Least-squares Plane Research Articles

Autonomous countertraction for secure field of view in laparoscopic surgery using deep reinforcement learning.

Countertraction is a vital technique in laparoscopic surgery, stretching the tissue surface for incision and dissection. Due to the technical challenges and frequency of countertraction, autonomous countertraction has the potential to significantly reduce surgeons' workload. Despite several methods proposed for automation, achieving optimal tissue visibility and tension for incision remains unrealized. Therefore, we propose a method for autonomous countertraction that enhances tissue surface planarity and visibility. We constructed a neural network that integrates a point cloud convolutional neural network (CNN) with a deep reinforcement learning (RL) model. This network continuously controls the forceps position based on the surface shape observed by a camera and the forceps position. RL is conducted in a physical simulation environment, with verification experiments performed in both simulation and phantom environments. The evaluation was performed based on plane error, representing the average distance between the tissue surface and its least-squares plane, and angle error, indicating the angle between the tissue surface vector and the camera's optical axis vector. The plane error decreased under all conditions both simulation and phantom environments, with 93.3% of case showing a reduction in angle error. In simulations, the plane error decreased from to , and the angle error from to . In the phantom environment, the plane error decreased from to , and the angle error from to . The proposed neural network was validated in both simulation and phantom experimental settings, confirming that traction control improved tissue planarity and visibility. These results demonstrate the feasibility of automating countertraction using the proposed model.

Three-dimensional morphometry of the human thoracic aorta using centerline analysis based on least-squares plane fitting

ObjectiveA novel approach to 3-dimensional morphometry of the thoracic aorta was developed by applying centerline analysis based on least-squares plane fitting, and a preliminary study was conducted using computed tomography imaging data. MethodsWe retrospectively compared 3 groups of patients (16 controls without aortic disease, and 16 cases each with acute type B aortic dissection and congenital bicuspid aortic valve). In addition to the standard assessment indices for curvature κ and torsion τ, we conducted coordinate transformation based on the least-squares plane, divided the centerline into 3 representative features (transverse, anterior-posterior, and longitudinal displacements), and analyzed the overall and local displacement in each direction. The transverse displacement, represented by the distance of the centerline from the least-squares plane, was curve-fitted to the damped oscillation waveform. Thereafter, damped oscillation parameters were compared for each group. ResultsCurvature κ exhibited a bimodal distribution, with peaks observed in the ascending aorta and aortic arch, and torsion τ exhibited a transition from positive to negative values in the arch. There were significant differences in the mean displacement between the groups for each direction (transverse P = .0083, anteroposterior P = .010, longitudinal P = 1.32 × 10−6). Furthermore, interval integral analysis revealed that several intervals exhibited significant differences between groups in each direction. The amplitude of damped oscillation parameters was significantly larger in the bicuspid aortic valve group than in the control and type B aortic dissection groups. ConclusionsThe novel analytical approach permitted a quantitative assessment of the 3-dimensional morphological differences between the control, type B aortic dissection, and bicuspid aortic valve groups.

Autocollimators: plane angle measurand ambiguities and the impact of surface form

Abstract A phase shifting interferometer and a deformable mirror were used to study the impact of surface form on autocollimators, which detect the orientation of a plane reflecting surface. As real surfaces are not strictly planar, autocollimators must reduce a distribution of local surface orientations to a single reported angle, implicitly defining a measurand. Plausible choices of the summary statistic used to collapse an angle distribution to a single number can disagree by \SI{4}{\arcsecond} for a surface with a \SI{35}{mm} diameter and \SI{130}{nm} standard deviation from the best-fit plane. Combining a general framework for specifying autocollimator measurand definitions with Monte-Carlo simulation of random test surfaces yields estimates of the plausible differences between autocollimator measurands as a function of surface deformation amplitude, and shows the existence of three separate classes of measurands according to their sensitivity to subsets of the Zernike polynomials. Uncertainties due to surface form and measurand ambiguity can be eliminated by explicitly specifying a plane angle measurand for imperfect surfaces, such as a least-squares plane fit realized using an interferometer.

(31E,32Z,71E,72Z)-4,8-Bis(3,5-di-chloro-phen-yl)-14,33,53,73-tetra-propyl-11H,32H,51H,72H-1,5(2,5),3,7(5,2)-tetra-pyrrola-2,6(2,5)-di-thiophena-cyclo-octa-phane.

Purple crystals of the title compound, C50H44Cl4N4S2 were obtained from the reaction of 2,5-bis-(4-propyl-1H-pyrrol-2-yl)thio-phene and 3,5-di-chloro-benzaldehyde in the presence of tri-fluoro-acetic acid for 3 h and subsequent addition of p-chloranil. The macrocycle in the title compound can be described as a highly planar structure wthe the average deviation of the 32 macrocyclic atoms from the least-squares plane being 0.0416 Å. Its mol-ecular conformation is stabilized by two intra-molecular N-H⋯N bonds and a three-dimensional network is formed by C-H⋯π inter-actions.

Accuracy and inter-cloud precision of low-cost mobile LiDAR technology in estimating soil disturbance in forest operations

Forest operations can cause long-term soil disturbance, leading to environmental and economic losses. Mobile LiDAR technology has become increasingly popular in forest management for mapping and monitoring disturbances. Low-cost mobile LiDAR technology, in particular, has attracted significant attention due to its potential cost-effectiveness, ease of use, and ability to capture high-resolution data. The LiDAR technology, which is integrated in the iPhone 13–14 Pro Max series, has the potential to provide high accuracy and precision data at a low cost, but there are still questions on how this will perform in comparison to professional scanners. In this study, an iPhone 13 Pro Max equipped with SiteScape and 3D Scanner apps, and the GeoSlam Zeb Revo scanner were used to collect and generate point cloud datasets for comparison in four plots showing variability in soil disturbance and local topography. The data obtained from the LiDAR devices were analyzed in CloudCompare using the Iterative Closest Point (ICP) and Least Square Plane (LSP) methods of cloud-to-cloud comparisons (C2C) to estimate the accuracy and intercloud precision of the LiDAR technology. The results showed that the low-cost mobile LiDAR technology was able to provide accurate and precise data for estimating soil disturbance using both the ICP and LSP methods. Taking as a reference the point clouds collected with the Zeb Revo scanner, the accuracy of data derived with SiteScape and 3D Scanner apps varied from RMS = 0.016 to 0.035 m, and from RMS = 0.017 to 0.025 m, respectively. This was comparable to the precision or repeatability of the professional LiDAR instrument, Zeb Revo (RMS = 0.019–0.023 m). The intercloud precision of the data generated with SiteScape and 3D Scanner apps varied from RMS = 0.015 to 0.017 m and from RMS = 0.012 to 0.014 m, respectively, and were comparable to the precision of Zeb Revo measurements (RMS = 0.019–0.023 m). Overall, the use of low-cost mobile LiDAR technology fits well to the requirements to map and monitor soil disturbances and it provides a cost-effective and efficient way to gather high resolution data, which can assist the sustainable forest management practices.

5,6,7,8-Tetra-hydro-[1,2,4]triazolo[5,1-b]quinazolin-9(4H)-one.

The triazole ring in the title mol-ecule, C9H10N4O, is not quite coplanar with the six-membered ring to which it is fused, the dihedral angle between the two least-squares planes being 2.52 (6)°. In the crystal, a layered structure is formed by N-H⋯N and C-H⋯O hydrogen bonds plus slipped π-stacking inter-actions, with the fused cyclo-hexene rings projecting to either side.

Filtering Airborne LiDAR Data in Forested Environments Based on Multi-Directional Narrow Window and Cloth Simulation

Ground filtering is one of the essential steps for processing airborne light detection and ranging data in forestry applications. However, the performance of existing methods is still limited in forested areas due to the complex terrain and dense vegetation. To overcome this limitation, we proposed an improved surface-based filter based on multi-directional narrow window and cloth simulation. The innovations mainly involve two aspects as follows: (1) sufficient and uniformly distributed ground seeds are identified by merging the lowest points and line segments from the point clouds within a multi-directional narrow window; (2) complete and accurate ground points are extracted using a cyclic scheme that includes incorrect ground point elimination using the internal force adjustment of cloth simulation, terrain reconstruction with moving least-squares plane fitting, and ground point extraction based on progressively refined terrain. The proposed method was tested in five forested sites with various terrain characteristics and vegetation distributions. Experimental results showed that the proposed method could accurately separate ground points from non-ground points in different forested environments, with the average kappa coefficient of 88.51% and total error of 4.22%. Moreover, the comparative experiments proved that the proposed method performed better than the classical methods involving the slope-based, mathematical morphology-based and surface-based methods.

Roughness Evaluation of Burnished Topography with a Precise Definition of the S-L Surface

Studies of surface topography including processes of measurement and data analysis have an influence on the description of machined parts with their tribological performance. Usually, surface roughness is analysed when a scale-limited (S-L) surface, excluding short (S-) and length (L-) components from the raw measured data, is defined. Errors in the precise definition of the S-L surface can cause the false estimation of detail properties, especially its tribological performance. Errors can arise when the surface contains some burnished details such as oil pockets, dimples, scratches, or, generally, deep or wide features. The validation of proposed methods for S-L surface definition can also affect the accuracy of the ISO 25178 surface topography parameter calculation. It was found that the application of commonly used procedures, available in commercial software (e.g., least-square fitted cylinder element or polynomial planes, regular or robust Gaussian regression, spline, median or fast Fourier transform filters) can be suitable for precise S-L surface definition. However, some additional analyses, based on power spectral densities, autocorrelation function, texture direction graphs, or spectral characterisation, are strongly required. The effect of the definition of the S-L surface on the values of the ISO 25178 parameters was also comprehensively studied. Some proposals of guidance on how to define an appropriate S-L surface with, respectively, an objective evaluation of surface roughness parameters, were also presented.

Synthesis, single crystal, electrochemical and study of fluorogenic dibenzodiaza-crown-appended with bis(ZnTPP) azo-tweezer and spectroscopic elucidation of photo-induced macrocycle-deformation-based chromotropism

In the present research, a new tweezer T bearing azobenzene linker 1 was prepared, characterized by applying FT-IR spectroscopy, fluorescence spectroscopy, UV–visible spectroscopy, and elemental analysis 1H and 13C{1H} NMR. T crystals were obtained by reaction of 1 with ZnTPP in CHCl3/acetone. Under irradiation with a mercury lamp to achieve the trans-to-cis isomerization, a dramatic color change from violet to green in chloroform was observed. The X-ray crystallography of T revealed an observable macroring deformation of the ZnTPP for the trans isomer. We observed a deviation of 0.11 Å from planarity for the least-squares plane of ZnTPP owing to the axial coordination by the pyridine derivative of the parent dibenzodiaza-crown moieties of 1. Hence, we suggested the existence of oop deformations for this photo-responsive chromogenic colour change. Fluorescence (FL) spectrophotometry was applied to elucidate the observed colour change in terms of the ring deformation of ZnTPP, resulting from the trans-to-cis photo-isomerization of the azo-linker moiety of L. This is the first report on the gradual reversible photochromism of ZnTPP moiety, based on the macrocycle-deformation mechanism, wherein colour color change of T was reversible at 60 °C. The CVs of ZnTPP in various concentrations of 1 were examined. The titration of ZnTPP by 1 displays the positive shift of the oxidation potential of ZnTPP in the CV, indicating the complex formation between ZnTPP and 1 in CH2Cl2.

Crystal structure and Hirshfeld surface analysis of ethyl (3E)-5-(4-fluoro-phen-yl)3-{[(4-meth-oxy-phen-yl)formamido]-imino}-7-methyl-2H,3H,5H-[1,3]thia-zolo[3,2-a]pyrimidine-6-carboxyl-ate 0.25-hydrate.

In the title compound, C24H23FN4O4S·0.25H2O, the di-hydro-pyrimidine ring is distinctly non-planar, with the flap C atom deviating by 0.297 (2) Å from the least-squares plane. In the crystal, zigzag chains are formed by N-H⋯N hydrogen bonds parallel to [010] and are connected into layers parallel to (100) by O-H⋯O, O-H⋯F, C-H⋯O, C-H⋯F and C-H⋯N hydrogen bonds. Additional C-H⋯O hydrogen bonds connect the layers into a three-dimensional network. A Hirshfeld surface analysis indicates that the most significant contributions to the crystal packing are from H⋯H (42.6%), O⋯H/H⋯O (16.8%) and C⋯H/H⋯C (15.5%) contacts.

Slow Phase Transition-Induced Scan Rate Dependence of Spin Crossover in a Two-Dimensional Supramolecular Fe(III) Complex

Slow Phase Transition-Induced Scan Rate Dependence of Spin Crossover in a Two-Dimensional Supramolecular Fe(III) Complex

Re-Orienting Smartphone-Collected Car Motion Data Using Least-Squares Estimation and Machine Learning.

Smartphone sensors can collect data in many different contexts. They make it feasible to obtain large amounts of data at little or no cost because most people own mobile phones. In this work, we focus on collecting motion data in the car using a smartphone. Motion sensors, such as accelerometers and gyroscopes, can help obtain information about the vehicle’s dynamics. However, the different positioning of the smartphone in the car leads to difficulty interpreting the sensed data due to an unknown orientation, making the collection useless. Thus, we propose an approach to automatically re-orient smartphone data collected in the car to a standardized orientation (i.e., with zero yaw, roll, and pitch angles with respect to the vehicle). We use a combination of a least-square plane approximation and a Machine Learning model to infer the relative orientation angles. Then we populate rotation matrices and perform the data rotation. We trained the model by collecting data using a vehicle physics simulator.

Crystal structure and Hirshfeld surface analysis of 6-((E)-2-{4-[2-(4-chloro-phen-yl)-2-oxoeth-oxy]phen-yl}ethen-yl)-4,5-di-hydro-pyridazin-3(2H)-one.

The pyridazine ring in the title compound, C20H17ClN2O3, adopts a screw-boat conformation. The whole mol-ecule is flattened, the dihedral angles subtended by the least-squares plane of the central aromatic ring with those of the terminal benzene and pyridazine rings being 15.18 (19) and 11.23 (19)°, respectively. In the crystal, the mol-ecules are linked by pairs of N-H⋯O bonds into centrosymmetric dimers and by C-H⋯π contacts into columns. The results of the Hirshfeld surface analysis show that the most prominent inter-actions are H⋯H, accounting for 36.5% of overall crystal packing, and H⋯O/O⋯H (18.6% contribution) contacts.

ML-based re-orientation of smartphone-collected car motion data

Smartphone sensors can collect data in many different contexts. They make it feasible to obtain large amounts of data at little or no cost because most people own mobile phones. In this work, we focus on the collection of smartphone data in the car. Motion sensors, such as accelerometers and gyroscopes, can help obtain information about the vehicle’s dynamics. The possible spatial orientations of the smartphone in the car are infinite, and this can be a problem in an attempt to extract patterns from the data. Thus, we propose an approach to automatically re-orient smartphone data collected in the car to a standardized orientation (i.e. with 0 yaw, roll, and pitch angles with respect to the vehicle). We use a combination of a least-square plane approximation and an ML model to infer the relative orientation angles. Then we populate rotation matrices and perform the data rotation. We trained the model by collecting data both in an actual vehicle and using a vehicle physics simulator.

Dimethyl 4,5-di-chloro-phthalate.

While endeavoring to synthesize new chlorinated ligands for ruthenium-based metathesis catalysts, the title compound dimethyl 4,5-di-chloro-phthalate, C10H8Cl2O4, was prepared from commercially available 4,5-di-chloro-phthalic acid in ∼77% yield. The title mol-ecule, which also finds utility as a precursor mol-ecule for the synthesis of drugs used in the treatment of Alzheimer's disease, shows one carbonyl-containing methyl ester moiety lying nearly co-planar with the chlorine-derivatized aromatic ring while the second methyl ester shows a significant deviation of 101.05 (12)° from the least-squares plane of the aromatic ring. Within the crystal, structural integrity is maintained by the concerted effects of electrostatic inter-actions involving the electron-deficient carbonyl carbon atom and the electron-rich aromatic ring along the a-axis direction and C-H⋯O hydrogen bonds between neighboring mol-ecules parallel to b.

Crystal structure, Hirshfeld surface analysis and inter-action energy calculation of 4-(furan-2-yl)-2-(6-methyl-2,4-dioxo-pyran-3-yl-idene)-2,3,4,5-tetra-hydro-1H-1,5-benzodiazepine.

The title compound {systematic name: (S,E)-3-[4-(furan-2-yl)-2,3,4,5-tetra-hydro-1H-benzo[b][1,4]diazepin-2-yl-idene]-6-methyl-2H-pyran-2,4(3H)-dione}, C19H16N2O4, is constructed from a benzodiazepine ring system linked to furan and pendant di-hydro-pyran rings, where the benzene and furan rings are oriented at a dihedral angle of 48.7 (2)°. The pyran ring is modestly non-planar [largest deviation of 0.029 (4) Å from the least-squares plane] while the tetra-hydro-diazepine ring adopts a boat conformation. The rotational orientation of the pendant di-hydro-pyran ring is partially determined by an intra-molecular N-HDiazp⋯ODhydp (Diazp = diazepine and Dhydp = di-hydro-pyran) hydrogen bond. In the crystal, layers of mol-ecules parallel to the bc plane are formed by N-HDiazp⋯ODhydp hydrogen bonds and slipped π-π stacking inter-actions. The layers are connected by additional slipped π-π stacking inter-actions. A Hirshfeld surface analysis of the crystal structure indicates that the most important contributions for the crystal packing are from H⋯H (46.8%), H⋯O/O⋯H (23.5%) and H⋯C/C⋯H (15.8%) inter-actions, indicating that van der Waals inter-actions are the dominant forces in the crystal packing. Computational chemistry indicates that in the crystal the N-H⋯O hydrogen-bond energy is 57.5 kJ mol-1.

Crystal structure and Hirshfeld surface analysis of dimethyl 5-[2-(2,4,6-trioxo-1,3-diazinan-5-yl-idene)hydrazin-1-yl]benzene-1,3-di-carboxyl-ate 0.224-hydrate.

In the crystal, the whole mol-ecule of the title compound, C14H12N4O7·0.224H2O, is nearly planar with a maximum deviation from the least-squares plane of 0.352 (1) Å. The mol-ecular conformation is stabilized by an intra-molecular N-H⋯O hydrogen bond, generating an S(6) ring motif. In the crystal, mol-ecules are linked by centrosymmetric pairs of N-H⋯O hydrogen bonds, forming ribbons along the c-axis direction. These ribbons connected by van der Waals contacts, forming sheets parallel to the ac plane. There are also inter-molecular van der Waals contacts and and C-H⋯π inter-actions between the sheets. A Hirshfeld surface analysis indicates that the most prevalent inter-actions are O⋯H/H⋯O (41.2%), H⋯H (19.2%), C⋯H/H⋯C (12.2%) and C⋯O/ O⋯C (8.4%).

2-Amino-4-(4-chloro-1-ethyl-2,2-dioxo-1H-benzo[c][1,2]thia-zin-3-yl)-7,7-dimethyl-5-oxo-5,6,7,8-tetra-hydro-4H-chromene-3-carbo-nitrile: single-crystal X-ray diffraction study and Hirshfeld surface analysis.

In the title compound, C22H22ClN3O4S, which has potential non-steroidal anti-inflammatory activity, the benzo-thia-zine and cyclo-hexenone rings both adopt a distorted sofa conformation while the 4H-pyrane ring adopts a very flattened sofa conformation. The two bicyclic fragments are skewed to each other, with the dihedral angle between their least-squares planes being 72.8 (1)°. In the crystal, the mol-ecules form a hydrogen-bonded chain parallel to the a axis due to N-H⋯O and N-H⋯Cl hydrogen bonds. Neighbouring chains are linked by C-H⋯N, C-H⋯O and π-π stacking inter-actions. Hirshfeld surface analysis was used to investigate the importance of the different types of inter-molecular inter-actions whose contributions are: H⋯H = 44.7%, O⋯H/H⋯O = 21.8%, N⋯H/H⋯N = 11.9%, C⋯H/H⋯C = 9.5%, Cl⋯H/H⋯Cl = 7.2%. Parts of the mol-ecule, viz. the phenyl ring and the ethyl side chain, are equally disordered over two sets of sites.

Least-squares gamma estimation in fringe projection profilometry.

This paper introduces a novel, to the best of our knowledge, method to estimate and compensate the nonlinear gamma factor introduced by the optical system in fringe projection profilometry. We propose to determine this factor indirectly by adjusting the least-squares plane to the estimated phase coming from the reference plane. We only require a minimal set of three fringe sinusoidal images to estimate the gamma factor. This value can be used to rectify computational legacy data and also to generate and project the new set of fringe patterns for which we perform the inverse gamma compensation. Experimental results demonstrate the feasibility of the proposed method to estimate and correct the gamma distortion.

Crystal structure of [3,10-bis-(4-fluoro-pheneth-yl)-1,3,5,8,10,12-hexa-aza-cyclo-tetra-deca-ne]nickel(II) diperchlorate.

The square-planar nickel(II) title complex, [Ni(C24H36F2N6)](ClO4)2 or [NiL](ClO4)2 (L = 3,10-bis-(4-fluoro-pheneth-yl)-1,3,5,8,10,12-hexa-aza-cyclo-tetra-deca-ne) was synthesized by a one-pot reaction of template condensation and its X-ray crystal structure was determined. The nickel(II) ion lies close by a twofold axis and the complex displays whole-mol-ecule disorder. Ligand L, a hexa-aza-cyclo-tetra-decane ring having 4-fluoro-phenethyl side chains attached to uncoordinated nitro-gen atoms, adopts a trans III (R,R,S,S) configuration. The average Ni-N bond distance is 1.934 (9) Å, which is quite similar to those of other nickel(II) complexes with similar ligands. The nickel(II) ion is located 0.051 (7) Å above the least-squares plane through the four coordinated N atoms. The average C-N bond distance and C-N-C angle involving uncoordinated nitro-gen atoms are 1.425 (12) Å and 118.0 (9)°, respectively, indicating a significant contribution of sp 2 hybridization for these N atoms. The inter-molecular N-H⋯O, C-H⋯O/F hydrogen bonds of the complex form a network structure, which looks like a seamless floral lace pattern.