Shape Reconstruction Method Research Articles

Skull shape reconstruction using cascaded convolutional networks

Designing a cranial implant to restore the protective and aesthetic function of the patient’s skull is a challenging process that requires a substantial amount of manual work, even for an experienced clinician. While computer-assisted approaches with various levels of required user interaction exist to aid this process, they are usually only validated on either a single type of simple synthetic defect or a very limited sample of real defects. The work presented in this paper aims to address two challenges: (i) design a fully automatic 3D shape reconstruction method that can address diverse shapes of real skull defects in various stages of healing and (ii) to provide an open dataset for optimization and validation of anatomical reconstruction methods on a set of synthetically broken skull shapes.We propose an application of the multi-scale cascade architecture of convolutional neural networks to the reconstruction task. Such an architecture is able to tackle the issue of trade-off between the output resolution and the receptive field of the model imposed by GPU memory limitations. Furthermore, we experiment with both generative and discriminative models and study their behavior during the task of anatomical reconstruction.The proposed method achieves an average surface error of 0.59mm for our synthetic test dataset with as low as 0.48mm for unilateral defects of parietal and temporal bone, matching state-of-the-art performance while being completely automatic. We also show that the model trained on our synthetic dataset is able to reconstruct real patient defects.

Morphological reconstruction method of irregular shaped ballast particles and application in numerical simulation of ballasted track

Abstract To quantitatively investigate the morphological features of railway ballast, a new statistical index, Curvature Index (CI), was presented. With a set of 584 digitized railway ballast particles obtained through 3D scanning, the statistical distribution functions of CI and existing global shape indices (i.e., long axis, middle axis, short axis and sphericity index) were obtained. Then, based on Proper Orthogonal Decomposition (POD) and Radial Basis Function (RBF) Neural Network, a new shape reconstruction method was proposed to generate an arbitrary number of ballast particles that met the desired probability density distribution of morphological indices. And based on local curvature distribution on particle surface, a new simplification algorithm was implemented to reduce the number of contour points of each particle to no more than 31 on the premise of preserving global and local morphological features, which improved the efficiency of numerical simulations. These methods were used to reconstruct and simplify the arbitrary shapes of gravel ballast particles. Then, a DEM-FEM coupling model of ballasted track-subgrade was established by applying the regenerated ballast particles to analyze the contact stress at the ballast-soil interface. The numerical simulations can effectively reflect the contact stress distributions resulted from laboratory tests, which further confirmed that the reconstruction of the ballast particles reflected the morphological characteristics of real ballast.

Solving a kind of inverse scattering problem of acoustic waves based on linear sampling method and neural network

This paper explores the inverse scattering problem that reconstructs the obstacle shape with far-field information in the acoustic environment. Taking the planar wave as the incident wave, the authors put forward a shape reconstruction method for an impenetrable obstacle with a sound-soft boundary. Firstly, the linear sampling method (LSM) was performed to acquire the prior information about the obstacle shape. Next, a shape parameter inversion model was constructed based on neural network and gating thought, and it was denoted as the SPIMNNG. The model parameters were updated through self-learning. After that, the shape parameters of obstacle boundary were inversed according to the far-field information and the prior information about obstacle shape. On this basis, the boundary shape of the obstacle was reconstructed. The computing complexity of the SPIMNNG model was also calculated. Finally, several numerical experiments were carried out to verify the proposed method. The results show that our method can effectively inverse the shape parameters of obstacles.

Shape and Reflectance Reconstruction Using Concentric Multi-Spectral Light Field.

Recovering the shape and reflectance of non-Lambertian surfaces remains a challenging problem in computer vision since the view-dependent appearance invalidates traditional photo-consistency constraint. In this paper, we introduce a novel concentric multi-spectral light field (CMSLF) design that is able to recover the shape and reflectance of surfaces of various materials in one shot. Our CMSLF system consists of an array of cameras arranged on concentric circles where each ring captures a specific spectrum. Coupled with a multi-spectral ring light, we are able to sample viewpoint and lighting variations in a single shot via spectral multiplexing. We further show that our concentric camera and light source setting results in a unique single-peak pattern in specularity variations across viewpoints. This property enables robust depth estimation for specular points. To estimate depth and multi-spectral reflectance map, we formulate a physics-based reflectance model for the CMSLF under the surface camera (S-Cam) representation. Extensive synthetic and real experiments show that our method outperforms the state-of-the-art shape reconstruction methods, especially for non-Lambertian surfaces.

A Fast Inclusion Boundary Reconstruction Framework for Electrical Impedance Tomography With Parametric Snake Model

Electrical impedance tomography (EIT) is a noninvasive technique estimating the conductivity inside an observation domain from its peripheral measurements and owns many industrial and biomedical applications. Inclusion reconstruction is one of the key problems in EIT. However, the high-resolution inclusion reconstruction is challenging due to the ill-posedness and nonlinearity of EIT. The shape reconstruction methods focusing on recovering the shape of the inclusion is one kind of advanced methods to enhance the EIT resolution. To achieve high-performance shape reconstruction, a parametric geometric constraint boundary reconstruction (PGCBR) framework is proposed. The shape reconstruction is implemented by minimizing the energy function of the inclusion boundary represented by the parametric snake model. To accelerate the convergence, the Newton method is adopted to solve the energy minimization problem. The first- and second-order partial derivatives of the energy terms are calculated with the EIT shape sensitivity formula. A series of numerical tests evaluated the influences of the key factors, e.g., the basis function and the number of the knot and interpolating points, of PGCBR on its reconstruction performance and proved its robustness against the measurement noise. The following experimental tests, including both single- and multiphase conductivity cases, further proved the advantages of PGCBR over the nonparametric method.

A Point Constrained Boundary Reconstruction Framework for Ultrasound Guided Electrical Impedance Tomography

As a non-invasive and radiation-free imaging modality, electrical impedance tomography (EIT) has attracted much attention in the field of industrial measurement. However, image reconstruction with EIT is a non-linear and ill-posed inverse problem, causing it to suffer from low spatial resolution and high noise sensitivity. To overcome this problem, a point-constrained framework is proposed to guide inclusion boundary reconstruction in EIT with ultrasound point detection. The boundary reconstruction problem is formulized with an energy minimization approach. The energy function consists of the residual, point constraint, geometric and re-parameterisation terms. The residual term fits the actual EIT data by adjusting the inclusion shape and conductivity with a computable forward model. The point constraint term drags the estimated boundary toward the ultrasound detected ‘at-boundary’ points and pushes it away from the ultrasound detected ‘outside-inclusion’ points. The geometric and re-parameterisation terms regularize the boundary reconstruction problem and diffuse the point constraint energy along the inclusion boundary. According to the numerical results, the proposed method is robust to measurement noise, as well as the super parameter and initial boundary guess issues. An experimental phantom study with a water tank model further proved that the dual-modality shape reconstruction method outperforms the single-modality shape reconstruction method in both single-phase and multiphase conductivity cases.

Local Spherical Harmonics for Facial Shape and Albedo Estimation

In this paper, we present a novel facial albedo and 3D shape recovery method with a local spherical harmonic illumination model. From a face in an image, the proposed method can produce a high-quality 3D shape and albedo using a novel parameterization of local illuminations. Because a facial shape is partially convex, a single spherical harmonics is generally used for the illumination of a face within a constrained illumination environment. However, when a facial image is captured in an unconstrained scene, the illumination is inappropriately estimated due to the presence of shadow and specular reflections. To address this issue, we propose a novel local spherical harmonic illumination model for representing the illumination of a face. Unlike the existing parameterization of local illumination, our local spherical harmonic illumination model utilizes a smooth weight function for the seamless representation of natural illumination. Therefore, the albedo and shape information in an image can be precisely estimated using the first-order spherical harmonics. For accurate estimation of albedo, we also utilize facial albedo statistics to prevent the estimated albedo from becoming biased toward input image. Furthermore, we developed an accurate and reliable 3D shape reconstruction method from a normal map based on tetrahedron-based deformation. Comparing to the Laplacian deformation based method, our method is applicable to any mesh regardless of its structure. Through rigorous experiments, we demonstrate that the proposed local spherical harmonic illumination model is effective in estimating the complex illumination and can recover a high-quality facial albedo and 3D shape.

Inverse Fluid-solid Interaction Scattering Problem Using Phased and Phaseless Far Field Data

We consider the inverse fluid-solid interaction scattering of incident plane wave from the knowledge of the phased and phaseless far field patterns. For the phased data, one direct sampling method for location and shape reconstruction is proposed. Only inner product is involved in the computation, which makes it very simple and fast to be implemented. With the help of the factorization of the far field operator, we give a lower bound of the proposed indicator functional for the sampling points inside the elastic body. While for the sampling points outside, we show that the indicator functional decays like the Bessel function as the points go away from the boundaries of the elastic body. We also show that the proposed indicator functional continuously dependents on the far field patterns, which further implies that the novel sampling method is extremely stable with respect to data error. For the phaseless data, to overcome the translation invariance, we consider the scattering of point sources simultaneously. By adding a reference sound-soft obstacle into the scattering system, we show some uniqueness results with phaseless far field data. Numerically, we introduce a phase retrieval algorithm to retrieve the phased data without the additional obstacle. The novel phase retrieval algorithm can also be combined with the sampling method for phased data. We also design two novel direct sampling methods using the phaseless data directly. Finally, some numerical simulations in two dimensions are conducted with noisy data, and the results further verify the effectiveness and robustness of the proposed numerical methods.

Shape reconstructions and morphing kinematics of an eagle during perching manoeuvres**Project supported by the National Natural Science Foundation of China (Grant No. 51705459) and the China Postdoctoral Science Foundation.

The key to high manoeuvre ability in bird flight lies in the combined morphing of wings and tail. The perching of a wild Haliaeetus Albicilla without running or wing flapping is recorded and investigated using a high-speed digital video. A shape reconstruction method is proposed to describe wing contours and tail contours during perching. The avian airfoil geometries of the Aquila Chrysaetos are extracted from noncontact surface measurements using a ROMBER 3D laser scanner. The wing planform, chord distribution and twist distribution are fitted in convenient analytical expressions to obtain a 3D wing geometry. A three-jointed arm model is proposed to associate with the 3D wing geometry, while a one-joint arm model is proposed to describe the kinematics of tail. Therefore, a 3D bird model is established. The perching sequences of the wild eagle are recaptured and regenerated with the proposed 3D bird model. A quasi-steady aerodynamic model is applied in the aerodynamic predictions, a four-step Adams–Bashforth method is used to calculate the ordinary differential equations, thus a BFGS based optimization method is established to predict the perching motions.

Distributed Curvature Sensing and Shape Reconstruction for Soft Manipulators With Irregular Cross Sections Based on Parallel Dual-FBG Arrays

This article presents a distributed curvature sensing and shape reconstruction method based on parallel dual fiber Bragg grating (FBG) arrays for a type of cable-driven soft manipulator with irregular cross sections. The curvature at each measured point can be detected by the differential response of the relevant dual-FBG sensing unit with less interference from the temperature and axial driven force. The shape of the manipulator can be completely reconstructed by using the integration of the piecewise curvature functions. The measurement principle of curvature and shape reconstruction method have been investigated and derived. Experiments indicate that the constant temperature-induced error for the detected curvature is less than 0.1042 m−1. The error of the detected curvature is small less than −0.0824 m−1 within a changing temperature from 30 °C to 50 °C. The shape of the manipulator can be reconstructed with a small error of less than 1 mm under a constant or changing temperature environment. Static and dynamic grasping experiments for the manipulator have been implemented, which indicates a feasible shape tracking with resistance for axial force effect. Such merits further validate the effectiveness of the proposed approach for distributed curvature sensing and shape tracking of the manipulator with irregular cross sections.

Shape from focus based on 3D structure tensor using optical microscopy.

Shape from focus (SFF) is a widely used passive optical method for 3D shape reconstruction. In SFF, a focus measure, which is used to estimate the relative focus level, plays a critical role in depth estimation. In this article, we present a new focus measure for accurate 3D shape estimation in optical microscopy based on the analysis of 3D structure tensor. First, the 3D tensors are computed from the input image sequence for each pixel. Then, each tensor is decomposed into point, curve, and surface tensors by decomposing tensors into eigenvalues and eigenvectors. Finally, the surfaceness is used to measure the quality of sharpness. The proposed focus measure provides accurate focus values and better resistance against noise. The proposed measure is evaluated by conducting experiments using image sequences of simulated and microscopic real objects. The comparative analysis demonstrates the effectiveness of the proposed focus measure in recovering 3D shape.

Inverse elastic scattering problems with phaseless far field data

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for inverse elastic scattering problems with phaseless far field data. The phaseless far field data is closely related to the outward energy flux, which is easily measured in practice. Systematically, we study two basic models, i.e. inverse scattering of plane waves by rigid bodies and inverse scattering of sources with compact support. For both models, we show that the phaseless far field data is invariant under translation of the underlying scattering objects, which implies that the location of the objects can not be uniquely recovered by the data. To solve this problem, we consider simultaneously the incident point sources with one fixed source point and at most three scattering strengths. With this technique, we establish some uniqueness results for source scattering problem with multi-frequency phaseless far field data. Furthermore, a fast and stable phase retrieval approach is proposed based on a simple geometric result which provides a stable reconstruction of a point in the plane from three distances to given points. Difficulties arise for inverse scattering by rigid bodies due to the additional unknown far field pattern of the point sources. To overcome this difficulty, we introduce an artificial rigid body into the system and show that the underlying rigid bodies can be uniquely determined by the corresponding phaseless far field data at a fixed frequency. Noting that the far field pattern of the scattered field corresponding to point sources is very small if the source point is far away from the scatterers, we propose an appropriate phase retrieval method for obstacle scattering problems, without using the artificial rigid body. Finally, we propose several sampling methods for shape reconstruction with phaseless far field data directly. For inverse obstacle scattering problems, two different direct sampling methods are proposed with data at a fixed frequency. For inverse source scattering problems, we introduce two direct sampling methods for source supports with sparse multi-frequency data. The phase retrieval techniques are also combined with the classical sampling methods for the shape reconstructions. Extended numerical examples in two dimensions are conducted with noisy data, and the results further verify the effectiveness and robustness of the proposed phase retrieval techniques and sampling methods.

Reconstruction of a complex profile shape by weighting basic characterization results for nanometrology.

Scatterometry has become an essential method of characterization during the fabrication process of nanostructures. This nondestructive technique based on diffracted light analysis is composed of two steps: the measurement of the optical signatures and the treatment to reconstruct the profile of the periodic structure. The artificial neural network has proved its effectiveness in solving the inverse scattering problem. Usually the scatterometry characterization process requires a previous geometrical profile shape to be defined. This study proposes a method for the profile reconstruction of any geometrical shape, not necessarily one that is included in the initial model. For example, this could include the detection or the identification of an incorrect profile shape in a lithography or etching process. This so-called weighting profile approach consists in combining several results of basic characterizations for the reconstruction of the real profile shape. In this study, the feasibility of this method is demonstrated on theoretical samples to satisfy the requirements of scatterometry. Finally, the weighting profile method is compared with a classical scatterometry method involving a generic profile shape.

Real-time pose and shape reconstruction of two interacting hands with a single depth camera

We present a novel method for real-time pose and shape reconstruction of two strongly interacting hands. Our approach is the first two-hand tracking solution that combines an extensive list of favorable properties, namely it is marker-less, uses a single consumer-level depth camera, runs in real time, handles inter- and intra-hand collisions, and automatically adjusts to the user's hand shape. In order to achieve this, we embed a recent parametric hand pose and shape model and a dense correspondence predictor based on a deep neural network into a suitable energy minimization framework. For training the correspondence prediction network, we synthesize a two-hand dataset based on physical simulations that includes both hand pose and shape annotations while at the same time avoiding inter-hand penetrations. To achieve real-time rates, we phrase the model fitting in terms of a nonlinear least-squares problem so that the energy can be optimized based on a highly efficient GPU-based Gauss-Newton optimizer. We show state-of-the-art results in scenes that exceed the complexity level demonstrated by previous work, including tight two-hand grasps, significant inter-hand occlusions, and gesture interaction. 1

Strain Gauges Based 3D Shape Monitoring of Beam Structures Using Finite Width Gauge Model

This paper presents a new approach validated experimentally to reconstruct with strain gauges the deformed shape of a straight beam with circular cross section. It is based on a novel beam-specific strain gauge model that improves the strain measurement by taking into account the width of the gauges. These improved strain measurements are used by a 3D finite strain large displacement beam shape reconstruction method to recover the deformed shape iteratively. The whole reconstruction approach has been validated experimentally with 3D deformations of a beam instru-mented with strain gauges. Results show that the strain gauge model developed improves reconstruction accuracy and that beam reconstruction can be achieved effectively .

Phaseless inverse source scattering problem: Phase retrieval, uniqueness and direct sampling methods

Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the underlying sources. Furthermore, the phaseless far field pattern is also invariant if the source is multiplied by any complex number with modulus one. Therefore, the source can not be uniquely determined, even the multi-frequency phaseless far field patterns are considered. By adding a reference point source into the model, we propose a simple and stable phase retrieval method and establish several uniqueness results with phaseless far field data. We proceed to introduce a novel direct sampling method for shape and location reconstruction of the source by using broadband sparse phaseless data directly. We also propose a combination method with the novel phase retrieval algorithm and the classical direct sampling methods with phased data. Numerical examples in two dimensions are also presented to demonstrate their feasibility and effectiveness.

Discrete Element Analysis of the Reconstruction Method for Randomly Shaped Pebbles

The pebble shape is a critical factor that affects the bearing characteristics of truck escape ramps. In this paper, a reconstruction method was proposed for randomly shaped pebbles used in truck escape ramps, and statistical analysis was conducted on the results of pebble compression tests. First, 100 pebble samples were randomly selected, and the pebble outlines were fitted in three views. The overlapping method was implemented to fill the three views with ball elements, and the ball elements were then extended into three-dimensions. The results demonstrated that the proposed method satisfactorily monitored the real pebble shapes. Second, statistical analyses were conducted on the parameters of the outlines, and corresponding data sets were built. The key parameters of the pebble DEM model, such as the friction coefficient, were calibrated based on the compression test results, and repeated simulation results verified the feasibility of the proposed pebble DEM model. Next, statistical analysis was conducted on the probability distribution of the contact forces. Third, simulations were conducted with different pressing plate velocities and pebble shapes. The results indicated that the pressing plate velocities had minor effects on the contact forces. As the pressing plate velocity increased, the slope of the contact forces correspondingly increased. The particle shape was a critical factor affecting the simulation results. With the same contact parameters, the simulation results of different pebble shapes varied greatly, which further indicated the importance of the proposed pebble shape reconstruction method. The proposed pebble DEM model could be further used in the design of truck escape ramps.

Inverse Electromagnetic Source Scattering Problems with MultiFrequency Sparse Phased and Phaseless Far Field Data

This paper is concerned with uniqueness, phase retrieval, and shape reconstruction methods for solving inverse electromagnetic source scattering problems with multifrequency sparse phased or phaseless far field data. With the phased data, we show that the smallest strip containing the source support with the observation direction as the normal can be uniquely determined by the multifrequency far field pattern at a single observation direction. A phased direct sampling method is also proposed to reconstruct the strip. The phaseless far field data is closely related to the outward energy flux, which can be measured more easily in practice. We show that the phaseless far field data is invariant under the translation of the sources, which implies that the location of the sources cannot be uniquely recovered by the data. To solve this problem, we consider simultaneously the scattering of magnetic dipoles with one fixed source point and at most three scattering strengths. With this technique, a fast and stable phase retrieval approach is proposed based on a simple geometrical result which provides a stable reconstruction of a point in the plane from three distances to the given points. A novel phaseless direct sampling method is also proposed to reconstruct the strip. The phase retrieval approach can also be combined with the phased direct sampling method to reconstruct the strip. Finally, to obtain a source support, we just need to superimpose the indicators with respect to the sparse observation directions. Extended numerical examples in three dimensions are conducted with noisy data, and the results further verify the effectiveness and robustness of the proposed phase retrieval approach and direct sampling methods.

A novel mode shape reconstruction method for damage diagnosis of cracked beam

Abstract This paper presents a novel mode shape reconstruction method for damage diagnosis of cracked beam. The proposed method uses output-only data of damaged structure to identify and reconstruct the mode shape of healthy structure. Following that, the curvature mode shapes (CMS) is employed as a damage sensitive feature to locate the damage. In order to identify the mode shape of a target structure with measurement noises, EMD with intermittency criteria is applied to separate dynamic responses into individual modal responses of all grid points on the target structure. A statistical analysis is proposed to evaluate mode shapes from obtained modal responses. Then the Fourier series fitting is employed to mathematically represent the mode shape of the healthy structure. After that, the curvature mode shapes (CMS) which has been investigated as a promising feature for damage identification are acquired by a central difference approximation. Numerical studies are conducted for methodology illustration and validation. Effects of broader damage, multiple damage and measurement noise level are investigated in detail. The accuracy and effectiveness of the proposed method are demonstrated and verified by comparison with conventional method. Finally, a two-span continuous steel I-girder bridge is used to demonstrate the proposed method for more practical applications.

A novel 3D shape reconstruction method based on maximum correntropy Kalman filtering

PurposeThis paper aims to investigate a novel shape from focus (SFF) algorithm based on maximum correntropy Kalman filtering (SFF-MCKF) for solving the problem that traditional SFF methods are weak in de-noising and spatial continuity.Design/methodology/approachTo be specific, it was first assumed that the predicted depth of next pixel is equal to the depth of the current pixel according to spatial continuity. Besides, the observing data are derived from the estimation of traditional SFF and the corresponding covariance of noise is adaptively calculated by the entropy along the optical axis. Finally, to enhance robustness, we systematically conduct MCKF iteratively in four transfer directions that are 0°, 90°, 45° and −45°, respectively.FindingsThe experimental results indicate that the robustness of SFF-MCKF facing noises as well as the spatial continuity is better than that of the existing representative ones.Research limitations/implicationsAs the proposed method is aimed at precision objects, high demand is for experimental device. Unstable device unregister the source images, which is unfavorable for observing data.Originality/valueSFF-MCKF can be applied to many precision object measurements without significant drifts, such as the surface reconstruction of metal objects and electronic components. Besides, the computation cost is low, and SFF-MCKF has a wide range of real-time industrial applications.