Free-form Surface Reconstruction Research Articles

Three-dimensional surface reconstruction from reflectance direction fields with orthogonal multicolor filters

A three-dimensional (3D) freeform surface reconstruction method is proposed, specifically designed to handle complex surfaces, even those with steep inclinations. This method utilizes a one-shot color mapping imaging system to obtain reflectance direction fields using a stripe multicolor filter positioned in two orthogonal orientations. This imaging system can capture reflectance directions that are identifiable by corresponding colors. The multicolor filter consists of multiple stripe regions, each with a different transmission spectrum. Theoretically, an equation that describes the relationship between reflectance direction fields and the reflective 3D surface can be derived based on geometrical optics. By solving this equation using a deep neural network (DNN) as a gradient descent method without any training data, the 3D surface can be accurately reconstructed, even for surfaces with steep inclinations. The effectiveness of this method is validated through numerical demonstrations on several 3D surfaces, including complex ones with concave and convex areas, as well as steep inclinations.

Agent-Based Principal Strips Modeling for Freeform Surfaces in Architecture

The principal curvature (PC) of a freeform surface, as an important indicator of its fundamental features, is frequently used to guide their rationalization in the field of architectural geometry. The division of a surface using its PC lines into principal strips (PSs) is an innovative way to break down a freeform surface for construction. However, the application of PC networks in architectural design is hindered by the difficulty to generate them and flexibly control their density. This paper introduces a method for PS-based reconstruction of freeform surfaces with different umbilical conditions in the early stages of design. An agent-based modeling approach is developed to find the umbilics and increase the degree of control over the spacing of PC lines. This research can effectively expand the application range of PS-based surface reconstruction methods for freeform architectures.

Gravitational Discriminative Optimization for Multiview Reconstruction of Free-Form Surface

Automatic free-form surface reconstruction enables flexible and efficient industrial manufacturing. However, due to the performance of the 3-D measurement system, accurate and robust reconstruction is quite difficult due to corrupted data, discontinuous scanning, etc. To address these issues, in this article, we propose a novel gravitational discriminative optimization (GDO) method based on a multiview reconstruction framework for free-form blades. Our method consists of a training phase and a reconstruction phase. In the training phase, we introduce a novel gravitational distribution feature that is robust against the perturbations caused by corrupted data to instruct the sequence of update maps (SUM) learning process of GDO. To deal with the low overlap caused by the limited and discontinuous scanning, we propose a sequential scenes-to-model framework. Equipped with the trained SUM, we design the reconstruction phase to perform the blade model reconstruction accurately and robustly by partitioning it into inference with a gravitation map, an adaptive maps scheme to boost convergence, and an iterative closest point refinement. Experiments on both limited scanning-based synthetic data and real scene reconstruction of four blade models with different profiles show that GDO outperforms five other methods in terms of both accuracy and robustness.

Calibration method of laser scanning measurement system for large-scale component using a free-form surface reconstruction model

For large dimensional scanning measurement, the calibration method is limited by the standard part with the scale in millimeters or centermeters. In this paper, a novel calibration method suitable for large-scale components in meters has been developed based on the free-form surface reconstruction model. The Non-Uniform Rational B-Splines (NURBS) surface is approximated from the discrete measurement points obtained by high-precision detection using the least-squares method. The deviation between the measurement points and reference model is defined by statistical results and represented by the standard deviation of the distances from the measurement points to the corresponding closest points on the surface. Furthermore, the uncertainty components introduced in the procedure of coordinate registration and surface approximation are considered to estimate the combined uncertainty of a reconstructed surface. Finally, a scanning measurement device can be calibrated by the reconstruction model consisting of a NURBS surface expression and its uncertainty prediction. To validate the proposed calibration method, the surface of a standard part with a 4-meter diameter is detected to acquire a set of measurement points and subsequently reconstructed to a parametric surface, the uncertainty of which is analyzed considering errors introduced by both device accuracy and data processing. For the reconstruction model with degree of 4, the result shows that the calibration accuracy is superior to 30 μm with a tolerance error of less than 12 μm.

Robust Multipoint-Sets Registration for Free-Form Surface Based on Probability

Free-form surface reconstruction using point clouds is a common issue in manufacturing. In this article, a robust joint registration approach for multiview point clouds is proposed to address the problems brought by coarse initialization, outliers, and noise. The basic idea is that minimizing the L2 distance between probability distributions of integrated and standard models, such that a robust initialization is provided for fine registration to avoid local minima. The fine registration is formulated as a joint closet point problem, which is implicitly constrained by closed-loop consistency. In addition, a Lie algebra solution is derived to enforce rigid transformations. The robust initialization is judged by the simulated annealing algorithm. Finally, a probabilistic distance is defined and a maximum likelihood estimation of multiview transformations is designed to resist noise. The experiment on simulated and real data illustrate better robustness of our method to initial errors, outliers, and noise.

Adaptive sampling strategy of five-axis inspection for free-form surface reconstruction

Five-axis inspection is widely used for measuring free-form surfaces, which require high-precision surface reconstruction for quality analysis, remanufacturing and so on. Nevertheless, existing sampling strategies for five-axis inspection neither make full use of surface characteristics nor are they able to pre-calculate the number of paths based on the required surface reconstruction error. To solve these problems, we propose an adaptive sampling strategy aiming at improving the precision of surface reconstruction without affecting the inspection efficiency. The proposed algorithm uses the chord height of corresponding points between two adjacent sampling paths as a criterion to determine the distribution and shape adjustment of the sampling paths. Experiments proved that the proposed algorithm can improve the surface reconstruction by 26.3% in terms of the maximum error and 19.5% in terms of the mean error compared with two traditional sampling algorithms.

Deep-learning-based deflectometry for freeform surface measurement.

We propose a deep-learning based deflectometric method for freeform surface measurement, in which a deep neural network is devised for freeform surface reconstruction. Full-scale skip connections are adopted in the network architecture to extract and incorporate multi-scale feature maps from different layers, enabling the accuracy and robustness of the testing system to be greatly enhanced. The feasibility of the proposed method is numerically and experimentally validated, and its excellent performance in terms of accuracy and robustness is also demonstrated. The proposed method provides a feasible way to achieve the general measurement of freeform surfaces while minimizing the measurement errors due to noise and system geometry calibration.

基于彩色结构光的自由曲面三维重建方法

基于彩色结构光的自由曲面三维重建方法

Efficient analysis-suitable T-spline fitting for freeform surface reconstruction and intelligent sampling

Optical scanning instruments require sampling and reconstruction with high accuracy and low computational cost. T-splines have recently been developed that allow significant reductions in the number of control parameters by overcoming some of the topological constraints of B-splines and NURBS. As a subset of T-splines, analysis-suitable T-splines (ASTS) show promise due to the linear independence and partition of unity of their basis functions. In this paper, a computationally efficient ASTS fitting algorithm for freeform surface reconstruction is proposed. This algorithm starts with adaptive construction of an initial analysis-suitable T-mesh according to the distribution of high-curvature feature points. A local refinement and local optimisation algorithm of the analysis-suitable T-mesh is then iteratively performed until a preset accuracy condition is satisfied. Our experimental results show that the proposed ASTS fitting can produce over 50% root-mean-square reconstruction error reduction compared to NURBS fitting, with the same number of control parameters. The computing efficiency of the proposed algorithm is equivalent to or higher than that for simple T-spline fitting. Fast derivative analysis of the ASTS has also been carried out, where two automatic intelligent sampling design methods have been developed, namely element area sampling and element curvature sampling. Up to 50% reconstruction error reduction is observed when compared to uniform and statistically optimised sampling designs. With the novel reconstruction and compatible intelligent sampling design techniques, freeform surface measurement accuracy and efficiency could be effectively improved using coordinate measuring machines.

Preliminary Study on Development of 3D Free-Form Surface Reconstruction System Using a Webcam Imaging Technique

Reverse engineering faces challenges when it comes to data extraction using indirect contact method. There are 3D scanners capable of extracting data from distance more than a few meters away without contacting the objects but yet limited to same space range only. Although synchronizing the 3D scanners from another place can enable long distance data extraction, synchronizing devices over long distance can lead to other issues such as lagging. Moreover, the uses of 3D scanners usually involve quite long consumption time regardless of same space range or long distance range application. To overcome these issues, this study introduces a 3D surface reconstruction system by including a webcam imaging technique to produce a 3D point cloud, which is the same as that produced by a 3D scanner, and thus, eliminate the use of a 3D scanner. Through webcam imaging, image data can be transferred over the Internet and can be shared instantly even in different locations. Hence, webcam imaging is an alternative to using a 3D scanner. This system will continuously generate 3D free-form surfaces to resemble the surface profile of physical objects. Acquiring data until the surface fitting process will take less time compared with using a combination of 3D scanner and CAD software. In addition, results produced from the webcam imaging technique are compared with conventional results from a 3D scanner.

Design and Construction of a Device for Free Form Surfaces 3D Reconstruction Using Microsoft Kinect

There is an increasing need for geometric 3D reconstruction models in the Reverse engineering which is ones of computer Vision applications, reconstruction from a sequence of 2D images is much cheaper than 3D scanners and coordinate measurement machine and also been able to take advantage of the developments in digital cameras and the increasing resolution and quality of images. This work aims to develop a concept of 3D free form surface reconstruction rig and generate the dimension of the surface depending on proposed image processing technique. Through the results obtained is observed that. The overall of calibration accuracy the Root mean square (RMS) value of the point was produced the residuals value in the image space was (0.2830 mm) in the IR images.

Research on Laser Additive and Milling Subtractive Composite Remanufacturing Process of Compressor Blade

As an important energy conversion mechanism, centrifugal compressors play an important role in the national economy. The blade is one of the most critical components of the compressor. Damaged blades contain extremely high added value for remanufacturing. Thus, remanufacturing research on damaged and retired impeller/blade is getting more and more attention. Laser additive and milling subtractive composite remanufacturing technology is an effective means to achieve metal parts remanufacturing. In this paper, an advanced methodology for the remanufacturing of complex geometry and expensive components via reverse engineering, free-form surface modeling, laser additive repaired and machining is presented. The approach involves the integration of 3D non-contact digitization to obtain the point cloud data of damaged parts, adaptive free-form surface reconstruction to get the digital model of damage location, and laser additive manufacturing process containing slicing and path planning and subsequent multi-axis milling operation. The methodology has been successfully implemented on thin-curved centrifugal compressor blades. The results have shown that the composite remanufacturing method is an effective solution to realize the remanufacturing of damaged blades, and can be applied to the remanufacturing of other complicated parts.

The model of feature extraction for free-form surface based on topological transformation

• A topology-based rigid spherical quadrilateral mesh method is proposed in this paper. • The nondifferentiable problem of free-form surface is solved based on topological transformation. • The model of feature extraction for free-form surface based on topological transformation is built. • The tangent bundle of smooth free-form surface manifold is analyzed. Free-form surface reconstruction is the key technology of mathematical modeling of engineering. It is important for accurate reconstruction of the entity model that conforms to the design. In order to improve the measurement accuracy of the workpiece, a method for free-form surface feature recognition based on topological transformation is proposed in this paper. Firstly, the information of scanning points is expressed as the form of topological space. Based on this, a method of surface constructing that selects the natural-quadratic-surface as the manifold of free-form surface is proposed. Then, the free-form surface that is constructed from the original point cloud is transformed into a smooth free-form surface which is homeomorphic to the original free-form surface based on the theory of topological embedding. The features of the transformed free-form surface can be easily analyzed and recognized. Finally, the qualitative description of an arbitrary point on the surface is obtained by analyzing the tangent bundle of smooth free-form surface manifolds. The feature recognition of free-form surface for workpiece is realized. The experimental results on workpiece model are reported in this paper, which validate the effectiveness of the proposed method.

광학식 자유곡면 형상복원 알고리즘 개발

광학식 자유곡면 형상복원 알고리즘 개발

A multi-sensor approach for rapid and precise digitization of free-form surface in reverse engineering

Reverse engineering (RE) has emerged as a crucial tool in product design for facilitating reuse of design and relevant knowledge, by which new design can be accelerated. Reconstruction of free-form surface is the main focus of RE. To meet the demand of rapidly and precisely digitizing unknown complex free-form surface, which is the first step of RE, a multi-sensor approach characterized by an integrated use of a contact scanning probe (SP) and a point laser probe (PLP) is proposed. Both of the two digitizers are mounted on the Z axis arm of a coordinate measuring machine (CMM), and the distance between the laser beam of the PLP and the stylus of the SP in feed motion direction is adjusted to be equal to the specified scanning line spacing, so that the PLP is capable of measuring SP’s next scanning path as the SP is performing digitization task. With the priori path information acquired using PLP, measurement path planning algorithms are applied to program the next scanning path for SP real-timely. The planned scanning path can be subsequently used to automatically guide the SP and the CMM for fast and precise digitization of complex surfaces. A prototype system has been developed to demonstrate the feasibility of the proposed new method through experiment. Experimental results indicate that the proposed approach enables rapid, flexible, and high-precision digitization of complex free-form surface in reverse engineering.

Reverse engineering of free-form surface based on the closed-loop theory.

To seek better methods of measurement and more accurate model of reconstruction in the field of reverse engineering has been the focus of researchers. Based on this, a new method of adaptive measurement, real-time reconstruction, and online evaluation of free-form surface was presented in this paper. The coordinates and vectors of the prediction points are calculated according to a Bézier curve which is fitted by measured points. Final measured point cloud distribution is in agreement with the geometric characteristics of the free-form surfaces. Fitting the point cloud to a surface model by the nonuniform B-spline method, extracting some check points from the surface models based on grids and a feature on the surface, review the location of these check points on the surface with CMM and evaluate the model, and then update the surface model to meet the accuracy. Integrated measurement, reconstruction, and evaluation, with the closed-loop reverse process, established an accurate model. The results of example show that the measuring points are distributed over the surface according to curvature, and the reconstruction model can be completely expressed with micron level. Meanwhile, measurement, reconstruction and evaluation are integrated in forms of closed-loop reverse system.

Reconstruction of freeform surfaces for metrology

The application of freeform surfaces has increased since their complex shapes closely express a product's functional specifications and their machining is obtained with higher accuracy. In particular, optical surfaces exhibit enhanced performance especially when they take aspheric forms or more complex forms with multi-undulations. This study is mainly focused on the reconstruction of complex shapes such as freeform optical surfaces, and on the characterization of their form. The computer graphics community has proposed various algorithms for constructing a mesh based on the cloud of sample points. The mesh is a piecewise linear approximation of the surface and an interpolation of the point set. The mesh can further be processed for fitting parametric surfaces (Polyworks® or Geomagic®). The metrology community investigates direct fitting approaches. If the surface mathematical model is given, fitting is a straight forward task. Nonetheless, if the surface model is unknown, fitting is only possible through the association of polynomial Spline parametric surfaces. In this paper, a comparative study carried out on methods proposed by the computer graphics community will be presented to elucidate the advantages of these approaches. We stress the importance of the pre-processing phase as well as the significance of initial conditions. We further emphasize the importance of the meshing phase by stating that a proper mesh has two major advantages. First, it organizes the initially unstructured point set and it provides an insight of orientation, neighbourhood and curvature, and infers information on both its geometry and topology. Second, it conveys a better segmentation of the space, leading to a correct patching and association of parametric surfaces.

The Technology of Fast 3D Reconstruction Based on Stereo Vision

Reverse engineering has become an independent research area in CAD/CAM system with the development of modern manufacturing. The 3D reconstruction technology of generating a digit model from physical model is an important part of reverse engineering. The 3D reconstruction technology based on stereo vision has advantages such as non-contact measurement, simple system structure, being fast and efficient. In this paper, a fast 3D reconstruction technology based on stereo vision is presented. Firstly, BP neural network is used to simulate the mapping relationship between the 3D object and its images. Then, the epipole positions and adjusting coefficients for epipolar lines are calculated according to the epipolar line constraint. After the rectification transformations on the left and right image planes is conducted, the pairs of conjugate epipolar lines become collinear and parallel to the horizontal image axis. Therefore, when the stereo correspondences between the left and right images are being performed, the search is done only along the horizontal lines of the rectified images, which is highly advantageous to fast image matching for stereo vision and 3D reconstruction of free-form surface.

Inspection of freeform surfaces considering uncertainties in measurement, localization and surface reconstruction

Inspection of a manufactured freeform surface can be conducted by building its surface model and comparing this manufactured surface model with the ideal design surface model and its tolerance requirement. The manufactured freeform surface model is usually achieved by obtaining measurement points on the manufactured surface, transforming these measurement points from the measurement coordinate system to the design coordinate system through localization, and reconstructing the surface model using the localized measurement points. In this research, a method was developed to estimate the locations and their variances of any selected points on the reconstructed freeform surface considering different sources of uncertainties in measurement, localization and surface reconstruction processes. In this method, first locations and variances of the localized measurement points are calculated considering uncertainties of the measurement points and uncertainties introduced in the localization processes. Then locations and variances of points on the reconstructed freeform surface are obtained considering uncertainties of the localized measurement points and uncertainties introduced in the freeform surface reconstruction process. Two case studies were developed to demonstrate how these three different uncertainty sources influence the quality of the reconstructed freeform curve and freeform surface in inspection.

Dynamic deflectometry: A novel approach for the on-line reconstruction of specular freeform surfaces

The dynamic inspection and reverse engineering of specular freeform surfaces is a challenge so far largely unsolved. Products produced in high quantities in industrial environments are still inspected manually which is labour intensive, expensive, monotonous and subjective. We propose a novel deflectometric hardware setup and methodology to overcome this shortfall. The reflection of a line laser from a moving specular surface is captured on a translucent screen. The resulting complex line provides detailed data about the surface gradients at the intersection of the laser light plane and the surface but cannot create correspondence between points of reflections and surface points. The latter is inherent in a traditional active light scanning setup whose data alone will, for specular surfaces, be subject to high levels of noise. We propose a novel method that by simulation of the reflection fuses the two data sets to allow digitalising moving specular surfaces with the high slope sensitivity of deflectometric methods.