Best-fit Plane Research Articles

Cardiovascular morphometry with high-resolution 3D magnetic resonance: First application to left ventricle diastolic dysfunction

In this study, an image-based morphometry toolset quantifying geometric descriptors of the left ventricle, aorta and their coupling is applied to investigate whether morphological information can differentiate between subjects affected by diastolic dysfunction (patient group) and their age-matched controls (control group). The ventriculo-aortic region of 20 total participants (10 per group) were segmented from high-resolution 3D magnetic resonance images, from the left ventricle to the descending aorta. Each geometry was divided into segments in correspondence of anatomical landmarks. The orientation of each segment was estimated by least-squares fitting of the respective centerline segment to a plane. Curvature and torsion of vessels’ centerlines were automatically extracted, and aortic arch was characterized in terms of height and width.Tilt angle between subsequent best-fit planes in the left ventricle and ascending aorta regions, curvature and cross-sectional area in the descending aorta resulted significantly different between patient and control groups (P-values< 0.05). Aortic volume (P = 0.04) and aortic arch width (P = 0.03) resulted significantly different between the two groups. The observed morphometric differences underlie differences in hemodynamics, by virtue of the influence of geometry on blood flow patterns.The present exploratory analysis does not determine if aortic geometric changes precede diastolic dysfunction, or vice versa. However, this study (1) underlines differences between healthy and diastolic dysfunction subjects, and (2) provides geometric parameters that might help to determine early aortic geometric alterations and potentially prevent evolution toward advanced diastolic dysfunction.

Why do aftershocks occur? Relationship between mainshock rupture and aftershock sequence based on highly resolved hypocenter and focal mechanism distributions

In order to clarify the origin of aftershocks, we precisely analyze the hypocenters and focal mechanisms of the aftershocks following the 2000 Western Tottori Earthquake, which occurred in the western part of Japan, using data from dense seismic observations. We investigate whether aftershocks occur on the mainshock fault plane on which coseismic slip occurred or they represent the rupture of fractures surrounding the mainshock fault plane. Based on the hypocenter distribution of the aftershocks, the subsurface fault structure of the mainshock is estimated using principal component analysis. As a result, we can obtain the detail fault structure composed of 8 best-fit planes. We demonstrate that the aftershocks around the mainshock fault are distributed within zones of 1.0–1.5 km in thicknesses, and their focal mechanisms are significantly diverse. This result suggests that most of the aftershocks represent the rupture of fractures surrounding the mainshock fault rather than the rerupture of the mainshock fault. The aftershocks have a much wider zone compared with the exhumed fault zone in field observations, suggesting that many aftershocks occur outside the fault damage zone. We find that most aftershocks except in and around the large-slip region are well explained by coseismic stress changes. These results suggest that the thickness of the aftershock distribution may be controlled by the stress changes caused by the heterogeneous slip distribution during the mainshock. The aftershock is also distributed within a much wider zone than the hypocenter distribution observed in swarm activity in the geothermal region, which is thought to be caused by the migration of hydrothermal fluid. This result implies a difference in generation processes: Stress changes due to the mainshock contribute primarily to the occurrence of aftershocks, whereas earthquake swarms in the geothermal region are caused by fluid migration within the localized zone. Graphical abstract.

Three-Dimensional Computed Tomography Analysis of the Posterior Tibial Slope in 100 Knees

BackgroundThe posterior tibial slope (PTS) is an important consideration in knee arthroplasty. However, there is still no consensus for the optimal slope. The objectives of this study were (1) to reliably determine the native PTS in this population using 3-dimensional computed tomography scans and (2) to determine the normal reference range for PTS in this population. MethodsOne hundred computed tomography scans of disease-free knees were analyzed. A 3-dimensional reconstructed image of the tibia was generated and aligned to its anatomic axis in the coronal and sagittal planes. The tibia was then rotationally aligned to the tibial plateau (tibial centroid axis) and PTS was measured from best-fit planes on the surface of the proximal tibia and individually for the medial and lateral plateaus. This was then repeated with the tibia rotationally aligned to the ankle (transmalleolar axis). ResultsWhen rotationally aligned to the tibial plateau, the mean PTS, medial PTS, and lateral PTS were 11.2° ± 3.0 (range, 4.7°-17.7°), 11.3° ± 3.2 (range, 2.7°-19.7°), and 10.9° ± 3.7 (range, 3.5°-19.4°), respectively. When rotationally aligned to the ankle, the mean PTS, medial PTS, and lateral PTS were 11.4° ± 3.0 (range, 5.3°-19.3°), 13.9° ± 3.7 (range, 3.1°-24.4°), and 9.7° ± 3.6 (range, 0.8°-17.7°), respectively. ConclusionThe PTS in the normal Asian knee is on average 11° (mean) with a reference range of 5°-17° (mean ± 2 standard deviation). This has implications to surgery and implant design.

{(3S,5R)-5-(2,4-Difluorophenyl)-5-[(1H-1,2,4-triazol-1-yl)methyl]tetrahydrofuran-3-yl}methyl 4-methylbenzenesulfonate

In the title compound, C21H21F2N3O4S, the tetrahydrofuran ring adopts an envelope conformation with the β-C atom positioned at the flap. The triazole, difluorophenyl and tolyl rings of the various substituents on the tetrahydrofuran ring are inclined at 77.88 (12), 83.81 (10) and 81.00 (10)°, respectively, to the best-fit mean plane through the five atoms of the tetrahydrofuran ring. In the crystal, weak C—H...O and C—H...F hydrogen bonds link the molecules into a three-dimensional structure, with molecules stacked along thea-axis direction.

Robust Estimation of Object Dimensions and External Defect Detection with a Low-Cost Sensor

The measurement of object dimensions as well as the detection and localization of external defects are of large importance for many sectors in industry including agriculture, transportation and production. In this paper we investigate the feasibility of using commercial depth-sensing devices, based on a time-of-flight technology, such as the Kinect v2 camera, for the measurement and inspection of cuboidal objects (boxes). This paper presents a simplified system using only one Kinect sensor. At the beginning, object dimensions are roughly estimated by discovering the best-fit planes for a cloud of point based on a modified version of RANSAC (RANdom Sample Consensus). The precise geometry and morphology of the objects are then achieved by a transformation from depth to RGB representation of the points estimated as belonging to the object. RGB representation is finally processed (using scanlines on the RGB plane perpendicular to the initial edge estimate) to approximate at best the contour of the bounding box. In addition to the above, the paper proposes a method to automatically highlight defects on the objects’ surfaces: this inspection task is performed through the analysis of both the 2D object contours and the histogram of the normalized depth values. The proposed methodology takes a few seconds to deliver the results for the monitored object and, it experienced encouraging results in terms of accuracy. Indeed, the system measured the dimensions of a set of cuboidal objects with an average error of 5 mm and it was able to identify and locate defects and holes on lateral and topmost surfaces. The experimental outcomes pointed out that the system could be effectively exploited within industrial inspection applications, even more so if the low cost of the system is taken under consideration.

4-(Benzo[d]thiazol-2-yl)-N,N-dimethylaniline

The whole molecule of the title compound, C15H14N2S, is approximately planar, with an r.m.s. deviation of 0.0382 Å from the best-fit mean plane through all 18 non-H atoms. In the crystal, dimers form through π–π stacking interactions between the benzene rings of adjacent benzothiazole ring systems, with a centroid–centroid separation of 3.6834 (16) Å.

On the origins of three-dimensionality in drug-like molecules.

Many medicinal chemistry-relevant structures and core scaffolds tend toward geometric planarity, which hampers the optimization of physicochemical properties desirable in drug-like molecules. As challenging drug target classes emerge, the exploitation of molecular three-dimensionality in lead optimization is becoming increasingly important. While recent interest has emphasized the importance of enhanced three-dimensionality in molecular fragment designs, the extent to which this is required in core scaffolds remains unclear. Three computational methods, Scaffold Tree deconstruction, Synthetic Disconnection Rules retrosynthetic deconstruction and virtual library enumeration, are applied, together with the descriptors plane of best fit and principal moments of inertia, to investigate the origins of three-dimensionality in drug-like molecules. This study informs on the stage at which molecular three-dimensionality should be considered in drug design.

Reference data sets for testing metrology software

Many fields of metrology rely on calculations that are implemented in software. When such software is used to provide a measurement result, which is required to be traceable, it is necessary to recognise explicitly the software and show it to be operating correctly. An approach to testing the performance of calculation software is based on using reference pairs each of which comprises reference input data applied as input to the software and corresponding reference output data against which the output data of the software is compared. However, to make the reference pair useful for verifying and validating calculation software, information is needed about the numerical accuracy of the reference pair, the numerical sensitivity of the reference output data to perturbations in the reference input data, and the measurement uncertainty associated with the reference output data arising from simulated measurement uncertainty associated with the reference input data. Such information is important as a means to express quantitatively the quality of the reference pair as a numerical artefact to test calculation software, and as a basis for performance metrics to express quantitatively the numerical performance of software. In this paper these additional components of a reference data set are described, and various approaches to calculating them are discussed. An example, concerned with the calculation of the Gaussian (least-squares) best-fit plane to measured data, which is typical of calculations undertaken in coordinate metrology, is used to illustrate the ideas presented.

The 3D inversion of airborne gamma-ray spectrometric data

We present a new method for the inversion of airborne gamma-ray spectrometric line data to a regular grid of radioelement concentration estimates on the ground. The method incorporates the height of the aircraft, the 3D terrain within the field of view of the spectrometer, the directional sensitivity of rectangular detectors, and a source model comprising vertical rectangular prisms with the same horizontal dimensions as the required grid cell size. The top of each prism is a plane surface derived from a best-fit plane to the digital elevation model of the earth’s surface within each grid cell area.The method is a significant improvement on current methods, and gives superior interpolation between flight lines. It also eliminates terrain effects that would normally remain in the data after the conventional processing of these data assuming a flat-earth model.

D-(−)-2-Azaniumyl-2-(4-hydroxyphenyl)acetate: an orthorhombic polymorph

The title compound, C8H9NO3, is the zwitterionic form of D-(−)-4-hydroxyphenylglycine. The plane of the hydroxybenzene ring is inclined at an angle of 88.89 (5)° to the best-fit plane through the five non-H atoms of the aminoacetate substituent. In the crystal, N—H...O and O—H...O hydrogen bonds link adjacent molecules, forming a three-dimensional network. Weak C—H...π interactions are also observed.

Robust best-fit planes from geospatial data

Total least squares regression is a reliable and efficient way to analyze the geometry of a best-fit plane through georeferenced data points. The suitability of the input data, and the goodness of fit of the data points to the best-fit plane are considered in terms of their dimensionality, and they are quantified using two parameters involving the minimum and intermediate eigenvalues from the regression, as well as the spatial precision of the data.

Crystal structure of [butane-2,3-dione bis-(4-methyl-thio-semicarbazonato)-κ(4) S,N (1),N (1'),S'](pyridine-κN)zinc(II).

In the structure of the title complex, [Zn(C8H14N6S2)(C5H5N)], the Zn(II) ion has a pseudo-square-pyramidal coordination environment and is displaced by 0.490 Å from the plane of best fit defined by the bis-(thio-semicarbazonate) N2S2 donor atoms. Chains sustained by intermolecular N-H⋯N and N-H⋯S hydrogen-bonding interactions extend parallel to [10-1].

Structural Analysis of the Hero Range in the Qaidam Basin, Northwestern China, Using Integrated UAV, Terrestrial LiDAR, Landsat 8, and 3-D Seismic Data

Quantitative structural analysis is a useful approach for studying geologic structures. It is particularly important in remote and complex fold-thrust belts where outcrop data and high-quality seismic reflection images are challenging to obtain. In this study, we integrated terrestrial light detection and ranging (LiDAR), unmanned aerial vehicle (UAV), and Landsat 8 (L8) data to extract high-resolution topographic and surface geologic information and constrain interpretations of three-dimensional (3-D) seismic reflection data in the Hero Range of the Qaidam Basin (QB) in northwestern China. UAV images were used to obtain a digital elevation model (DEM) and to measure the orientation of sedimentary bedding. Terrestrial LiDAR data were used to generate high-resolution digital outcrops and to evaluate the accuracy of the UAV-based DEM. L8 images were used to distinguish different stratigraphic units. The random sample consensus (RANSAC) algorithm was adopted to ascertain the best-fit plane of bedding. The results show that UAV images can be used to construct a DEM with <;1 m resolution and orthophotos with 0.15-m resolution. Collectively, these data improve the ability to identify and measure small exposures of bedding surfaces. The RANSAC algorithm improves the accuracy of measuring bedding orientations by removing erroneous selection points and facilitating the recognition of second-order variations in bedding orientation. The integrated analysis of remotely sensed and 3-D seismic data indicates that, of the three anticlines within the Hero Range, two are fault-propagation folds (the Shizigou and Youshashan anticlines) and one is associated with a pop-up structure (Ganchaigou anticline).

Crystal structure of 4-formyl-pyridine semicarbazone hemihydrate.

The mol­ecule of the title compound C7H8N4O·0.5H2O, alternatively called (E)-1-(pyridin-4-yl­methyl­ene)semi­carb­azide hemihydrate, is in the E conformation and is almost planar; the r.m.s. deviation of the positions of the atoms of the pyridine ring from the best-fit plane is 0.0039 Å. The C, N and O atoms of the rest of the mol­ecule sits close on this plane with a largest deviation of 0.115 (4) Å for the O atom of the semicarbazone moiety. There is an intra­molecular N—H⋯N hydrogen bond. In the crystal, mol­ecules are linked into an infinite three-dimensional network by classical N—H⋯Os (s = semicarbazone) and Ow—H⋯N (w = water) hydrogen bonds.

Error Suppression via Tension for Flexible Square Antenna Panels and Panel Arrays

The concept of passive surface error control via tension is explored for flexible square panels and for a rectangular array of such panels suspended with four catenaries. The panels are 1 mm thick 1 m square graphite-epoxy composite plates with a four-ply symmetric layup. Individual panel response to a uniform through-thickness temperature gradient field both alone and combined with in-plane tension (stretch) are examined. When integrated into a grid (a simple phased array configuration), the effects of a transient slew are considered. Characteristic responses are identified and studied symbolically as well as numerically. The results demonstrate the feasibility of combined global and component-level error suppression for the considered structure, exercised singularly by global prestress that also maintains the integrity of the tension structure. Limited attention is paid to mission-specific issues such as stowage and deployment. Assuming an X-band radar context, surface errors are related to a 1 mm limit. Out-of-flatness is evaluated with three metrics relevant to different aspects of signal processing: the maximum depth of the deformed surface, its maximum lateral deviation from the best-fit plane, and the phased-array radiometric rms surface error.

Rigorous error propagation for terrestrial laser scanning with application to snow volume uncertainty

AbstractEstimates of point-cloud positional accuracies in terrestrial laser scanning (TLS) datasets are currently limited to rudimentary combinations of GPS position error and manufacturer precision specifications. However, rigorous error propagation techniques can be applied to the three-dimensional TLS points and potentially integrated into software visualization and analysis products. Beyond the immediate value of qualitatively observing the distribution of expected TLS errors within a point cloud, rigorously estimated point errors can be further propagated to quantify expected errors in derived products such as point-to-point distance measurements, best-fit planes or volume computations. We review TLS error sources, detail their propagation through a rigid registration and illustrate the application of estimated TLS point errors to propagated snow volume uncertainties for a large and small TLS dataset. The resulting volume errors are of negligible size compared to the volume magnitudes, in no case exceeding 0.007% of the computed snow volume. For a dataset generating a large snow volume, the method of surface representation (e.g. grid or triangulated mesh) was more influential than the estimated TLS point errors on volume uncertainty. This suggests the random errors inherent in TLS measurement techniques are not a limiting factor in achievable snow volume accuracies.

A new arc–chord ratio (ACR) rugosity index for quantifying three-dimensional landscape structural complexity

Rugosity is an index of surface roughness that is widely used as a measure of landscape structural complexity in studies investigating spatially explicit ecological patterns and processes. This paper identifies and demonstrates significant issues with how we presently measure rugosity and, by building on recent advances, proposes a novel rugosity index that overcomes these issues. The new arc-chord ratio (ACR) rugosity index is defined as the contoured area of the surface divided by the area of the surface orthogonally projected onto a plane of best fit (POBF), where the POBF is a function (interpolation) of the boundary data only. The ACR method is described in general, so that it may be applied to a range of rugosity analyses, and its application is detailed for three common analyses: (a) measuring the rugosity of a two-dimensional profile, (b) generating a rugosity raster from an elevation raster (a three-dimensional analysis), and (c) measuring the rugosity of a three-dimensional surface. Two case studies are used to compare the ACR rugosity index with the rugosity index most commonly used (i.e. surface ratio rugosity), demonstrating the advantages of the ACR index. The ACR method for quantifying rugosity is simple, accurate, extremely versatile, and consistent in its principles independent of data dimensionality (2-D or 3-D), scale and analysis software used. It overcomes significant issues presented by traditional rugosity indices (e.g. decouples rugosity from slope) and is a promising new landscape metric. To further increase ease of use I provide multiple ArcGIS® resources in the electronic supplementary materials (e.g. Online Appendix 1: a downloadable ArcToolbox containing two ACR rugosity geoprocessing model tools).

A novel approach for determining three-dimensional acetabular orientation: results from two hundred subjects.

The inherently complex three-dimensional morphology of both the pelvis and acetabulum create difficulties in accurately determining acetabular orientation. Our objectives were to develop a reliable and accurate methodology for determining three-dimensional acetabular orientation and to utilize it to describe relevant characteristics of a large population of subjects without apparent hip pathology. High-resolution computed tomography studies of 200 patients previously receiving pelvic scans for indications not related to orthopaedic conditions were selected from our institution's database. Three-dimensional models of each osseous pelvis were generated to extract specific anatomical data sets. A novel computational method was developed to determine standard measures of three-dimensional acetabular orientation within an automatically identified anterior pelvic plane reference frame. Automatically selected points on the osseous ridge of the acetabulum were used to generate a best-fit plane for describing acetabular orientation. Our method showed excellent interobserver and intraobserver agreement (an intraclass correlation coefficient [ICC] of >0.999) and achieved high levels of accuracy. A significant difference between males and females in both anteversion (average, 3.5°; 95% confidence interval [CI], 1.9° to 5.1° across all angular definitions; p < 0.0001) and inclination (1.4°; 95% CI, 0.6° to 2.3° for anatomic angular definition; p < 0.002) was observed. Intrapatient asymmetry in anatomic measures showed bilateral differences in anteversion (maximum, 12.1°) and in inclination (maximum, 10.9°). Significant differences in acetabular orientation between the sexes can be detected only with accurate measurements that account for the entire acetabulum. While a wide range of interpatient acetabular orientations was observed, the majority of subjects had acetabula that were relatively symmetrical in both inclination and anteversion. A highly accurate and reproducible method for determining the orientation of the acetabulum's aperture will benefit both surgeons and patients, by further refining the distinctions between normal and abnormal hip characteristics. Enhanced understanding of the acetabulum could be useful in the diagnostic, planning, and execution stages for surgical procedures of the hip or in advancing the design of new implant systems.

N-[(9H-Fluoren-9-yl-idene)(2-meth-oxy-phen-yl)meth-yl]-1,1,1-tri-methyl-silanamine.

The title mol­ecule, C24H25NOSi, is a hydrolysis product of the reaction between 9-tri­methyl­silyfluorenyl lithium and 2-meth­oxy­benzo­nitrile. The fluorene ring system is substanti­ally planar, with an r.m.s. deviation of 0.0288 Å from the best-fit plane through its 13 C atoms. This plane forms a dihedral angle of 58.07 (7)° with the 2-meth­oxy­benzyl­amine ring plane. In the crystal, mol­ecules are linked by N—H⋯π and C—H⋯π inter­actions, which leads to the formation of two-dimensional network lying parallel to the bc plane.

Characterization of the Centroidal Geometry of Human Ribs

While a number of studies have quantified overall ribcage morphology (breadth, depth, kyphosis/lordosis) and rib cross-sectional geometry in humans, few studies have characterized the centroidal geometry of individual ribs. In this study, a novel model is introduced to describe the centroidal path of a rib (i.e., the sequence of centroids connecting adjacent cross-sections) in terms of several physically-meaningful and intuitive geometric parameters. Surface reconstructions of rib levels 2-10 from 16 adult male cadavers (aged 31-75 years) were first extracted from CT scans, and the centroidal path was calculated in 3D for each rib using a custom numerical method. The projection of the centroidal path onto the plane of best fit (i.e., the "in-plane" centroidal path) was then modeled using two geometric primitives (a circle and a semiellipse) connected to give C1 continuity. Two additional parameters were used to describe the deviation of the centroidal path from this plane; further, the radius of curvature was calculated at various points along the rib length. This model was fit to each of the 144 extracted ribs, and average trends in rib size and shape with rib level were reported. In general, upper ribs (levels 2-5) had centroidal paths which were closer to circular, while lower ribs (levels 6-10) tended to be more elliptical; further the centroidal curvature at the posterior extremity was less pronounced for lower ribs. Lower ribs also tended to exhibit larger deviations from the best-fit plane. The rib dimensions and trends with subject stature were found to be consistent with findings previously reported in the literature. This model addresses a critical need in the biomechanics literature for the accurate characterization of rib geometry, and can be extended to a larger population as a simple and accurate way to represent the centroidal shape of human ribs.