Shape Reconstruction Method Research Articles

A fast reconstruction method for three-dimensional shape measurement using dual-frequency grating projection and phase-to-height lookup table

Phase-to-height mapping is indispensable part of three-dimensional (3D) shape measurement system based on phase analysis, which guarantees the accuracy of 3D reconstruction. In this paper, a fast 3D shape reconstruction method based on dual-frequency grating projection and phase-to-height lookup table is proposed. In this proposed method, the reference plane is moved with known interval along the measurement depth direction to establish the mapping lookup table between the phase of the high and low frequency projected grating and their corresponding spatial height pixel by pixel respectively. Then, two methods to establish the lookup table with the unwrapped and the wrapped phase have been respectively introduced according to the characteristics of dual-frequency grating. The actual experimental results show that the two methods can effectively extend the measurement range of the current wrapped phase-to-height lookup method, and the reconstruction accuracy is better than the traditional phase-to-height quadratic fitting method. At the same time, the consumed time for 3D shape reconstruction of the tested object by the two methods is compared and analyzed. Finally, combining the high performance parallel computation of GPU, the fast 3D shape reconstruction is realized with the speed of 60fps.

A level set method for shape reconstruction in seismic full waveform inversion using a linear elastic model in 2D

We present a novel shape reconstruction technique for seismic full waveform inversion that uses a linear elastic system in 2D for modeling wave propagation in the Earth and a level set technique for performing shape evolution. A cost functional is formulated and minimized by a gradient based descent technique with backtracking line search and an Armijo condition. The three distributed elastic parameter profiles are in our model assumed to follow a given reference profile inside an unknown region D, and a different reference profile outside of D. The task is to reconstruct the unknown region D from seismic data obtained at or close to the surface. We present numerical experiments that address the imaging of salt domes buried in the Earth. The results demonstrate that our new algorithm is able to reconstruct shapes with non-trivial topology from a simpler starting guess in few iterations.

Experimental study on slippery droplet dynamics using optical correction method

When a droplet is placed on an inclined plane, it can slide down the plane by gravitational force. This phenomenon can occur in many industrial applications such as surface coating and printing, as well as in evaluating the characteristics of a surface. The slippery droplet can be analyzed from the balance between the gravitational force and the sum of the capillary and resistance forces. Researchers have suggested various equations of force balance with several hypotheses. To increase the reliability of the force balance correlation, it is important to obtain an accurate inside velocity profile and the three-dimensional (3D) shape of a droplet. In this paper, an analysis system of the slippery droplet was developed which includes optical correction based on a ray tracing method for velocity field measurement and an ellipse fitting method for droplet shape reconstruction. These correction methods were verified by a numerical simulation and applied to a slippery droplet on an inclined plate coated with Poly methyl methacrylate (PMMA). The wall shear force calculated from the velocity field and that calculated from the force balance were in good agreement.

Design, Measurement and Shape Reconstruction of Soft Surgical Actuator Based on Fiber Bragg Gratings

Soft actuators are the components responsible for organs and tissues adsorptive fixation in some surgical operations, but the lack of shape sensing and monitoring of a soft actuator greatly limits their application potential. Consequently, this paper proposes a real-time 3D shape reconstruction method of soft surgical actuator which has an embedded optical fiber with two Fiber Bragg Grating (FBG) sensors. First, the design principle and the sensing of the soft actuator based on FBG sensors are analyzed, and the fabrication process of soft actuator which has an embedded optical fiber with two FBG sensors is described. Next, the calibration of the FBG sensors is conducted. Based on curvatures and curve fitting functions, the strategy of 3D shapes reconstruction of the soft actuator is presented. Finally, some bending experiments of the soft actuator are carried out, and the 3D shapes of the soft actuator at different bending states are reconstructed. This well reconstructed 3D shape of a soft actuator demonstrates the effectiveness of the shape reconstruction method that is proposed in this paper, as well as the potential and increased applications of these structures for real soft surgical actuators.

Shape reconstruction of large optical surface with high-order terms in fringe reflection technique

A fast and effective shape reconstruction method of large aspheric specular surfaces with high order terms is proposed in fringe reflection technique, which combines modal estimation with high-order finitedifference algorithm. The iterative equation with highorder truncation errors is derived for calculating the specular surface with large aperture based on high-order finite-difference algorithm. To achieve the wavefront estimation and improve convergence speed, the numerical orthogonal transformation method based on Zernike polynomials is implemented to obtain the initial iteration value. The reconstruction results of simulated surface identified the advantages of the proposed method. Furthermore, a freeform in illuminating system has been used to demonstrate the validity of the improved method in practical measurement. The results show that the proposed method has the advantages of making the reconstruction of different shape apertures accurate and rapid. In general, this method performs well in measuring large complex objects with high frequency information in practical measurement.

Shape reconstruction based on zero-curl gradient field estimation in a fringe reflection technique.

A novel shape reconstruction method based on zero-curl gradient field estimation is presented in this paper. Zero-curl field estimation makes the most of curl information to obtain the ideal gradient data, and achieves the reconstruction with the quality map path integration method. In the estimation process, an algebraic approach is adopted to enforce integrability, which maintains the local information well. Moreover, we use the residual gradients of surface obtained from the Southwell zonal reconstruction algorithm as the raw gradient data in zero-curl field estimation, which has a stable tradeoff between smoothness and local shape confinement. The performance of the proposed method over antinoise capability is discussed and demonstrated by the simulations. The measurement experiment of an ultraprecision sphere mirror identifies the validity over general shapes, and the reconstruction results of hyperbolic surface with a local shape map demonstrate the better performance on local details retention. Therefore, this method performs well in handling complex objects with local mutation regions and high accuracy requirement of local information in practical measurement.

A Linear Method for Shape Reconstruction Based on the Generalized Multiple Measurement Vectors Model

In this paper, a novel linear method for shape reconstruction is proposed based on the generalized multiple measurement vectors (GMMV) model. Finite difference frequency domain (FDFD) is applied to discretized Maxwell's equations, and the contrast sources are solved iteratively by exploiting the joint sparsity as a regularized constraint. Cross validation (CV) technique is used to terminate the iterations, such that the required estimation of the noise level is circumvented. The validity is demonstrated with an excitation of transverse magnetic (TM) experimental data, and it is observed that, in the aspect of focusing performance, the GMMV-based linear method outperforms the extensively used linear sampling method (LSM).

Direct sampling methods for inverse elastic scattering problems

We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using the different component of the far field patterns. Only inner products are involved in the computation, thus the novel sampling methods are 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 functionals for sampling points inside the scatterers. While for the sampling points outside the scatterers, we show that the indicator functionals decay like the Bessel functions as the sampling point goes away from the boundary of the scatterers. We also show that the proposed indicator functionals continuously dependent on the far field patterns, which further implies that the novel sampling methods are extremely stable with respect to data error. For the case when the observation directions are restricted into the limited aperture, we firstly introduce some data retrieval techniques to obtain those data that can not be measured directly and then use the proposed direct sampling methods for location and shape reconstructions. Finally, some numerical simulations in two dimensions are conducted with noisy data, and the results further verify the effectiveness and robustness of the proposed sampling methods, even for multiple multiscale cases and limited-aperture problems.

Extension of the GMMV-Based Linear Method to Quantitative Inverse Scattering

The linear shape reconstruction method based on the generalized multiple measurement vectors model is a newly proposed approach that is able to effectively retrieve the morphological information of dielectric/metallic scatterers with competitive imaging resolution. In this letter, we have extended this approach to quantitative inversion, with which a coarse estimation of the dielectric parameters can be obtained in an efficient way. The inversion of the transverse magnetic polarized Fresnel datasets from the year 2005 demonstrates applicability of the proposed method to real-life applications.

Reconstruction of granular railway ballast based on inverse discrete Fourier transform method

This paper presents a particle shape characterization and reconstruction method to describe the geometrical information of granular railway ballast. The outline of a real granular particle is segmented and transformed as discrete time domain signals based on Fourier transform method. Then, the discrete Fourier transform algorithm is developed and applied to convert discrete time domain signals into a discrete Fourier spectrum. Meanwhile, the normalized amplitudes are defined as Fourier descriptors, which is found to be applicable to characterize and reconstruct particle contour. Further, the proposed method is validated by comparing the contours of the real particle with that of reconstructed particle. Moreover, the shape indexes of particles Fourier descriptors and reconstruction of ballasted gravel are illustrated and the the results show that the geometrical parameters can be classified as three levels which can represent the geometrical characteristics in terms of macroscopical and microscopic structure. The inverse discrete Fourier transform can quantitatively control the shape of reconstructed particles by controlling the value and distribution of Fourier descriptors, which matchs the three levels of shape indexes. Furthermore, it can be found that a large number of virtual particles with similar geometrical features can be reconstructed using the proposed Fourier descriptors in a rapid and convenient manner, which is beneficial for providing a virtual test sample for the numerical modeling of realistic granular materials.

Unified Tracking and Shape Estimation for Concentric Tube Robots

Tracking and shape estimation of flexible robots that navigate through the human anatomy are prerequisites to safe intracorporeal control. Despite extensive research in kinematic and dynamic modeling, inaccuracies and shape deformation of the robot due to unknown loads and collisions with the anatomy make shape sensing important for intraoperative navigation. To address this issue, vision-based solutions have been explored. The task of 2-D tracking and 3-D shape reconstruction of flexible robots as they reach deep-seated anatomical locations is challenging, since the image acquisition techniques usually suffer from low signal-to-noise ratio or slow temporal responses. Moreover, tracking and shape estimation are thus far treated independently despite their coupled relationship. This paper aims to address tracking and shape estimation in a unified framework based on Markov random fields. By using concentric tube robots as an example, the proposed algorithm fuses information extracted from standard monoplane X-ray fluoroscopy with the kinematics model to achieve joint 2-D tracking and 3-D shape estimation in realistic clinical scenarios. Detailed performance analyses of the results demonstrate the accuracy of the method for both tracking and shape reconstruction.

Dip transform for 3D shape reconstruction

The paper presents a novel three-dimensional shape acquisition and reconstruction method based on the well-known Archimedes equality between fluid displacement and the submerged volume. By repeatedly dipping a shape in liquid in different orientations and measuring its volume displacement, we generate the dip transform : a novel volumetric shape representation that characterizes the object's surface. The key feature of our method is that it employs fluid displacements as the shape sensor. Unlike optical sensors, the liquid has no line-of-sight requirements, it penetrates cavities and hidden parts of the object, as well as transparent and glossy materials, thus bypassing all visibility and optical limitations of conventional scanning devices. Our new scanning approach is implemented using a dipping robot arm and a bath of water, via which it measures the water elevation. We show results of reconstructing complex 3D shapes and evaluate the quality of the reconstruction with respect to the number of dips.

Building an Urban Spatial Structure from Urban Land Use Data: An Example Using Automated Recognition of the City Centre

It has been suggested that the method of constructing an urban spatial structure typically follows a forward process from planning and design up to expression, as reflected in both graphic and text descriptions of urban planning. Although unorthodox, the original status structures can be extracted and constructed from an existing urban land-use map. This approach not only provides the methodological foundation for urban spatial structure evolution and allows for a comparative and quantitative analysis between the existing and planned conditions, but also lays a theoretical basis for failure in scientific decision making during the planning phase. This study attempts to achieve this by identifying the city centre (a typical element of the urban spatial structure) from urban land use data. The city centre is a special region consisting of several units with particular spatial information, including geometric attributes, topological attributes, and thematic attributes. In this paper, we develop a methodology to support the delineation of the city centre, considering these factors. First, using commercial land data, we characterise the city centre as units based on a series of indicators, including geometric and thematic attributes, and integrate them into a composite index of “urban centrality”; Second, a graph-based spatial clustering method that considers both topological proximity and attribute similarity is designed and used to identify the city centre. The precise boundary of the city centre is subsequently delimited using a shape reconstruction method based on the cluster results. Finally, we present a case study to demonstrate the effectiveness and practicability of the methodology.

Sparse transfer for facial shape-from-shading

We present an image-based 3D face shape reconstruction method which transfers shape cues inferred from source face images to guide the reconstruction of the target face. Specifically, a sparse face shape adaption mechanism is used to generate a target-specific reference shape by adaptively and selectively combining source face shapes. This reference shape can also facilitate the reconstruction optimization for the target shape. As an off-line process, each source shape has been derived from a set of given sufficient source images (more than 9) based on a non-Lambertian reflectance model. Such a process allows for the existence of cast shadow and specularity, and more accurately infers the source shape. Guided by the target-specific reference shape, the shape of a target face can be estimated using a small number of images (even only one). The proposed reconstruction method refers to a lighting estimation and an albedo estimation for the target face. No standard 3D shape (such as the high-precision scanned 3D face) is required in the reconstruction process. Compared to the state-of-the-arts including the Photometric Stereo, Tensor Spline, the single reference based method, and the GEM algorithm, the proposed sparse transfer model can produce visually better facial details and obtain smaller reconstruction errors.

Visual Hull Method for Realistic 3D Particle Shape Reconstruction Based on High-Resolution Photographs of Snowflakes in Free Fall from Multiple Views

AbstractA visual hull method for reconstruction of realistic 3D shapes of snowflakes and other hydrometeors based on high-resolution photographs of particles in free fall from multiple views captured by a multiangle snowflake camera (MASC), or another similar instrument, is proposed and presented. The visual hull of an object is the maximal domain that gives the same silhouettes as the object from a certain set of viewpoints. From the measured fall speed and the particle shape reconstruction, the particle density and dielectric constant are estimated. This is the first time 3D shape reconstructions based on multiple high-resolution photographs of real (measured) snowflakes are performed. The results are clearly much better than any similar data in the literature. They demonstrate—in experiments involved in real snowstorm observations and those with simulated and fake 3D-printed snowflakes—sufficient silhouette information from the five cameras of the expanded MASC system and excellent performance of the implemented mechanical calibration and software self-calibration of the system. In addition to enabling realistic “particle by particle” computations of polarimetric radar measurables for winter precipitation, the visual hull 3D shape reconstructions of hydrometeors can be used for microphysical characteristics analyses, hydrometeor classification, and improvement of radar-based estimations of liquid-equivalent snow rates.

Extra Facial Landmark Localization via Global Shape Reconstruction.

Localizing facial landmarks is a popular topic in the field of face analysis. However, problems arose in practical applications such as handling pose variations and partial occlusions while maintaining moderate training model size and computational efficiency still challenges current solutions. In this paper, we present a global shape reconstruction method for locating extra facial landmarks comparing to facial landmarks used in the training phase. In the proposed method, the reduced configuration of facial landmarks is first decomposed into corresponding sparse coefficients. Then explicit face shape correlations are exploited to regress between sparse coefficients of different facial landmark configurations. Finally extra facial landmarks are reconstructed by combining the pretrained shape dictionary and the approximation of sparse coefficients. By applying the proposed method, both the training time and the model size of a class of methods which stack local evidences as an appearance descriptor can be scaled down with only a minor compromise in detection accuracy. Extensive experiments prove that the proposed method is feasible and is able to reconstruct extra facial landmarks even under very asymmetrical face poses.

An elastodynamic computational time-reversal method for shape reconstruction of traction-free scatterers

This study proposes an elastodynamic time-reversal imaging method for the shape reconstruction of flaws with the traction-free boundary. The proposed method is a generalization of the synthetic aperture focusing technique (SAFT) implemented with the aid of time-reversal back-propagation computation. The reconstruction formula is derived from the boundary condition applied on the flaw boundary without using a diffraction theory yielding an inherently normalized objective function. No restriction is imposed on the wave source or the material properties as long as the wave medium is linearly elastic and lossless. There are two major advantages with the proposed method. First, it is free from ray tracing. The method can thus work with an arbitrary source and the wave modes including inhomogeneous waves. Second, signal conditioning is not required to focus a scattered field to the correct location in the reconstructed image. Numerical examples are presented to demonstrate the performance and benefits of the proposed method. In the numerical examples, the shape of cavities and cracks in an elastic layer is reconstructed from synthetic data. The results show that the method works well with the reverberating incident fields in which inhomogeneous and body waves coexist. Also demonstrated is that the curvature of the cavities is resolved well at the scale of the incident wave length. Through the numerical examples, the method is shown to be a versatile imaging method potentially useful for ultrasonic nondestructive characterization of small flaws.

Stereo imaging camera model for 3D shape reconstruction of complex crystals and estimation of facet growth kinetics

The principle that the 3D shape of crystals that grow from a solution can be characterised in real-time using stereo imaging has been demonstrated previously. It uses the 2D images of a crystal that are obtained from two or more cameras arranged in defined angles as well as a mathematical reconstruction algorithm. Here attention is given to the development of a new and more robust 3D shape reconstruction method for complicated crystal structures. The proposed stereo imaging camera model for 3D crystal shape reconstruction firstly rotates a digitised crystal in the three-dimensional space and varies the size dimensions in all face directions. At each size and orientation, 2D projections of the crystal, according to the angles between the 2D cameras, are recorded. The contour information of the 2D images is processed to calculate Fourier descriptors and radius-based signature that are stored in a database. When the stereo imaging instrument mounted on a crystalliser captures 2D images, the images are segmented to obtain the contour information and processed to obtain Fourier descriptors and radius-based information. The calculated Fourier descriptors and radius-based signature are used to find the best matching in the database. The corresponding 3D crystal shape is thus found. Potash alum crystals that each has 26 habit faces were used as a case study. The result shows that the new approach for 3D shape reconstruction is more accurate and significantly robust than previous methods. In addition, the growth rates of {111}, {110} and {100} faces were correlated with relative supersaturation to derive models of facet growth kinetics.

Shape Sensing Techniques for Continuum Robots in Minimally Invasive Surgery: A Survey.

Continuum robots provide inherent structural compliance with high dexterity to access the surgical target sites along tortuous anatomical paths under constrained environments and enable to perform complex and delicate operations through small incisions in minimally invasive surgery. These advantages enable their broad applications with minimal trauma and make challenging clinical procedures possible with miniaturized instrumentation and high curvilinear access capabilities. However, their inherent deformable designs make it difficult to realize 3-D intraoperative real-time shape sensing to accurately model their shape. Solutions to this limitation can lead themselves to further develop closely associated techniques of closed-loop control, path planning, human-robot interaction, and surgical manipulation safety concerns in minimally invasive surgery. Although extensive model-based research that relies on kinematics and mechanics has been performed, accurate shape sensing of continuum robots remains challenging, particularly in cases of unknown and dynamic payloads. This survey investigates the recent advances in alternative emerging techniques for 3-D shape sensing in this field and focuses on the following categories: fiber-optic-sensor-based, electromagnetic-tracking-based, and intraoperative imaging modality-based shape-reconstruction methods. The limitations of existing technologies and prospects of new technologies are also discussed.

An Analysis of Reconstruction Algorithms Applied to 3D Building Modeling

Objectives: The process of reconstructing a city cannot be fully automated. More human intervention is required to achieve high quality mass modeling. Our objectives are to provide a guide for the 3D graphic designers and 3D modelers in developing 3D building models. Methods: We present an up-to-date survey of the reconstruction algorithms which are further classified as point cloud based reconstruction methods and structure-aware shape reconstruction methods. We introduce various existing 3D reconstruction techniques and have compared those techniques based on shape simplification, surface completion and shape modeling methodologies. Findings: We have identified the pipeline process and technical issues encountered in each phase of the reconstruction process from a given image layout. As stated, the inverse procedural reconstruction approaches are best oriented towards the reconstruction of buildings from a given input 2D image. Also, there is a lack of systems that are capable of generating procedural rules from user interaction. Improvements: We propose a new 3D reconstruction methodology and novel framework that combines component based structure capturing and rule based modeling techniques that would best be suitable for 3D building modeling, resembling the real world buildings in future systems.