Curvature Model Research Articles

Color image restoration and inpainting via multi-channel total curvature

The multi-channel total variation (MTV) based on L2 norm is capable of preserving object edges and smoothing flat regions in color images. However, it will lead to loss of image contrast, smear object corners, and produce staircase artifacts in the restored images. In order to remedy these side effects, we propose a new multi-channel total curvature model based on L1 norm (MTC-L1) for vector-valued image restoration in this paper. By introducing some auxiliary variables and Lagrange multipliers, we develop a fast algorithm based alternating direction method of multipliers (ADMM) for the proposed model, which allows the use of the fast Fourier transform (FFT), generalized soft threshold formulas and projection method. Extensive experiments have been conducted on both synthetic and real color images, which validate the proposed approach for better restoration performance, and show advantages of the proposed ADMM over algorithms based on traditional gradient descent method (GDM) in terms of computational efficiency.

Research on Influence and Prediction Model of Urban Traffic Link Tunnel curvature on Fire Temperature Based on Pyrosim--SPSS Multiple Regression Analysis

The underground space, also known as the “fourth dimension” of the city, reflects the efficient use of urban development intensive. Urban traffic link tunnel is a typical underground limited-length space. Due to the geographical location, the special structure of space and the curvature of the tunnel, high-temperature smoke can easily form the phenomenon of “smoke turning” and the fire risk is extremely high. This paper takes an urban traffic link tunnel as an example to focus on the relationship between curvature and the temperature near the fire source, and use the pyrosim built different curvature fire model to analyze the influence of curvature on the temperature of the fire, then using SPSS Multivariate regression analysis simulate curvature of the tunnel and fire temperature data. Finally, a prediction model of urban traffic link tunnel curvature on fire temperature was proposed. The regression model analysis and test show that the curvature is negatively correlated with the tunnel temperature. This model is feasible and can provide a theoretical reference for the urban traffic link tunnel fire protection design and the preparation of the evacuation plan. And also, it provides some reference for other related curved tunnel curvature design and smoke control measures.

Dynamical Symmetries, Super-coherent States and Noncommutative Structures: Categorical and Geometrical Quantization Analysis

The relation between fundamental spacetime structures and dynamical symmetries are treated beyond the geometrical and topological viewpoint. To this end analyze, taking into account the concept of categories and quasi hamiltonian structures, a recent research (Cirilo-Lombardo and Arbuzov in Int J Geom Methods Mod Phys 15(01):1850005, 2017) where one linear and one quadratic in curvature models were constructed and where a dynamical breaking of the \(\textit{SO}(4,2)\) group symmetry arises. We explain there how and why coherent states of the Klauder-Perelomov type are defined for both cases taking into account the coset geometry and some hints on the possibility to extend they to the categorical (functorial) status are given. The new spontaneous compactification mechanism that was defined in the subspace invariant under the stability subgroup is commented in the context of future developments as the main tool for the treatment of the internal symmetries, as the electroweak in the Standard Model (SM). The physical implications of the symmetry rupture as the introduction of a noncommutative structure in the context of non-linear realizations and direct gauging are analyzed and briefly discussed in this new theoretical framework.

3D surface pressure measurement with single light-field camera and pressure-sensitive paint

A novel technique that simultaneously measures three-dimensional model geometry, as well as surface pressure distribution, with single camera is demonstrated in this study. The technique takes the advantage of light-field photography which can capture three-dimensional information with single light-field camera, and combines it with the intensity-based pressure-sensitive paint method. The proposed single camera light-field three-dimensional pressure measurement technique (LF-3DPSP) utilises a similar hardware setup to the traditional two-dimensional pressure measurement technique, with exception that the wind-on, wind-off and model geometry images are captured via an in-house-constructed light-field camera. The proposed LF-3DPSP technique was validated with a Mach 5 flared cone model test. Results show that the technique is capable of measuring three-dimensional geometry with high accuracy for relatively large curvature models, and the pressure results compare well with the Schlieren tests, analytical calculations, and numerical simulations.

Variational total curvature model for multiplicative noise removal

The multiplicative noise removal problem has received considerable attention recently. To solve this problem, various variational models have been proposed, which minimise an energy functional composed of the data term and the regularisation term. Regarding the regularisation term, a first-order model is frequently used to remove multiplicative noise, which may cause staircase effect and loss of contrast in the output image. In this study, the authors use a second-order model, the total curvature (TC), to solve the above problem. The TC model has the benefit of removing the staircase effect and maintaining image edges, contrasts and corners. The augmented Lagrange method is utilised to solve the proposed TC model by introducing auxiliary variables, Lagrange multipliers and using alternating optimisation strategy. In each loop of optimisation, the fast Fourier transform, generalised soft threshold formulas, projection method and gradient descent method are integrated effectively. The experimental results show that the TC model can effectively remove staircase effect and preserve smoothness, via comparison with the first-order model (total variation regularisation and Perona-Malik regularisation). Furthermore, the TC model is better than another second-order model based on bounded Hessian regularisation in preserving contrast and corner.

Analytical displacement solutions for statically determinate beams based on a trilinear moment–curvature model

A standard approach is presented to obtain analytical solutions for deflection field of determinate beams subjected to conventional loading patterns. The solutions are based on a trilinear moment–curvature response using a deflection hardening behavior characterized by flexural crack initiation, inelastic response due to crack extension, and full plastic hinge formation. Methodology for full span deflection and rotation distributions are presented for multiple cases that include three‐ and four‐point bending, uniform load, concentrated moment, and cantilever beams. The proposed approach provides analytical expressions for the curvature, rotation, and deflection at any point along the beam, and correlated to stress or strain distribution. The procedure can therefore be integrated into a serviceability‐based design approach. A parametric study of the effects of model parameters on the stages of the response is addressed. Several case studies involving steel fiber reinforced concrete (SFRC), textile reinforced concrete (TRC) and ultra‐high performance concrete (UHPC) are conducted and the simulated load‐deflection responses are verified against the experimental data from several published experiments. Size effect on the serviceability limits of beams with spans ranging from 0.22 to 8.6 m is studied by tracking the full‐range moment–curvature and load‐deflection responses.

Modeling the Flat to Curved Transition during Clathrin Mediated Endocytosis

Clathrin-mediated endocytosis is essential for the cellular uptake of receptors and nutrients. Although under investigation since decades, the exact sequence of structural and molecular events remains elusive. There are two basic models that have been suggested for the way it proceeds. In the constant curvature model, it is assumed that clathrin-coated pits grow with constant curvature, determined by the geometry of clathrin triskelia. In the constant area model, it is assumed that clathrin triskelia first assemble into flat hexagonal arrays that later invaginate at constant surface area. This second model implicitly assumes that during bending, some hexagons are converted into pentagons. Here, we integrate data sets from correlative electron and light microscopy and quantify the sequence of ultrastructural rearrangements of the clathrin coat during endocytosis in mammalian cells with the help of some simple mathematical growth laws. Our main assumption is that the clathrin domain can grow only over the boundary. In the case of flat arrays, this requires some balancing process to prevent a run-away process, which we assume to grow in proportion to the domain area. In the case of curved arrays, pit closure is sufficient to limit growth and thus an additional process is not required. Our analysis shows that clathrin-coated structures initially grow flat but start to acquire curvature when 70% of the final clathrin content is reached. We find that this transition correlates with a change in the ratio of clathrin to adaptor protein AP2, and that membrane tension suppresses this transition. Hence, our analysis suggests that elements of both suggested models are present and that mechanical and cellular factors will decide about the relative weights of growth versus curvature formation.

Dynamical symmetries, coherent states and nonlinear realizations: The SO(2,4) case

Nonlinear realizations of the [Formula: see text] group are discussed from the point of view of symmetries. Dynamical symmetry breaking is introduced. One linear and one quadratic model in curvature are constructed. Coherent states of the Klauder–Perelomov type are defined for both cases taking into account the coset geometry. A new spontaneous compactification mechanism is defined in the subspace invariant under the stability subgroup. The physical implications of the symmetry rupture in the context of nonlinear realizations and direct gauging are analyzed and briefly discussed.

Covariant perturbations in the gonihedric string model

We provide a covariant framework to study classically the stability of small perturbations on the so-called gonihedric string model by making precise use of variational techniques. The local action depends on the square root of the quadratic mean extrinsic curvature of the worldsheet swept out by the string, and is reparametrization invariant. A general expression for the worldsheet perturbations, guided by Jacobi equations without any early gauge fixing, is obtained. This is manifested through a set of highly coupled nonlinear differential partial equations where the perturbations are described by scalar fields, [Formula: see text], living in the worldsheet. This model contains, as a special limit, to the linear model in the mean extrinsic curvature. In such a case the Jacobi equations specialize to a single wave-like equation for [Formula: see text].

Surface deformation during an action potential in pearled cells.

Electric pulses in biological cells (action potentials) have been reported to be accompanied by a propagating cell-surface deformation with a nanoscale amplitude. Typically, this cell surface is covered by external layers of polymer material (extracellular matrix, cell wall material, etc.). It was recently demonstrated in excitable plant cells (Chara braunii) that the rigid external layer (cell wall) hinders the underlying deformation. When the cell membrane was separated from the cell wall by osmosis, a mechanical deformation, in the micrometer range, was observed upon excitation of the cell. The underlying mechanism of this mechanical pulse has, to date, remained elusive. Herein we report that Chara cells can undergo a pearling instability, and when the pearled fragments were excited even larger and more regular cell shape changes were observed (∼10-100μm in amplitude). These transient cellular deformations were captured by a curvature model that is based on three parameters: surface tension, bending rigidity, and pressure difference across the surface. In this paper these parameters are extracted by curve-fitting to the experimental cellular shapes at rest and during excitation. This is a necessary step to identify the mechanical parameters that change during an action potential.

Higher curvature gravities, unlike GR, cannot be bootstrapped from their (usual) linearizations

We show that higher curvature order gravities, in particular the propagating quadratic curvature models, cannot be derived by self-coupling from their linear, flat space, forms, except through an unphysical version of linearization; only GR can. Separately, we comment on an early version of the self-coupling bootstrap.

Supersonic flow fields resulting from axisymmetric internal surface curvature

An experimental and numerical study was conducted to examine the effects of internal surface curvature and leading-edge angle on the shock waves and steady flow fields produced by axisymmetric ring wedges. Test models with leading-edge-radius-normalised internal radii of curvature of $R_{c}=\{1,1.5,2\}$ and leading-edge angles of $\unicode[STIX]{x1D6FC}=\{0^{\circ },4^{\circ },8^{\circ }\}$ were manufactured and tested. Experimental shadowgraph and schlieren results were obtained for Mach numbers ranging from 2.8 to 3.6 using a blowdown supersonic wind tunnel with accompanying numerical results for additional insight. The higher the internal surface curvature and leading-edge angle, the greater the flow fields were impacted. As a result, steeper compression waves were formed, thus curving the shock wave more noticeably. The internal surface curvature and leading-edge angle were both found to have an effect on the trailing-edge expansion fans. This altered the shape of downstream shock wave structures. The highest curvature models produced steady double reflection patterns due to the imposed internal surface curvature. The effects of conical and curved internal surfaces were explored for the presence of flow-normal curvature and the curving of the attached shock waves.

Onto a Skewness Approach to the Generalized Curvature Ocean Surface Scattering Model

The generalized curvature ocean surface scattering model [general curvature model (GCM)] is extended and revisited. Two key steps are addressed in this paper, namely, a necessary sea surface spectrum undressing procedure and the inclusion of a skewness phase-related component. Normalized radar cross-section (NRCS) simulations are generated at C-band for various wind conditions, polarizations, and incidence angles. Results are compared with CMOD5.n. Although the sea surface spectrum undressing procedure is a necessary step, the overall NRCS dynamic is notably affected only in low wind conditions (≤5 m/s). The inclusion of the skewness phase-related component makes the most impact to the NRCS dynamic where the upwind/downwind asymmetry is clearly detectable. A good agreement between the upwind/downwind asymmetry of the extended GCM and CMOD5.n is achieved for moderate winds (≈5–10 m/s) and moderate incidence angles (≈32°–40°). For low incidence angles (<26°), the GCM tends to overestimate the upwind/downwind asymmetry compared with CMOD5.n.

Study on asymmetrical deformation and curvature of heavy cylinder rolling

In this work, an analytical model based on slab method is proposed to calculate the force parameters in asymmetrical heavy cylinder rolling where the rolls radii, speeds, friction and contact arc lengths are different, moreover, an analytical bending curvature model to calculate the curvature at the exit of deformation zone of heavy cylinder rolling is also proposed. In these models, the non-uniform normal strain, non-uniform shear strain, tension and guide roll force are taken into account. To verify the validity of the proposed analytical solution, the analytical heavy cylinder rolling force was compared with the experimental results. Very good agreements are found. The influences of reduction, speed ratio, friction coefficient ratio, guide roll force on rolling force distribution and bending curvature are presented. The simulations show a good potential of these models in industrial application.

Simulation analysis on the influence of smoke flow in special section tunnel under mechanical ventilation

In this study, a special section tunnel model was established by using FDS (Fire Dynamics Simulator). In the condition of mechanical ventilation, studied the effect of the model for exhaust velocity interval and curvature, slope on the smoke flow. Finally, the longitudinal wind speed of 3m/s is determined, and the results show that the curvature and slope of the tunnel have no effect on the smoke flow.

The compressed breast during mammography and breast tomosynthesis: in vivo shape characterization and modeling

To characterize and develop a patient-based 3D model of the compressed breast undergoing mammography and breast tomosynthesis.During this IRB-approved, HIPAA-compliant study, 50 women were recruited to undergo 3D breast surface imaging with structured light (SL) during breast compression, along with simultaneous acquisition of a tomosynthesis image. A pair of SL systems were used to acquire 3D surface images by projecting 24 different patterns onto the compressed breast and capturing their reflection off the breast surface in approximately 12–16 s. The 3D surface was characterized and modeled via principal component analysis. The resulting surface model was combined with a previously developed 2D model of projected compressed breast shapes to generate a full 3D model.Data from ten patients were discarded due to technical problems during image acquisition. The maximum breast thickness (found at the chest-wall) had an average value of 56 mm, and decreased 13% towards the nipple (breast tilt angle of 5.2°). The portion of the breast not in contact with the compression paddle or the support table extended on average 17 mm, 18% of the chest-wall to nipple distance. The outermost point along the breast surface lies below the midline of the total thickness. A complete 3D model of compressed breast shapes was created and implemented as a software application available for download, capable of generating new random realistic 3D shapes of breasts undergoing compression.Accurate characterization and modeling of the breast curvature and shape was achieved and will be used for various image processing and clinical tasks.

Improved Research for 3D Mesh Segmentation Based on Watershed Algorithm

Most of the 3D mesh segmentation method now is based on the curvature model. This unified error method leads to poor segmentation results. In order to solve the problem of “the unified error”, in this paper, we used the watershed algorithm. We used region growing algorithm to improve the segmentation of watershed algorithm and apply the ROI conception to achieve interest segmentation. In this method, without considering the smoothness of the split edge, the 3D mesh model can achieve their desired segmentation effect.

A Geometry Deformation Model for Braided Continuum Manipulators

Continuum manipulators have gained significant attention in the robotic community due to their high dexterity, deformability and reachability. Modeling of such manipulators has been shown to be very complex and challenging. Despite many research attempts, a general and comprehensive modeling method is yet to be established. In this paper, for the first time, we introduce the bending effect in the model of a braided extensile pneumatic actuator with both stiff and bendable threads. Then, the effect of the manipulator cross section deformation on the constant curvature and variable curvature models is investigated using simple analytical results from a novel geometry deformation method and is compared to experimental results. We achieve 24% simulation accuracy using our constant curvature model for a braided continuum manipulator in presence of body load and 10% error using our variable curvature model in presence of extensive external loads. With proper model assumptions and taking to account the cross section deformation, an 8-20% increase in the simulation accuracy is achieved compared to a fixed cross section model. The presented models can be used for the exact modeling and design optimization of compound continuum manipulators by providing an analytical tool for the sensitivity analysis of the manipulator performance. Our main aim is the application in minimal invasive manipulation with limited workspaces and manipulators with regional tuneable stiffness in their cross section.

Cosmological backreaction within the Szekeres model and emergence of spatial curvature

This paper discusses the phenomenon of backreaction within the Szekeres model. Cosmological backreaction describes how the mean global evolution of the Universe deviates from the Friedmannian evolution. The analysis is based on models of a single cosmological environment and the global ensemble of the Szekeres models (of the Swiss-Cheese-type and Styrofoam-type). The obtained results show that non-linear growth of cosmic structures is associated with the growth of the spatial curvature Ωℛ (in the FLRW limit Ωℛ → Ωk). If averaged over global scales the result depends on the assumed global model of the Universe. Within the Swiss-Cheese model, which does have a fixed background, the volume average follows the evolution of the background, and the global spatial curvature averages out to zero (the background model is the ΛCDM model, which is spatially flat). In the Styrofoam-type model, which does not have a fixed background, the mean evolution deviates from the spatially flat ΛCDM model, and the mean spatial curvature evolves from Ωℛ =0 at the CMB to Ωℛ ∼ 0.1 at 0z =. If the Styrofoam-type model correctly captures evolutionary features of the real Universe then one should expect that in our Universe, the spatial curvature should build up (local growth of cosmic structures) and its mean global average should deviate from zero (backreaction). As a result, this paper predicts that the low-redshift Universe should not be spatially flat (i.e. Ωk ≠ 0, even if in the early Universe Ωk = 0) and therefore when analysing low-z cosmological data one should keep Ωk as a free parameter and independent from the CMB constraints.

Skewness and kurtosis of height distribution of thin films simulated by larger curvature model with noise reduction techniques

Time varying skewness (S) and kurtosis (Q) of height distribution of (2+1)-dimensional larger curvature (LC) model with and without noise reduction techniques (NRTs) are investigated in both transient and steady state regimes. In this work, effects of the multiple hit NRT (m>1 NRT) and the long surface diffusion length NRT (ℓ>1 NRT) on the surface morphologies and characteristics of S and Q are studied. In the early growth time, plots of S and Q versus time of the m>1 morphologies show pronounced oscillation indicating the layer by layer growth. Our results show that S=0 and Q<0 at every half layer while S=0 and Q>0 at every complete layer. The results are confirmed by the same plots of the results from the Das Sarma–Tamborenea (DT) model. The ℓ>1 LC model, on the other hand, has no evidence of the layer by layer growth mode due to the rapidly damped oscillation of S and Q. In the steady state, the m>1 and ℓ>1 NRTs affect weakly on the values of S and Q and the mounded morphologies of the film. This lead to the evidence of universality of S and Q in the steady state of the LC models with various m and ℓ. The finite size effect on the values of S and Q is found to be very weak in the LC model. By extrapolating to L→∞, we obtain SL→∞≈0.05 and QL→∞≈−0.62 which are in agreement with the NRTs results.