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We revisit the classic situation in functional data analysis in which curves are observed at discrete, possibly sparse and irregular, arguments with observation noise. We focus on the reconstruction of individual curves by prediction intervals and bands. The standard approach consists of two steps: first, one estimates the mean and covariance function of curves and observation noise variance function by, e.g. penalized splines, and second, under Gaussian assumptions, one derives the conditional distribution of a curve given observed data and constructs prediction sets with required properties, usually employing sampling from the predictive distribution. This approach is well established, commonly used and theoretically valid but practically, it surprisingly fails in its key property: prediction sets constructed this way often do not have the required coverage. The actual coverage is lower than the nominal one. We investigate the cause of this issue and propose a computationally feasible remedy that leads to prediction regions with a much better coverage. Our method accounts for the uncertainty of the predictive model by sampling from the approximate distribution of its spline estimators whose covariance is estimated by a novel sandwich estimator. Our approach also applies to the important case of covariate-adjusted models. [ABSTRACT FROM AUTHOR]

The open hole well area located in the eastern part of the Yanchang Oilfield has an earlier logging time. There are only three logging data in this area: SP, GR and R2. 5. Due to the lack of logging curves such as AC and RT, refined research on reservoir geology is difficult to meet. The region has the characteristics of long development time and low single well production, so it is infeasible and uneconomical to carry out logging again. Long short-term memory (LSTM ) model can be used to reconstruct missing logging curves. It is an economical and effective method suitable for stratigraphic logging sequence data. However, the application effect of this model in the eastern part of Yanchang Oilfield is poor. The reason is that the loess layer overlying the shallow oil reservoirs in the eastern region has significant interference with logging data signals. To address this issue, the LSTM model was constrained by geological stratification and a new model was established to achieve curve reconstruction. The logging data of each well with a length of 6 layers is intercepted by layered data as sample data. This method not only retains the advantages of LSTM model for sequential data processing, but also avoids the interference of overlying loess layer logging data on the model. Open hole wells with complete logging data were utilized for model training and validation. The accuracy of LSTM logging curve reconstruction considering geological stratification constraints was discussed. The results indicate that by introducing geological stratification constraints, the accuracy of model reconstruction logging curves is higher. The optimized model was used to reconstruct AC and RT curves for 50 wells in the open hole area with only GR, SP, and R2. 5 curve data. Secondary interpretation work was carried out on 142 perforated sections of 50 wells, and the coincidence rate of interpretation results compared to oil testing conclusions reached 89. 4% . The practicality and effectiveness of this method in reconstructing logging curves have been verified. [ABSTRACT FROM AUTHOR]

Curve reconstruction is a fundamental task in many visual computing applications. In this paper, a data-driven approach for curve reconstruction is proposed. We present an inception layered deep neural network structure, capable of learning simultaneously the number of control points and their positions in order to reconstruct the curve. To train the network, a large set of general synthetic data is generated. The reconstructed uniform B-spline closely approximates any arbitrary input curve, with or without intersections. Because the network predicts the number of control points required for the B-spline reconstruction, redundancy is reduced in the curve representation. We demonstrate our approach on various examples. [ABSTRACT FROM AUTHOR]

Realistic sensory feedback is paramount for amputees as it improves prosthetic limb control and boosts functionality, safety, and overall quality of life. This sensory restoration relies on the direct electrostimulation of residual peripheral nerves. Computational models are instrumental in simulating these neurostimulation effects, offering solutions to the complexities tied to extensive animal/human trials and costly materials. Central to these models is the detailed mapping of nerve geometry, necessitating the delineation of internal nerve structures, such as fascicles, across various cross-sections. In our modeling process, we faced the challenge of organizing an originally unstructured set of points into coherent contours. We introduced a parameter-free curve-reconstruction algorithm that combines valley-seeking clustering, an adaptive Kalman filter, and the nearest neighbor classification technique. While intuitively simple for humans, the task of reconstructing multiple open and/or closed lines with pronounced corners from a nonuniform point set is daunting for many algorithms. Additionally, the precise differentiation of adjacent curves, commonly encountered in realistic nerve models, remains a formidable challenge even for top-tier algorithms. Our proposed method adeptly navigates the complexities inherent to nerve structure reconstruction. While our algorithm is chiefly designed for closed curves, as dictated by nerve geometry, we believe it can be reconfigured with appropriate code adjustments to handle open curves. Beyond neuroprosthetics, our proposed model has the potential to be applied and spark innovations in biomedicine and a variety of other fields. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Computer-Aided Design & Computer Graphics / Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We propose a new strategy for curve reconstruction in an image through an off-the-grid variational framework, inspired by spike reconstruction in the literature. We introduce a new functional CROC on the space of 2-dimensional Radon measures with finite divergence denoted V, and we establish several theoretical tools through the definition of a certificate. Our main contribution lies in the sharp characterization of the extreme points of the unit ball of the V -norm: there are exact measures supported on 1-rectifiable oriented simple Lipschitz curves, thus enabling a precise characterization of our functional minimizers and further opening a promising avenue for the algorithmic implementation. [ABSTRACT FROM AUTHOR]

• Revealed an error source of FBG straightness perception of scraper conveyor. • Proposed the 2D curve reconstruction accuracy compensation model. • Designed an experiment on the curvature error response characteristics. The straightness perception of scraper conveyor is a technology that helps to achieve intelligent operation of coal mine working faces. However, there is a problem of accuracy degradation caused by sensor torsion based on fiber Bragg grating (FBG) shape sensing technology. This paper proposes an accuracy compensation method based on torsion angle, and verifies the effectiveness of accuracy compensation through simulation and experimental research. Experimental tests have shown that when the torsion angle of the sensing substrate is 10° and 20°, the end accuracy of the reconstructed curve after accuracy compensation is increased by 2.77% and 1.93% compared to before compensation, respectively. This study indicates that compensation based on the torsion angle can significantly improve the accuracy of two-dimensional (2D) curve reconstruction, and it has broad engineering application prospects in fields such as straightness perception of scraper conveyors and monitoring of underwater pipelines. [ABSTRACT FROM AUTHOR]

Realistic sensory feedback is paramount for amputees as it improves prosthetic limb control and boosts functionality, safety, and overall quality of life. This sensory restoration relies on the direct electrostimulation of residual peripheral nerves. Computational models are instrumental in simulating these neurostimulation effects, offering solutions to the complexities tied to extensive animal/human trials and costly materials. Central to these models is the detailed mapping of nerve geometry, necessitating the delineation of internal nerve structures, such as fascicles, across various cross-sections. In our modeling process, we faced the challenge of organizing an originally unstructured set of points into coherent contours. We introduced a parameter-free curve-reconstruction algorithm that combines valley-seeking clustering, an adaptive Kalman filter, and the nearest neighbor classification technique. While intuitively simple for humans, the task of reconstructing multiple open and/or closed lines with pronounced corners from a nonuniform point set is daunting for many algorithms. Additionally, the precise differentiation of adjacent curves, commonly encountered in realistic nerve models, remains a formidable challenge even for top-tier algorithms. Our proposed method adeptly navigates the complexities inherent to nerve structure reconstruction. While our algorithm is chiefly designed for closed curves, as dictated by nerve geometry, we believe it can be reconfigured with appropriate code adjustments to handle open curves. Beyond neuroprosthetics, our proposed model has the potential to be applied and spark innovations in biomedicine and a variety of other fields.

We propose a curve reconstruction model based on material frame and twisted multicore fiber (MCF), which can reconstruct the position and orientation of MCF simultaneously. The twisted MCF is approximated as a ribbon, whose centerline and surface characteristics are used to characterize the position and orientation of MCF. Material frame corresponding to the ribbon is established, and quantitative analysis is realized by the differential equations between frame basis vectors and fiber deformation parameters. Bending, twisting-strain model is established according to the approximate development of the twisted MCF, and the deformation parameters are obtained. Further, position and orientation of MCF can be reconstructed under the interference of twisting deformation. In simulation, the influence of curvature, torsion of target curves and twist bias, twisting deformation of MCF on curve reconstruction is analyzed. The results indicate that the proposed model is applicable to curves with zero curvature and variable curvature. With 10 rad/m sinusoidal twisting deformation, the deterioration of reconstruction accuracy can be effectively suppressed by introducing twist bias into MCF. For S-shaped curve with curvature and torsion within 1–50 m−1 and −10-10 rad/m, the tip position error and tip orientation error are less than 5 mm and 5 mrad over the length of 1 m.

• A high precision T-mesh blade modeling method based on 2D and 3D knot adaptive refinement is proposed. • LSPIA method combined with curvature-constrained refinement is employed to reconstruct blade cross-sectional profiles. • The concept of periodic curves/surfaces is introduced to the blade modeling process since the early 2D stage. • A local T-spline surface skinning method based on Mid-Closest Refinement for blade surface modeling is proposed. • A synthetic curvature extracting method by bidirectional curves is proposed during the surface adjusting process. The aerodynamic shape of blades in turbo machinery is a key factor that affects blade efficiency, pressure ratio and other performance indicators. To address the lack of global continuity and difficulty in ensuring fairing quality in blade modeling, this paper proposes a novel blade modeling method that uses curvature constraints and a Mid-Closest Criterion to achieve adaptive knot refinement in 2D profile reconstructing and 3D T-mesh establishing process respectively. To begin with, the proposed Curvature-Constrained Periodic Reconstruction (CCPR) is used to reconstruct discrete sampling points of the section profile into a globally fairing periodic curve, and meets minimal error requirement. Additionally, the distribution of control points matches with curvature variation of the curve itself. Next, the Double Curves-guided Mid-Closest T-spline Surface skinning (DCM-TS) is used to construct a T-mesh from the stacked cross-sectional profile curves automatically, and the control vertices of the T-mesh are in a controllable scale and reasonably distributed. Further, the modeling precision is allocated with the curvature information of the ideal blade contour, and based on that, a T-spline skinning surface is obtained through LSPIA method, which updates the model and realizes blade modeling that considers both the design efficiency and accuracy. Eventually the proposed method is verified and compared with several traditional surface skinning methods in practical modeling cases. The result unveils that the presented method is compatible with traditional aerofoil parameterization methods, generates surface with global continuity and high fairing quality, and has sharply reduced and evenly distributed control vertices. [ABSTRACT FROM AUTHOR]

In many application fields (closed curve noise data reconstruction, time series data fitting, image edge smoothing, skeleton extraction, etc.), curve reconstruction based on noise data has always been a popular but challenging problem. In a single domain, there are many methods for curve reconstruction of noise data, but a method suitable for multi-domain curve reconstruction has received much less attention in the literature. More importantly, the existing methods have shortcomings in time consumption when dealing with large data and high-density point cloud curve reconstruction. For this reason, we hope to propose a curve fitting algorithm suitable for many fields and low time consumption. In this paper, a curve reconstruction method based on clustering and point cloud principal component analysis is proposed. Firstly, the point cloud is clustered by the K++ means algorithm. Secondly, a denoising method based on point cloud principal component analysis is proposed to obtain the interpolation nodes of curve subdivision. Finally, the fitting curve is obtained by the parametric curve subdivision method. Comparative experiments show that our method is superior to the classical fitting method in terms of time consumption and effect. In addition, our method is not constrained by the shape of the point cloud, and can play a role in time series data, image thinning and edge smoothing. [ABSTRACT FROM AUTHOR]

Curve network reconstruction from a set of unorganized points is an important problem in reverse engineering and computer graphics. In this paper, we propose an automatic method to extract curve segments and reconstruct curve networks from unorganized spatial points. Our proposed method divides reconstruction of curve networks into two steps: 1) detecting nodes of curve segments and 2) reconstructing curve segments. For detection of nodes of curve segments, we present a principal component analysis-based algorithm to obtain candidate nodes from unorganized spatial points and a Euclidean distance-based iterative algorithm to remove peripheral nodes and find the actual nodes. For reconstruction of curve segments, we propose an extraction algorithm to obtain the points on each of curve segments. We present quite a number of examples which use our proposed method to reconstruct curve networks from unorganized spatial points. The results demonstrate the effectiveness of our proposed method and its advantages of good automation and high reconstruction efficiency.

Three-dimensional (3D) reconstruction of objects and scenes from camera images is of great interests due to its wide applications. Reconstruction based on feature point correspondence is an established approach. Existing research on curve-based reconstruction is limited to certain type of curves and constrained by case-dependent reconstruction accuracy. In view of that, this paper developed a new method to reconstruct general 3D curves from stereo images. Under proposal, a B-spline curve fitting is applied to sets of 2D edge points extracted from acquired stereo images. Derived approximating parametric curves are then used to construct conic surfaces. Further, robust iterative algorithms are developed to get intersection of corresponding conic surfaces to recover 3D curve. Due to the method design, proposed approach can reconstruct general 3D curves including both open and closed curves. The curve fitting technique and developed robust algorithms can meet accuracy requirement of many real applications. Validity of the proposed method is verified through experiments on a cylinder and teacup in laboratory and a real forging within a workshop. [ABSTRACT FROM AUTHOR]

In many application fields (closed curve noise data reconstruction, time series data fitting, image edge smoothing, skeleton extraction, etc.), curve reconstruction based on noise data has always been a popular but challenging problem. In a single domain, there are many methods for curve reconstruction of noise data, but a method suitable for multi-domain curve reconstruction has received much less attention in the literature. More importantly, the existing methods have shortcomings in time consumption when dealing with large data and high-density point cloud curve reconstruction. For this reason, we hope to propose a curve fitting algorithm suitable for many fields and low time consumption. In this paper, a curve reconstruction method based on clustering and point cloud principal component analysis is proposed. Firstly, the point cloud is clustered by the K++ means algorithm. Secondly, a denoising method based on point cloud principal component analysis is proposed to obtain the interpolation nodes of curve subdivision. Finally, the fitting curve is obtained by the parametric curve subdivision method. Comparative experiments show that our method is superior to the classical fitting method in terms of time consumption and effect. In addition, our method is not constrained by the shape of the point cloud, and can play a role in time series data, image thinning and edge smoothing.

This paper reports an algorithm to chop point cloud into layer-wise slices for additive manufacturing. It starts with intersecting slicing plane with the 3D input points, generating planar samples. Then, an online learning model, known as competitive segments representation (CSR), extracts their implicit topology and distribution. CSR structure is a restricted graph that equals to multiple polylines, which are meanwhile piecewise linear approximation to the principal curves of samples. Edge segments of CSR compete with each other for representing consecutively given samples. They dynamically move, grow, shrink or rewire subject to several heuristic rules. Those rules are designed to depress abnormal data, enable lifelong learning, recover salient feature and ensure correct topology. Assembling them together allows online tracking of changing curves. Once CSR converges on one slice, learnt curves are reused as initial estimation for the next. By this practice, shape coherence of successive slices is efficiently utilized, and the ongoing learning output all subsequent slices incrementally. We have verified the feasibility of proposed algorithm both on synthesized data and scanned points. [ABSTRACT FROM AUTHOR]

Shape-from-Template (SfT) is the problem of using a shape template to infer the shape of a deformable object observed in an image. The usual case of SfT is 'Surface' SfT, where the shape is a 2D surface embedded in 3D, and the image is a 2D perspective projection. We introduce 'Curve' SfT, comprising two new cases of SfT where the shape is a 1D curve. The first new case is when the curve is embedded in 2D and the image a 1D perspective projection. The second new case is when the curve is embedded in 3D and the image a 2D perspective projection. We present a thorough theoretical study of these new cases for isometric deformations, which are a good approximation of ropes, cables and wires. Unlike Surface SfT, we show that Curve SfT is only ever solvable up to discrete ambiguities. We present the necessary and sufficient conditions for solvability with critical point analysis. We further show that unlike Surface SfT, Curve SfT cannot be solved locally using exact non-holonomic Partial Differential Equations. Our main technical contributions are two-fold. First, we give a stable, global reconstruction method that models the problem as a discrete Hidden Markov Model. This can generate all candidate solutions. Second, we give a non-convex refinement method using a novel angle-based deformation parameterization. We present quantitative and qualitative results showing that real curve shaped objects such as a necklace can be successfully reconstructed with Curve SfT. [ABSTRACT FROM AUTHOR]

Curve reconstruction is a fundamental problem in reverse engineering, which has intrigued researchers for decades. In this paper, we propose a topological understanding based method for reconstructing parametric curves robustly from unorganized point clouds. Given a point cloud, we firstly understand the number of closed curves which need to be reconstructed using persistent homology. Then, by calculating the persistent 1-cycles of the point cloud, the initial shapes of the reconstructed parametric curves are generated. Finally, the closed parametric curves are reconstructed with the weighted least-squares progressive iterative approximation (W-LSPIA) method. Due to the topological understanding, the reconstructed parametric curves are faithful to the salient topological structure of the point cloud. Moreover, the developed reconstruction method is robust, and the reconstructed curve is much less affected by noise points and outliers, compared with the conventional parametric curve reconstruction algorithms. Experimental results demonstrated in this paper show the effectiveness of the developed curve reconstruction method. • The number of reconstructed curves is understood from the given point cloud using persistence homology. • The initial reconstructed parametric curves are generated by extracting the 1-cycles representation. • The weighted LSPIA (W-LSPIA) is developed for reconstructing the parametric curves robustly. [ABSTRACT FROM AUTHOR]

Using the wavelet transform defined in the infinite domain to process the signal defined in finite interval, the wavelet transform coefficients at the boundary are usually very large. It will bring severe boundary effect, which reduces the calculation accuracy. The construction of interval wavelet is the most common method to reduce the boundary effect. By studying the properties of Shannon-Cosine interpolation wavelet, an improved version of the wavelet function is proposed, and the corresponding interval interpolation wavelet based on Hermite interpolation extension and variational principle is designed, which possesses almost all of the excellent properties such as interpolation, smoothness, compact support and normalization. Then, the multi-scale interpolation operator is constructed, which can be applied to select the sparse feature points and reconstruct signal based on these sparse points adaptively. To validate the effectiveness of the proposed method, we compare the proposed method with Shannon-Cosine interpolation wavelet method, Akima method, Bezier method and cubic spline method by taking infinitesimal derivable function cos(x) and irregular piecewise function as an example. In the reconstruction of cos(x) and piecewise function, the proposed method reduces the boundary effect at the endpoints. When the interpolation points are the same, the maximum error, average absolute error, mean square error and running time are 1.20 × 10−4, 2.52 × 10−3, 2.76 × 10−5, 1.68 × 10−2 and 4.02 × 10−3, 4.94 × 10−4, 1.11 × 10−3, 9.27 × 10−3, respectively. The four indicators mentioned above are all lower than the other three methods. When reconstructing an infinitely derivable function, the curve reconstructed by our method is smoother, and it satisfies C2 and G2 continuity. Therefore, the proposed method can better realize the reconstruction of smooth curves, improve the reconstruction efficiency and provide new ideas to the curve reconstruction method.

With the development of intelligent technology, it is of great significance to develop intelligent equipment with topography self-sensing function. The micro morphology perception technology applied to intelligent equipment is the key technology for development. In this paper, at first, topography perception theory based on the PVDF (Polyvinylidene Fluoride) technology is researched, then an experimental study is conducted to sense the characteristic points of the geometric curve of the preset topography surface used in the PVDF film, and then the Ferguson curve model is used to reconstruct the topography characteristic curve. The experimental results show that the reconstruction curve can truly reflect the features of the characteristic curve of the surface of the preset topography, and the feasibility of topography surface sensing technology by PVDF sensing technology is verified. The research provides technical support for the development of intelligent equipment with topography self-sensing function.

Copyright of Journal of Heilongjiang University of Science & Technology is the property of Journal of Heilongjiang University of Science & Technology Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We introduce CurveFusion, the first approach for high quality scanning of thin structures at interactive rates using a handheld RGBD camera. Thin filament-like structures are mathematically just 1D curves embedded in R3, and integration-based reconstruction works best when depth sequences (from the thin structure parts) are fused using the object's (unknown) curve skeleton. Thus, using the complementary but noisy color and depth channels, CurveFusion first automatically identifies point samples on potential thin structures and groups them into bundles, each being a group of a fixed number of aligned consecutive frames. Then, the algorithm extracts per-bundle skeleton curves using L1 axes, and aligns and iteratively merges the L1 segments from all the bundles to form the final complete curve skeleton. Thus, unlike previous methods, reconstruction happens via integration along a data-dependent fusion primitive, i.e., the extracted curve skeleton. We extensively evaluate CurveFusion on a range of challenging examples, different scanner and calibration settings, and present high fidelity thin structure reconstructions previously just not possible from raw RGBD sequences. [ABSTRACT FROM AUTHOR]

Curve reconstruction from data points is an important issue for advanced medical imaging techniques, such as computer tomography (CT) and magnetic resonance imaging (MRI). The most powerful fitting functions for this purpose are the NURBS (non-uniform rational B-splines). Solving the general reconstruction problem with NURBS requires computing all free variables of the problem (data parameters, breakpoints, control points, and their weights). This leads to a very difficult non-convex, nonlinear, high-dimensional, multimodal, and continuous optimization problem. Previous methods simplify the problem by guessing the values for some variables and computing only the remaining ones. As a result, unavoidable approximations errors are introduced. In this paper, we describe the first method in the literature to solve the full NURBS curve reconstruction problem in all its generality. Our method is based on a combination of two techniques: an immunological approach to perform data parameterization, breakpoint placement, and weight calculation, and least squares minimization to compute the control points. This procedure is repeated iteratively (until no further improvement is achieved) for higher accuracy. The method has been applied to reconstruct some outline curves from MRI brain images with satisfactory results. Comparative work shows that our method outperforms the previous related approaches in the literature for all instances in our benchmark. [ABSTRACT FROM AUTHOR]

Given a planar point set sampled from a curve, the curve reconstruction problem computes a polygonal approximation of the curve. In this paper, we propose a Delaunay triangulation-based algorithm for curve reconstruction, which removes the longest edge of each triangle to result in a graph. Further, each vertex of the graph is checked for a degree constraint to compute simple closed/open curves. Assuming ϵ-sampling, we provide theoretical guarantee which ensures that a simple closed/open curve is a piecewise linear approximation of the original curve. Input point sets with outliers are handled as part of the algorithm, without pre-processing. We also propose strategies to identify the presence of noise and simplify a noisy point set, identify self-intersections and enhance our algorithm to reconstruct such point sets. Perhaps, this is the first algorithm to identify the presence of noise in a point set. Our algorithm is able to detect closed/open curves, disconnected components, multiple holes and sharp corners. The algorithm is simple to implement, independent of the type of input, non-feature specific and hence it is a generalized one. We have performed extensive comparative studies to demonstrate that our method is comparable or better than other existing methods. Limitations of our approach have also been discussed. [ABSTRACT FROM AUTHOR]

For more precise measurement of outer diameter of spun ultra-thin-walled rotational parts, the on-machine measurement of the equivalent outer diameter based on the reconstructed cross section contour curve is proposed. In this method, three sets of line laser displacement sensors are distributed uniformly along the circumferential direction, and the outer contour data of the cross section of rotational part at any axial position is obtained by using the three sets of line laser displacement sensors and the axial movement module of the spinning roller frame. The complete cross section outer contour data is spliced by the coordinate transformation and matching of the cross section data obtained by the three sensors, the contour curve is reconstructed by the shape preserving curve reconstruction method of discrete data points, and the equivalent outer diameter ol the cross section is calculated according to length invariance of the same closed curve. Finally, the outer diameters of the mandrel and the thin-walled rotational parts are measured. The experimental results show thai the proposed method can be used to precisely measure the outer diameters of ullra-thiu-walled rotational parts with measuring accuracy 010.019 mm. [ABSTRACT FROM AUTHOR]

This paper presents a new method called multilayer embedded bat algorithm (ME-BAT) to solve the general curve reconstruction problem with free-form parametric B-splines. Opposed to previous approaches in the literature, this method computes the optimal values of all free variables (data parameters, breakpoints, and poles), a very difficult task because they are strongly intertwined in a highly nonlinear way. The method is based on the idea of applying the bat algorithm at different layers: a main bat algorithm at an upper layer to compute the breakpoints and a second bat algorithm at a lower layer to compute the data parameters. This second bat algorithm is embedded into the first one and executed for each breakpoint vector of the population and at each iteration step of the main algorithm. Then, the poles are calculated by least-squares minimization through SVD. The method has been applied to three real-world engineering examples. The experimental results show that the method performs very well, being able to recover the underlying shape of data with high accuracy. A comparison with eleven alternative methods (including six classical methods in the field and all the metaheuristic methods applied so far to this problem) shows that this method outperforms the previous approaches in the field for all instances in the benchmark. [ABSTRACT FROM AUTHOR]

Finding optimal sampling strategy is a central problem in surface reconstruction. In this paper a sampling strategy on different scales of a free-form surface is proposed. Non-Uniform Rational B-spline (NURBS) surfaces are used to represent the nominal shape; the decomposition is performed through the orthogonal B-wavelet basis. A sampling based on each level of the shape decomposition is then proposed to detect the points of interest that reflect the variations between different levels. The number of the samples is selected according to the complexity of the shape, which is represented by the number of the internal knots. [ABSTRACT FROM AUTHOR]

Accurate maps are increasingly important with the growth of smart phones and the development of location-based services. Several crowdsourcing based map generation protocols that rely on users to provide their traces have been proposed. Being creative, however, those methods pose a significant threat to user privacy as the traces can easily imply user behavior patterns. On the flip side, crowdsourcing-based map generation method does need individual locations. To address the issue, we present a systematic participatory-sensing-based high-quality map generation scheme, PMG, that meets the privacy demand of individual users. To be specific, the individual users merely need to upload unorganized sparse location points to reduce the risk of exposing users’ traces and utilize the Crust, a technique from computational geometry for curve reconstruction, to estimate the unobserved map as well as evaluate the degree of privacy leakage. Experiments show that our solution is able to generate high-quality maps for a real environment that is robust to noisy data. The difference between the ground-truth map and the produced map is less than 10 m, even when the collected locations are about 32 m apart after clustering for the purpose of removing noise. [ABSTRACT FROM PUBLISHER]