the purpose of the present study. Methods and MaterialsPatients with lung cancer received repeat helical 4-dimensional computed tomography scans, one prone and one supine, during the same radiation therapy simulation session. In the maximum-inhale and maximum-exhale phases, all thoracic structures were delineated by an expert radiation oncologist. Geometric centroid trajectories of delineated structures were compared between patient orientations. Motion amplitude was measured as the magnitude of difference in structure centroid position between inhale and exhale. ResultsAmplitude of organ motion was larger when the patient was in the prone position compared with supine for all structures except the lower left lobe and left lung as a whole. Across all 12 patients, significant differences in mean motion amplitude between orientations were identified for the right lung (3.0 mm, P = .01), T2 (0.5 mm, P = .01) and T12 (2.1 mm, P < .001) vertebrae, the middle third of the esophagus (4.0 mm, P = .03), and the lung tumor (1.7 mm, P = .02). ConclusionsRespiration-induced thoracic organ motion was quantified in the prone position and compared with that of the supine position for 12 patients with thoracic lesions. The prone position induced larger organ motion compared with supine, particularly for the lung tumor, likely requiring increases in planning margins compared with supine.

Design of a fast-stop centroid finder for Monolithic Active Pixel Sensor

The heavy-ion experiments at the Heavy Ion Research Facility in Lanzhou (HIRFL) and the future High-Intensity Heavy-Ion Accelerator Facility (HIAF) in China drives the development of Monolithic Active Pixel Sensor (MAPS) for particle tracking detectors. To reduce the data volume from the MAPS based detectors, a centroid finder that can calculate the geometric centroid of the region of the energy deposition quickly has been designed. The centroid calculation is realized by distance screening among the coordinates of the pixels in the fired region. Performance study with the data from heavy-ion experiments in HIRFL proves that the centroid finder can accurately find the centroids and reduce the data volume from the MAPS by approximately one order of magnitude.

A face-area-weighted ‘centroid’ formula for finite-volume method that improves skewness and convergence on triangular grids

This paper proposes a face-area-weighted ‘centroid’ as a superior alternative to the geometric centroid for defining a local origin in a cell-centered finite-volume method on triangular grids. It is demonstrated theoretically and numerically that the face-area-weighted ‘centroid’ can reduce grid skewness and improve iterative convergence for triangular grids. It is also shown that source terms do not have to be integrated over a cell and can be evaluated simply at the local origin without losing the design order of accuracy. Numerical results demonstrate that the face-area-weighted ‘centroid’ improves iterative convergence of an implicit defect-correction second-order finite-volume solver for inviscid and viscous flow problems on regular and irregular triangular grids.

Surface wave attenuation by vegetation with the stem, root and canopy

To experimentally study the performance of the stem, root and canopy on wave attenuation by vegetation, a total of 112 laboratory experiments were conducted with seven vegetation models, four vegetation densities, five wave heights and four water depths. Wave period was assumed constant, limiting the understanding of wave attenuation phenomena by vegetation. Frictional energy losses from sidewall and bottom were measured and removed by comparing with non-vegetated tests. Experimental results show that wave attenuation by vegetation with stems, roots and canopies varied with wave conditions due to vertically non-uniform physical vegetation properties. The root significantly impacted wave dissipation when the relative root height was greater than 0.167. Higher wave attenuation occurred when the still water level was located at the canopy geometrical centroid. The transmission coefficients of vegetation of the stem, root and canopy ranged from 0.21 to 0.83. An empirical formula for predicting transmission coefficients of vegetation with stems, roots and canopies was obtained based on experimental data. The wave energy dissipated by vegetation was estimated in terms of drag coefficients calculated by analytical models of Dalrymple et al. (1984) and Kobayashi et al. (1993). A semi-empirical analytical equation was proposed on the basis of experimental data for predicting wave attenuation by vegetation of the stem, root and canopy.

Estimating fetal dose from tube current-modulated (TCM) and fixed tube current (FTC) abdominal/pelvis CT examinations.

The purpose of this work was to estimate scanner-independent CTDIvol -to-fetal-dose coefficients for tube current-modulated (TCM) and fixed tube current (FTC) computed tomography (CT) examinations of pregnant patients of various gestational ages undergoing abdominal/pelvic CT examinations. For 24 pregnant patients of gestational age from <5 to 36weeks who underwent clinically indicated CT examinations, voxelized models of maternal and fetal (or embryo) anatomy were created from abdominal/pelvic image data. Absolute fetal dose (Dfetus ) was estimated using Monte Carlo (MC) simulations of helical scans covering the abdomen and pelvis for TCM and FTC scans. Estimated TCM schemes were generated for each patient model using a validated method that accounts for patient attenuation and scanner output limits for one scanner model and were incorporated into MC simulations. FTC scans were also simulated for each patient model with multidetector row CT scanners from four manufacturers. Normalized fetal dose estimates, nDfetus , was obtained by dividing Dfetus from the MC simulations by CTDIvol . Patient size was described using water equivalent diameter (Dw ) measured at the three-dimensional geometric centroid of the fetus. Fetal depth (DEf ) was measured from the anterior skin surface to the anterior part of the fetus. nDfetus and Dw were correlated using an exponential model to develop equations for fetal dose conversion coefficients for TCM and FTC abdominal/pelvic CT examinations. Additionally, bivariate linear regression was performed to analyze the correlation of nDfetus with Dw and fetal depth (DEf ). For one scanner model, nDfetus from TCM was compared to FTC and the size-specific dose estimate (SSDE) conversion coefficients (f-factors) from American Association of Physicists in Medicine (AAPM) Report 204. nDfetus from FTC simulations was averaged across all scanners for each patient . was then compared with SSDE f-factors and correlated with Dw using an exponential model and with Dw and DEf using a bivariate linear model. For TCM, the coefficient of determination (R2 ) of nDfetus and Dw was observed to be 0.73 using an exponential model. Using the bivariate linear model with Dw and DEf , an R2 of 0.78 was observed. For the TCM technology modeled, TCM yielded nDfetus values that were on average 6% and 17% higher relative to FTC and SSDE f-factors, respectively. For FTC, the R2 of with respect to Dw was observed to be 0.64 using an exponential model. Using the bivariate linear model, an R2 of 0.75 was observed for with respect to Dw and DEf . A mean difference of 0.4% was observed between and SSDE f-factors. Good correlations were observed for nDfetus from TCM and FTC scans using either an exponential model with Dw or a bivariate linear model with both Dw and DEf . These results indicate that fetal dose from abdomen/pelvis CT examinations of pregnant patients of various gestational ages may be reasonably estimated with models that include (a) scanner-reported CTDIvol and (b) Dw as a patient size metric, in addition to (c) DEf if available. These results also suggest that SSDE f-factors may provide a reasonable (within ±25%) estimate of nDfetus for TCM and FTC abdomen/pelvis CT exams.

Search of an ideal location of isocenter in intensity-modulated radiotherapy treatment plans: A dosimetrical approach.

The aim of this study is to identify an ideal location of isocenter in intensity-modulated radiotherapy (IMRT) treatment plans. A total of 28 clinical target volumes and 4 English capital letters (C, L, T, and H) target volumes were considered in this study. Two IMRT treatment plans were generated for each target volume in the ECLIPSETM treatment planning system (TPS), first one with isocenter automatically placed (ISOAUTO) by TPS and the second one with geometric center-based isocenter (ISOGEOM). The geometric center of a cuboid volume, which was formed encompassing around the target volume in sagittal, transverse, and frontal planes, is considered as the geometric center of the target volume as well as the isocenter (ISOGEOM) of the IMRT plans. While performing the IMRT treatment plans using the beam angle optimization and dose volume optimization, the normal tissue objectives and target volume objectives were kept similar in both the plans. The dosimetrical parameters between the two groups of plans were compared. The distance between ISOGEOM and ISOAUTO ranged from 0.16 cm to 3.04 cm with a mean and median of 0.85 cm and 0.69 cm, respectively. The ISOGEOM-based IMRT plans exhibited statistically significant advantages in total monitor units reduction (100% of cases, P ≤ 0.001), total number of field reduction (66% of cases, P ≤ 0.001), and reduction of patient mean dose (69% of cases, P ≤ 0.001) over ISOAUTO-based IMRT plans. The conformity index, homogeneity index and target mean dose were comparable between both group of plans. Significant dosimetrical advantages may be observed, when the geometric centroid of target volume is considered as isocenter of IMRT treatment plan.

The lateral collateral ligament complex of the elbow: quantitative anatomic analysis of the lateral ulnar collateral, radial collateral, and annular ligaments

Injury to the lateral ulnar collateral ligament (LUCL) complex of the elbow often results in posterolateral rotatory instability. Although surgical reconstruction of the LUCL is often required, gaps in our understanding of the LUCL complex remain. The purpose of this study was to provide a robust and accurate characterization of the lateral elbow ligamentous complex. The LUCLs, radial collateral ligaments, and annular ligaments in 10 cadaveric elbows were 3-dimensionally digitized and reconstructed using computed tomography. Surface areas, origin and insertion footprint areas, distances between perceived footprint centers and geometric footprint centroids, distances to key landmarks, and ligament isometry were measured. The mean surface area of the LUCL was 229.3 mm2. The mean origin and insertion footprint areas were 26.0 mm2 and 22.9 mm2, respectively. The mean distance between the apparent centers and the geometric centroids of the footprints was 1 mm. The center of the LUCL origin was 10.7 mm distal to the lateral epicondyle and 8.2 mm from the capitellar articular margin. The center of the LUCL insertion was 3.3 mm distal to the apex of the supinator crest. The LUCL showed anisometric properties as elbow flexion increased (P < .001). The LUCL origin center was 10.7 mm from the lateral epicondyle, whereas the insertion center was 3.3 mm from the apex of the supinator crest. The visually estimated footprint centers were generally within 1 mm of the geometric centroid. These geometries and distances to key landmarks will be informative for surgeons seeking to perform anatomic ligament reconstruction procedures.

Multiple Hidden Markov Model Post Processed with Support Vector Machine to Recognize English Handwritten Numerals

This paper presents rotation and size invariant English numerals recognition system with, competitive recognition rate. The novelty of this paper is the introduction of two unique methods of feature extraction namely Pixel Moment of Inertia (PMI) and Delta Distance Coding (DDC). The proposed Multiple Hidden Markov Model (MHMM) is a two tier model to neutralize the effect of two very frequent writing styles of numerals ‘4’ and ‘7’ on their recognition rates. The novelty of PMI is that it finds moment of all the pixels of a specified zone about the central pixel and not about geometrical centroid of image area. In this paper, PMI has been observed to have an upper hand over centroidal MI. DDC is a new technique of curvature coding, based on distance from a reference level and is similar to the logic behind Delta modulation scheme in Digital Communications. Thus, the current paper correlates two digital domains namely, Digital Image Processing and Digital Communications. Support Vector Machine differentiates two close output classes obtained from classification with MHMM. The overall recognition accuracy rate of 99.17% has been achieved based on MNIST database.

Adaptive biased random-key genetic algorithm with local search for the capacitated centered clustering problem

Abstract This paper proposes an adaptive Biased Random-key Genetic Algorithm (A-BRKGA), a new method with on-line parameter control for combinatorial optimization problems. A-BRKGA has only one problem-dependent component, the decoder and all other parts can be reused. To control diversification and intensification, a novel adaptive strategy for parameter tuning is introduced. This strategy is based on deterministic rules and self-adaptive schemes. For exploitation of specific regions of the solution space we propose a local search in promising communities. The proposed method is evaluated on the Capacitated Centered Clustering Problem (CCCP), which is an NP-hard problem where a set of n points, each having a given demand, is partitioned into m clusters each with a given capacity. The objective is to minimize the sum of the Euclidean distances between the points and their geometric cluster centroids. Computational results show that the A-BRKGA with local search is competitive with other methods of literature.

Multi-view object-based classification of wetland land covers using unmanned aircraft system images

Traditionally, the multiple images collected by cameras mounted on Unmanned Aircraft Systems (UAS) are mosaicked into a single orthophoto on which Object-Based Image Analysis (OBIA) is conducted. This approach does not take advantage of the Multi-View (MV) information of the individual images. In this study, we introduce a new OBIA approach utilizing multi-view information of original UAS images and compare its performance with that of traditional OBIA, which uses only the orthophoto (Ortho-OBIA). The proposed approach, called multi-view object-based image analysis (MV-OBIA), classifies multi-view object instances on UAS images corresponding to each orthophoto object and utilizes a voting procedure to assign a final label to the orthophoto object. The proposed MV-OBIA is also compared with the classification approaches based on Bidirectional Reflectance Distribution Function (BRDF) simulation. Finally, to reduce the computational burden of multi-view object-based data generation for MV-OBIA and make the proposed approach more operational in practice, this study proposes two window-based implementations of MV-OBIA that utilize a window positioned at the geometric centroid of the object instance, instead of the object instance itself, to extract features. The first window-based MV-OBIA adopts a fixed window size (denoted as FWMV-OBIA), while the second window-based MV-OBIA uses an adaptive window size (denoted as AWMV-OBIA). Our results show that the MV-OBIA substantially improves the overall accuracy compared with Ortho-OBIA, regardless of the features used for classification and types of wetland land covers in our study site. Furthermore, the MV-OBIA also demonstrates a much higher efficiency in utilizing the multi-view information for classification based on its considerably higher overall accuracy compared with BRDF-based methods. Lastly, FWMV-OBIA and AWMV-OBIA both show potential in generating an equal if not higher overall accuracy compared with MV-OBIA at substantially reduced computational costs.

Organ doses in pediatric patients undergoing cardiac-centered fluoroscopically guided interventions: Comparison of three methods for computational phantom alignment.

To assess various computational phantom alignment techniques within Monte Carlo radiation transport models of pediatric fluoroscopically guided cardiac interventional studies. Logfiles, including all procedure radiation and machine data, were extracted from a Toshiba infinix-I unit in the University of Florida Pediatric Catheterization Laboratory for a cohort of 10 patients. Two different alignment methods were then tested against a ground truth standard based upon identification of a unique anatomic reference point within images co-registered to specific irradiation events within each procedure. The first alignment method required measurement of the distance from the edge of the exam table to the top of the patient's head (table alignment method). The second alignment method fixed the anatomic reference point to be the geometric center of the heart muscle, as all 10 studies were cardiac in nature. Monte Carlo radiation transport simulations were performed for each patient and intervention using morphometry-matched hybrid computational phantoms for the reference and two tested alignment methods. For each combination, absorbed doses were computed for 28 organs and root mean square organ doses were assessed and compared across the alignment methods. The percent error in root mean square organ dose ranged from -57% to +41% for the table alignment method, and from -27% to +22% for the heart geometric centroid alignment method. Absorbed doses to specific organs, such as the heart and lungs, demonstrated higher accuracy in the heart geometric centroid alignment method, with average percent errors of 10% and 1.4%, respectively, compared to average percent errors of -32% and 24%, respectively, using the table alignment method. Of the two phantom alignment methods investigated in this study, the use of an anatomical reference point - in this case the geometric centroid of the heart - provided a reliable method for radiation transport simulations of organ dose in pediatric interventional cardiac studies. This alignment method provides the added benefit of requiring no physician input, making retrospective calculations possible. Moving forward, additional anatomical reference methods can be tested to assess the reliability of anatomical reference points beyond cardiac centered procedures.

A Source Coding Perspective on Node Deployment in Two-Tier Networks

Multi-tier networks have many applications in different fields. We define a novel two-tier quantizer that can be applied to different node deployment problems including the energy conservation in two-tier wireless sensor networks consisting of $N$ access points (APs) and $M$ fusion centers (FCs). We aim at finding an optimal deployment of APs and FCs to minimize the average weighted total, or Lagrangian, of sensor and AP powers. For one FC, $M=1$ , we show that the optimal deployment of APs is simply a linear transformation of the optimal $N$ -level quantizer for density $f$ , and the sole FC should be located at the geometric centroid of the sensing field. We also provide the exact expression of the AP-Sensor power function and prove its convexity. For more than one FC, $M>1$ , we provide a necessary condition for the optimal deployment. Furthermore, to numerically optimize the AP and FC deployment, we propose three Lloyd-like algorithms and analyze their convergence. Simulation results show that our algorithms outperform the existing algorithms.

Lateral-torsional buckling behavior of hot-rolled steel beams with flange upstands

The lateral-torsional buckling behavior of hot-rolled steel beams has been studied extensively. Much of the research carried out has been limited to doubly symmetric beams and a few other common geometries. The study of monosymmetric and non-symmetric geometries has not been as extensive. This paper presents a study of the lateral-torsional buckling behavior of monosymmetric beams having the monosymmetry introduced by flange end upstands. The study is carried out using finite element modelling. The behavior is investigated for various spans and with various heights of upstands. It is observed that the upstands increase the critical buckling moment of the section but that this increase diminishes with increase in upstand height. It is further observed that this unique behavior could be influenced by a movement in the relative position of the shear center to the geometric centroid as the flange upstands are adjusted. In addition there exists for these geometries unique points where the monosymmetric sections have properties typically associated with doubly symmetric sections. It is shown that the relative position of the shear center and centroid have some influence on the strength gain pattern observed.

Quantitative Anatomic Analysis of the Medial Ulnar Collateral Ligament Complex of the Elbow.

Background:A more detailed assessment of the anatomy of the entire medial ulnar collateral ligament complex (MUCLC) is desired as the rate of medial elbow reconstruction surgery continues to rise.Purpose:To quantify the anatomy of the MUCLC, including the anterior bundle (AB), posterior bundle (PB), and transverse ligament (TL).Study Design:Descriptive laboratory study.Methods:Ten unpaired, fresh-frozen cadaveric elbows underwent 3-dimensional (3D) digitization and computed tomography with 3D reconstruction. Ligament footprint areas and geometries, distances to key bony landmarks, and isometry were determined. A surgeon digitized the visual center of each footprint, and this location was compared with the geometric centroid calculated from the outline of the digitized footprint.Results:The mean surface area of the AB was 324.2 mm2, with an origin footprint of 32.3 mm2 and an elongated insertional footprint of 187.6 mm2 (length, 29.7 mm). The mean area of the PB was 116.6 mm2 (origin, 25.9 mm2; insertion, 15.8 mm2), and the mean surface area of the TL was 134.5 mm2 (origin, 21.2 mm2; insertion, 16.7 mm2). The geometric centroids of all footprints could be predicted within 0.8 to 1.3 mm, with the exception of the AB insertion centroid, which was 7.6 mm distal to the perceived center at the apex of the sublime tubercle. While the PB remained relatively isometric from 0° to 90° of flexion (P = .606), the AB lengthened by 2.2 mm (P < .001).Conclusion:Contrary to several historical reports, the insertional footprint of the AB was larger, elongated, and tapered. The TL demonstrated a previously unrecognized expansive soft tissue insertion directly onto the AB, and additional analysis of the biomechanical contribution of this structure is needed.Clinical Relevance:These findings may serve as a foundation for future study of the MUCLC and help refine current surgical reconstruction techniques.

Optimization of the energy consumption of a CNC machine cutting tool with hard-to-formalize restrictions

The energy consumption of a CNC machine cutting tool is largely determined by the tool’s path and depends on the length of idle and working motions, as well as on the number of insertion points. To reduce the consumption level, it is usually necessary to minimize all these parameters. However, the resulting paths are not always technologically acceptable, which can lead to defective products and damage the equipment. This article considers the automatic formation of a technologically acceptable path with the minimal energy consumption. The path formation is divided into the selection of the part-cutting procedure and the selection of the tool-insertion (entry and exit) points. The cutting procedure is selected according to the rules of detecting pockets of material formed by profiles of parts by using geometric centroids and convex cutting profile shells. The insertion points are selected by one of several versions of an intervallic search algorithm and depending on the number of cut-out parts. Cutting restrictions are considered, and cases of pocket formation are described. The restrictions are represented by a list of rules that formalize controversial cutting situations. The optimization criterion is the minimum total cutting time. The technique of penalty functions has made it possible to reject pocket-forming solutions. The general chart and a case of using the algorithm are given and considered.

Vision‐Based Natural Frequency Identification Using Laser Speckle Imaging and Parallel Computing

AbstractThis study focuses on the identification of the natural frequencies of structures through the analysis of the speckle pattern that a laser creates and a camera records. The laser pointer spreads its light over a target area on the structure and creates the speckle pattern. The ambient vibrations affect the pattern and a camera records the changes. The stream of images is fed into a graphics processing unit (GPU). The developed parallel code includes different algorithms: the speckle contrast image (SCI), the speckle flow imaging (SFI), and an innovative application of k‐means clustering that uses the geometrical centroid of each cluster as virtual sensors. The tracking of the centroid in time domain through the images creates a vibration signal. The signals from different clusters are processed together to extract the natural frequencies of the structure. This study applies the proposed method to different sample structures both in laboratory and in the field to demonstrate how the obtained signals are reliable and easy to handle. The GPU technology enhances the performance of the entire method and allows the achievement of real‐time processing. All these features create an inexpensive, portable, and efficient tool to inspect any structure or its components.

Technical Note: Using k-means clustering to determine the number and position of isocenters in MLC-based multiple target intracranial radiosurgery.

PurposeTo present the k‐means clustering algorithm as a tool to address treatment planning considerations characteristic of stereotactic radiosurgery using a single isocenter for multiple targets.MethodsFor 30 patients treated with stereotactic radiosurgery for multiple brain metastases, the geometric centroids and radii of each met were determined from the treatment planning system. In‐house software used this as well as weighted and unweighted versions of the k‐means clustering algorithm to group the targets to be treated with a single isocenter, and to position each isocenter. The algorithm results were evaluated using within‐cluster sum of squares as well as a minimum target coverage metric that considered the effect of target size. Both versions of the algorithm were applied to an example patient to demonstrate the prospective determination of the appropriate number and location of isocenters.ResultsBoth weighted and unweighted versions of the k‐means algorithm were applied successfully to determine the number and position of isocenters. Comparing the two, both the within‐cluster sum of squares metric and the minimum target coverage metric resulting from the unweighted version were less than those from the weighted version. The average magnitudes of the differences were small (−0.2 cm2 and 0.1% for the within cluster sum of squares and minimum target coverage, respectively) but statistically significant (Wilcoxon signed‐rank test, P < 0.01).ConclusionsThe differences between the versions of the k‐means clustering algorithm represented an advantage of the unweighted version for the within‐cluster sum of squares metric, and an advantage of the weighted version for the minimum target coverage metric. While additional treatment planning considerations have a large influence on the final treatment plan quality, both versions of the k‐means algorithm provide automatic, consistent, quantitative, and objective solutions to the tasks associated with SRS treatment planning using a single isocenter for multiple targets.

Modified Centroid for Estimating Sand, Silt, and Clay from Soil Texture Class

Core Ideas Knowledge of texture class and clay enables continuous estimates of sand and silt. Rosetta under predicted water retention compared with measured values. Rosetta performance differed by soil texture class. Rosetta estimates were similar for modified centroid and measured particle size. Models that require inputs of soil texture are often limited by the availability of soil information. While texture class is easier to obtain than particle size, texture classes do not represent the continuum of soil size fractions. Soil texture class and clay percentage are collected as a standard practice for many land management agencies (e.g., NRCS, BLM, FAO) and clay content is frequently estimated with acceptable accuracy (±5%). When clay and texture class is known, sand and silt can be constrained to a narrow range that may differ from the geometric centroid of a given texture class (gcent). I tested the concept of a modified centroid approach (mcent) using 75,736 soil samples from the National Cooperative Soil Survey pedon database that also had measured hydraulic soil properties. Comparisons were made using the Rosetta pedotransfer function (PTF) to test modeled values from gcent, mcent, and measured data in comparison with measured values of water content at field capacity (θ330) and wilting point (θ15000). The mcent approach produced a continuous distribution of values for sand and silt whereas gcent produced a stair‐step pattern for each of the 12 texture classes. Rosetta underestimated water content. Error metrics were similar when all texture classes were combined, but differences between models emerged when individual texture classes were compared. Results support the practice of collecting field estimates of clay percentage along with texture class to expand the use of soil profile data for both spatial and non‐spatial modeling of soil processes that will advance our understanding of soil contributions to ecosystem function.

Conservative handling of arbitrary non-conformal interfaces using an efficient supermesh

This work presents a new and efficient strategy to handle non-conformal interfaces with the aim of assuring the conservation of fluxes in Finite Volume problems. A conservative interpolation is developed for general transport equations. Due to the arbitrary connectivity between the interfaces, the interpolations require flux-based weights defining a complex numerical stencil. In this context, a new method is proposed to simplify the coupling at the interface based on the construction of a simplified supermesh. Here, a supermesh is not completely defined, instead, the interface faces are logically duplicated (or multiplied) to generate a one-to-one connectivity between them. The simplified supermesh named pseudo-supermesh eliminates the interpolations and assures the conservation of fluxes based on the trivial connectivity. The area and the geometrical centroid of the new faces are redefined according to the overlapped sector of the original faces using the local supermeshing approach. Since the arbitrary polygons resulting from the face intersections are not generated and introduced into the mesh, computational cost and implementation efforts are saved. The proposed method is tested focusing on the conservation of fluxes and on the accuracy, showing conservation to machine precision and second order convergence as expected. In order to be able to solve large problems, the methodology is designed and implemented to be run in parallel architectures showing an excellent efficiency.

3D Object Recognition in Cluttered Scenes With Robust Shape Description and Correspondence Selection

Recognizing 3-D objects in cluttered scenes is a challenging task. Common approaches find potential feature correspondences between a scene and candidate models by matching sampled local shape descriptors and select a few correspondences with the highest descriptor similarity to identify models that appear in the scene. However, real scans contain various nuisances, such as noise, occlusion, and featureless object regions. This makes selected correspondences have a certain portion of false positives, requiring adopting the time-consuming model verification many times to ensure accurate recognition. This paper proposes a 3-D object recognition approach with three key components. First, we construct a Signature of Geometric Centroids descriptor that is descriptive and robust, and apply it to find high-quality potential feature correspondences. Second, we measure geometric compatibility between a pair of potential correspondences based on isometry and three angle-preserving components. Third, we perform effective correspondence selection by using both descriptor similarity and compatibility with an auxiliary set of “less” potential correspondences. Experiments on publicly available data sets demonstrate the robustness and/or efficiency of the descriptor, selection approach, and recognition framework. Comparisons with the state-of-the-arts validate the superiority of our recognition approach, especially under challenging scenarios.