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In this article, we present and discuss three statistical methods for Surface Reconstruction. A typical input to a Surface Reconstruction technique consists of a large set of points that has been sampled from a smooth surface and contains uncertain data in the form of noise and outliers. We first present a method that filters out uncertain and redu...
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... the least-squares fitting plane is spanned by the two main principal axes v 1 i and v 2 i of E i and has the nor- mal v 3 i = n i . A 2D example is illustrated in Fig. 2. If normals are provided by the scanning device we use them instead of the estimated normals. Using the squared distance of x to the least-squares plane, we measure the likelihood L i (x) ...
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... Eq. 8 builds a multi-level approximation scheme based on a sequence of nested spaces; for more details, we refer the reader to [51]. If we get a complete sparsifica- tion, i.e., the iterative solver of the system of non-linear equations converges to the null solution, each approxi- mation is achieved by using the intermediate iterations (see Fig. ...
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Citations
... When the probability distribution function of the ICP parameters is necessary, the covariance is often obtained based on the calculation of the Hessian Matrix [24,[34][35][36]. In this method, the Hessian and covariance matrices are obtained from: ...
The rigid matching of two geometric clouds is vital in the computer vision and its intelligent applications, such as computational geometry, robotics, shape modelling, surface reconstruction and mapping, and many other fields. The variants of the iterative closest point algorithm were employed as the most noticeable matching algorithm. In traditional ICP algorithms applications for symmetrical geometry matching, the initial uncertainty and the multiple local minima of the distance function adversely affect the alignment process, which leads to weak performance, such as incorrect correspondence, narrow convergence region, and instability. In this study, the novel algorithm fused the ICP algorithm, particle filter and K-means clustering to correctly estimate the transformation ICP parameters. Further guide to initial values of parameters and their covariance obtained by k-means clustering. Then, a particle filter was implemented to estimate accurate values and perform global optimization. In the introduced PF-ICP algorithm, the alignment parameters: rotation angles, scale factor, and translation, were defined as particles elements optimized using a sequential importance resampling (SIR) particle filter. The proposed algorithm was implemented on a medical robot FPGA board and applied to “three symmetrical models” and “noisy and poor datasets.” The calculated variances and estimated parameters were compared with four modified ICP methods. The results show a significantly increasing accuracy and convergence region with an acceptable speed for the practical conditions.
... GNG overcomes the limitations of standard self-organizing map neural networks. The algorithm combines the growth mechanism of GCS neural network with the competitive Hebbian learning rule [28,29]. Moreover, this model does not have the dynamic structure of fixed dimension and adaptively learns the dimension of input sample and the input data in the process of training density. ...
In this research, new modeling strategy based hierarchical growing neural gas network (HGNG)-semicooperative for feature classifier of intrusion detection system (IDS) in a vehicular ad hoc network (VANET). The novel IDS mainly presents a new design feature for an extraction mechanism and a HGNG-based classifier. Firstly, the traffic flow features and vehicle location features were extracted in the VANET model. In order to effectively extract location features, a semicooperative feature extraction is used for collecting the current location information for the neighboring vehicles through a cooperative manner and the location features of the historical location information. Secondly, the HGNG-based classifier was designed for evaluating the IDS by using a hierarchy learning process without the limitation of the fix lattice topology. Finally, an additional two-step confirmation mechanism is used to accurately determine the abnormal vehicle messages. In the experiment, the proposed IDS system was evaluated, observed, and compared with the existing IDS. The proposed system performed a remarkable detection accuracy, stability, processing efficiency, and message load. View Full-Text
... GNG overcomes the limitations of standard self-organizing map neural networks. The algorithm combines the growth mechanism of GCS neural network with the competitive Hebbian learning rule [28,29]. Moreover, this model does not have the dynamic structure of fixed dimension and adaptively learns the dimension of input sample and the input data in the process of training density. ...
In this research, new modeling strategy based hierarchical growing neural gas network (HGNG)-semicooperative for feature classifier of intrusion detection system (IDS) in a vehicular ad hoc network (VANET). The novel IDS mainly presents a new design feature for an extraction mechanism and a HGNG-based classifier. Firstly, the traffic flow features and vehicle location features were extracted in the VANET model. In order to effectively extract location features, a semicooperative feature extraction is used for collecting the current location information for the neighboring vehicles through a cooperative manner and the location features of the historical location information. Secondly, the HGNG-based classifier was designed for evaluating the IDS by using a hierarchy learning process without the limitation of the fix lattice topology. Finally, an additional two-step confirmation mechanism is used to accurately determine the abnormal vehicle messages. In the experiment, the proposed IDS system was evaluated, observed, and compared with the existing IDS. The proposed system performed a remarkable detection accuracy, stability, processing efficiency, and message load.
... Although many algorithms have already been proposed for mesh generation from an unorganized point cloud [2][3][4][5][6][7], existing techniques have various limitations mainly in terms of their applicability to free-form objects, accuracy, efficiency, and the discriminating capability of the generated representation. An excellent survey of free-form object representation and recognition techniques can be found in [8]. ...
In this work, we propose the use of the Neural Gas (NG), a neural network with unsupervised competitive hebbian learning (CHL), to develop a reverse engineering process. This is a simple and accurate method to reconstruct objects from the point cloud obtained from overlapped multiple views using low cost sensors. In contrast to other methods that may need several stages that include downsampling, noise filtering and many other tasks, the NG automatically obtains the 3D model of the scanned objects. The combination of the acquired and reconstructed 3D models with virtual and augmented reality environments allows the users interaction and also permits developing a virtual design and manufacturing system.
To demonstrate the validity of our proposal we tested our method with several models and performed a study of the neural network parameterization calculating the quality of representation and also comparing results with other neural methods like Growing Neural Gas and Kohonen maps or clasical methods like Voxel Grid. We also reconstructed models acquired by low cost sensors that can be included in virtual and augmented reality environments to redesign or manipulation purpose. Since the NG algorithm has a strong computational cost we propose its acceleration. We have redesigned and implemented the NG learning algorithm to fit it onto a Graphic Processor Unit using CUDA. A speed-up of 180x faster is obtained compared to the sequential CPU version.
... A typical shortcoming of implicit methods is that they are sensitive to the outliers. With a view to overcoming this limitation, some new methods ( [10], [11], [12] and [13]), based on stratified reconstruction strategies, have been recently developed. ...
In a previous paper these authors presented a new mesh-growing approach based on the Gabriel 2 – Simplex (G2S) criterion. If compared with the Cocone family and the Ball Pivoting methods, G2S demonstrated to be competitive in terms of tessellation rate, quality of the generated triangles and defectiveness produced when the surface to be reconstructed was locally flat. Nonetheless, its major limitation was that, in the presence of a mesh which was locally non – flat or which was not sufficiently sampled, the method was less robust and holes and non – manifold vertices were generated. In order to overcome these limitations, in this paper, the performance of the G2S mesh- growing method is fully improved in terms of robustness. The performances of the new version of the G2S approach (in the following Robust G2S) has been compared with that of the old one, and that of the Cocone family and the Ball Pivoting methods in the tessellation of some benchmark point clouds and artificially noised test cases. The results obtained show that the use of the Robust G2S is advantageous, as opposed to the other methods here considered, even in the case of noised point clouds. Unlike the other methods, the one which is proposed preserves manifoldness and geometric details of the point cloud to be meshed.
... A typical shortcoming of implicit methods is that they are sensitive to the outliers. With a view to overcoming this limitation, some new methods ( [10], [11], [12] and [13]), based on stratified reconstruction strategies, have been recently developed. ...
In a previous paper these authors presented a new mesh-growing approach based on
the Gabriel 2 – Simplex (G2S) criterion. If compared with the Cocone family and the Ball
Pivoting methods, G2S demonstrated to be competitive in terms of tessellation rate,
quality of the generated triangles and defectiveness produced when the surface to be
reconstructed was locally flat. Nonetheless, its major limitation was that, in the
presence of a mesh which was locally non – flat or which was not sufficiently sampled,
the method was less robust and holes and non – manifold vertices were generated. In
order to overcome these limitations, in this paper, the performance of the G2S meshgrowing
method is fully improved in terms of robustness. The performances of the
new version of the G2S approach (in the following Robust G2S) has been compared
with that of the old one, and that of the Cocone family and the Ball Pivoting methods
in the tessellation of some benchmark point clouds and artificially noised test cases.
The results obtained show that the use of the Robust G2S is advantageous, as opposed
to the other methods here considered, even in the case of noised point clouds. Unlike
the other methods, the one which is proposed preserves manifoldness and geometric
details of the point cloud to be meshed.
... Most of these methods are sensitive to the accuracy of point orientations and varying sampling density. To handle noisy, incomplete and uncertain data statistical methods are also applied in the surface reconstruction domain [31]. However, they suffer from the need of user parameters and are relatively slow. ...
This work proposes a method to reconstruct surfaces with higher-order smoothness from noisy 3D measurements. The reconstructed surface is implicitly represented by the zero level-set of a continuous valued embedding function. The key idea is to find a function whose higher-order derivatives are regularized and whose gradient is best aligned with a vector field defined by the input point set. In contrast to methods based on the first-order variation of the function that are biased towards the constant functions and treat the extraction of the isosurface without aliasing artifacts as an afterthought, we impose higher-order smoothness directly on the embedding function. After solving a convex optimization problem with a multi-scale iterative scheme, a triangulated surface can be extracted using the marching cubes algorithm. We demonstrated the proposed method on several data sets obtained from raw laser-scanners and multi-view stereo approaches. Experimental results confirm that our approach allows us to reconstruct smooth surfaces from points in the presence of noise, outliers, large missing parts and very coarse orientation information.
... The model also has a hole above the eyebrow (Fig. 5a). We filtered the noise and outliers of the original model (Fig. 5d) using the method proposed by Saleem et al. (2007), and then performed the ALOP algorithm directly on both the noise model (top row of Fig. 5) and the filtered model (bottom row of Fig. 5). The comparison of results shows that our ALOP algorithm handled noise and outliers well and the hole had little effect on the algorithm. ...
... face point-cloud with noise and outliers. (a) The Face model consisting of three registered scans; (b) ALOP simplification of (a) via 20 iterations; (c) Close-up views; (d) Filtering the data of (a) by the methods inSaleem et al. (2007); (e, f ) ALOP simplification result of (d) via 20 iterations and the close-up views, respectively ...
We propose a novel curvature-aware simplification technique for point-sampled geometry based on the locally optimal projection
(LOP) operator. Our algorithm includes two new developments. First, a weight term related to surface variation at each point
is introduced to the classic LOP operator. It produces output points with a spatially adaptive distribution. Second, for speeding
up the convergence of our method, an initialization process is proposed based on geometry-aware stochastic sampling. Owing
to the initialization, the relaxation process achieves a faster convergence rate than those initialized by uniform sampling.
Our simplification method possesses a number of distinguishing features. In particular, it provides resilience to noise and
outliers, and an intuitively controllable distribution of simplification. Finally, we show the results of our approach with
publicly available point cloud data, and compare the results with those obtained using previous methods. Our method outperforms
these methods on raw scanned data.
... Zastosowanie metod statystycznych w filtracji chmury punktów przedstawili autorzy pracy [151]. Podstawą działania algorytmu jest estymacja funkcji gęstości punktów uwzględniającej wymagany stopień wygładzenia powierzchni -funkcja ta jest sumą funkcji Gaussa opisujących lokalną gęstość punktów. ...
... Ryc. 2.25. Filtracja odwzorowania twarzy uzyskanego za pomocą skanera światła strukturalnego[151] ...
... As expected, our method exhibits robustness to input artifacts. This work has been published previously as [Isgro05,Saleem04,Saleem07a] after which very similar work appeared in [do Rego07, do Rego09]. ...
... In this chapter, we present Neural Meshes [Ivrissimtzis03,Jeong03], work on which we earlier published in [Isgro05,Saleem04,Saleem07a]. A neural network is initialized as a triangle mesh, M, representing a tetrahedron. ...
