A mathematical model-driven algorithm for inverse precision measurement and error evaluation of complex surfaces

In this paper, we propose an approach for reconstruction of an anatomic surface model from point cloud data using the Screened Poisson Surface Reconstruction algorithm, which requires a collection of points and their normal vectors. Various algorithms exist for estimating normal vectors for point cloud data; however, in this work we describe a novel approach to estimating the normal vectors from a high-resolution prior model. In many medical applications, a preoperative high-resolution scan is acquired for diagnostic and planning purposes, whereas intraoperative, lower fidelity imaging is utilized during the procedure. This approach assumes an already existing registration between intra-operatively acquired data and the preoperative model. We conducted simulation experiments to evaluate the effect of registration error, point sampling rate, and noise levels on the acquired point cloud data samples. In addition, we evaluated the effect of using both the closest point, as well as a neighborhood of closest points on the prior model for estimating the normal. Our results showed that surface reconstruction error increases with higher registration error; however, acceptable performance was achieved with clinically-acceptable registration error. In addition, the best reconstruction was obtained when estimating the normal using only the closest point on the prior model, as opposed to utilizing a neighborhood of points. When combining the effect of all factors (Gaussian sampling noise of zero mean and σ=1.8mm; Gaussian translational error of zero mean and σ=2.0mm; and Gaussian rotational error of zero mean and σ=3°) the overall RMS reconstruction error was 0.88±0.03mm.

In recent years, the moving least-square (MLS) method has been extensively studied for approximation and reconstruction of surfaces. The MLS method involves local weighted least-squares polynomial approximations, using a fast decaying weight function. The local approximating polynomial may be used for approximating the underlying function or its derivatives. In this paper we consider locally supported weight functions, and we address the problem of the optimal choice of the support size. We introduce an error formula for the MLS approximation process which leads us to developing two tools: One is a tight error bound independent of the data. The second is a data dependent approximation to the error function of the MLS approximation. Furthermore, we provide a generalization to the above in the presence of noise. Based on the above bounds, we develop an algorithm to select an optimal support size of the weight function for the MLS procedure. Several applications such as differential quantities estimation and up-sampling of point clouds are presented. We demonstrate by experiments that our approach outperforms the heuristic choice of support size in approximation quality and stability.

Surfaces of stored grain bulk are often reconstructed from organized point sets with noise by 3-D laser scanner in an online measuring system. As a result, denoising is an essential procedure in processing point cloud data for more accurate surface reconstruction and grain volume calculation. A classified denoising method was presented in this research for noise removal from point cloud data of the grain bulk surface. Based on the distribution characteristics of cloud point data, the noisy points were divided into three types: The first and second types of the noisy points were either sparse points or small point cloud data deviating and suspending from the main point cloud data, which could be deleted directly by a grid method; the third type of the noisy points was mixed with the main body of point cloud data, which were most difficult to distinguish. The point cloud data with those noisy points were projected into a horizontal plane. An image denoising method, discrete wavelet threshold (DWT) method, was applied to delete the third type of the noisy points. Three kinds of denoising methods including average filtering method, median filtering method and DWT method were applied respectively and compared for denoising the point cloud data. Experimental results show that the proposed method remains the most of the details and obtains the lowest average value of RMSE (Root Mean Square Error, 0.219) as well as the lowest relative error of grain volume (0.086%) compared with the other two methods. Furthermore, the proposed denoising method could not only achieve the aim of removing noisy points, but also improve self-adaptive ability according to the characteristics of point cloud data of grain bulk surface. The results from this research also indicate that the proposed method is effective for denoising noisy points and provides more accurate data for calculating grain volume. Keywords: point cloud data, denoising, grid method, discrete wavelet threshold (DWT) method, 3-D laser scanning, stored grain DOI: 10.3965/j.ijabe.20160904.2333 Citation: Shao Q, Xu T, Yoshino T, Song N, Zhu H. Classified denoising method for laser point cloud data of stored grain bulk surface based on discrete wavelet threshold. Int J Agric & Biol Eng, 2016; 9(4): 123－131.

Moving least squares (MLS) surfaces representation directly defines smooth surfaces from point cloud data, on which the differential geometric properties of point set can be conveniently estimated. Nowadays, the MLS surfaces have been widely applied in the processing and rendering of point-sampled models and increasingly adopted as the standard definition of point set surfaces. We classify the MLS surface algorithms into two types: projection MLS surfaces and implicit MLS surfaces, according to employing a stationary projection or a scalar field in their definitions. Then, the properties and constrains of the MLS surfaces are analyzed. After presenting its applications, we summarize the MLS surfaces definitions in a generic form and give the outlook of the future work at last.

This paper focuses on the challenging problem of detecting the surface delamination damage during the drilling of carbon fiber reinforced polymer (CFRP). Considering the issues such as the low efficiency of traditional manual inspection, the limitations of non-destructive testing technologies, and the deficiencies of machine vision inspection algorithms, the point cloud processing technology is innovatively introduced. By analyzing the delamination damage mechanism and evaluation criteria, a drilling experiment is designed, and the point cloud data are collected. Voxel grid filtering and statistical filtering are applied to preprocess the point cloud. The moving least squares (MLS) method is adopted to smooth the point cloud. Based on the region growing algorithm and combined with the dual constraints of curvature and normal vector, the precise segmentation of the point cloud is realized. The experimental results demonstrate that the algorithm proposed in this paper achieves an accuracy rate of 91% for the detection of the surface delamination area with a repeatability accuracy of 1 mm 2 , and an accuracy rate of 93% for the depth detection with a repeatability accuracy of 40 μm. This provides a novel solution for the detection of surface delamination damage during the drilling of CFRP.

SLAM-based dense surface reconstruction in monocular Minimally Invasive Surgery and its application to Augmented Reality

Point cloud models acquired by passive three-dimensional reconstruction systems based on binocular or multi-view involve large amounts of noise and its distribution is uneven, which affects the accuracy of surface reconstruction. To tackle the problem, we proposed a three-dimensional surface reconstruction method based on Delaunay triangulation. First, use Delaunay triangulation to get a fully adaptive decomposition of point cloud, then the output triangular mesh was represented using dual graph, so by using graph cut optimization the initial surface model was obtained. Second, the deformation model was used to optimize the initial surface model, and then adopted photometric similarity function and Laplace operator to refine surface details. Finally, the refinement was transformed into an iterative procedure, by which the real surface of the object was accurately approximated. We experimented on four standard datasets of Castle-Entry, Castle, Fountain and Herzjesu. The result showed that compared with Poisson surface reconstruction and floating scale surface reconstruction algorithm, the proposed method was more adaptable and robust to noise and outliers, and the detailed information recovery of local surface reconstruction was better. It showed that the method proposed in this paper effectively improved the accuracy and completeness of surface reconstruction, which could reconstruct high quality three-dimensional surface models of object from the point cloud models with lots of noise and complex topological structures.

The k-nearest neighborhoods (kNN) of feature points of complex surface model are usually isotropic, which may lead to sharp feature blurring during data processing, such as noise removal and surface reconstruction. To address this issue, a new method was proposed to search the anisotropic neighborhood for point cloud with sharp feature. Constructing KD tree and calculating kNN for point cloud data, the principal component analysis method was employed to detect feature points and estimate normal vectors of points. Moreover, improved bilateral normal filter was used to refine the normal vector of feature point to obtain more accurate normal vector. The isotropic kNN of feature point were segmented by mapping the kNN into Gaussian sphere to form different data-clusters, with the hierarchical clustering method used to separate the data in Gaussian sphere into different clusters. The optimal anisotropic neighborhoods of feature point corresponded to the cluster data with the maximum point number. To validate the effectiveness of our method, the anisotropic neighbors are applied to point data processing, such as normal estimation and point cloud denoising. Experimental results demonstrate that the proposed algorithm in the work is more time-consuming, but provides a more accurate result for point cloud processing by comparing with other kNN searching methods. The anisotropic neighborhood searched by our method can be used to normal estimation, denoising, surface fitting and reconstruction et al. for point cloud with sharp feature, and our method can provide more accurate result comparing with isotropic neighborhood.

This paper examines the performance of the local level set method on the surface reconstruction problem for unorganized point clouds in three dimensions. Many laser-ranging, stereo, and structured light devices produce three dimensional information in the form of unorganized point clouds. The point clouds are sampled from surfaces embedded in R³ from the viewpoint of a camera focal plane or laser receiver. The reconstruction of these objects in the form of a triangulated geometric surface is an important step in computer vision and image processing. The local level set method uses a Hamilton-Jacobi partial differential equation to describe the motion of an implicit surface in threespace. An initial surface which encloses the data is allowed to move until it becomes a smooth fit of the unorganized point data. A 3D point cloud test suite was assembled from publicly available laser-scanned object databases. The test suite exhibits nonuniform sampling rates and various noise characteristics to challenge the surface reconstruction algorithm. Quantitative metrics are introduced to capture the accuracy and efficiency of surface reconstruction on the degraded data. The results characterize the robustness of the level set method for surface reconstruction as applied to 3D remote sensing.

The normal vector is one of the important properties of the 3D point cloud data, estimation methods have been important research in the field. The normal vector estimation is the basis of the 3D point cloud subsequent follow-up of the light treatment, curvature calculation and surface reconstruction. Introduced an automatic space by greatly increasing the speed of the point cloud neighborhood search, given the fast and efficient point cloud normal vector estimation and adjustment algorithm based on the normal vector near the point, the experiments show the effectiveness of the method.

Parabolic-cylindrical moving least squares surfaces

Abstract. The point cloud generated by multiple image matching is classified as an unstructured point cloud because it is not regularly point spaced and has multiple viewpoints. The surface reconstruction technique is used to generate mesh model using unstructured point clouds. In the surface reconstruction process, it is important to calculate correct surface normals. The point cloud extracted from multi images contains position and color information of point as well as geometric information of images used in the step of point cloud generation. Thus, the surface normal estimation based on the geometric constraints is possible. However, there is a possibility that a direction of the surface normal is incorrectly estimated by noisy vertical area of the point cloud. In this paper, we propose an improved method to estimate surface normals of the vertical points within an unstructured point cloud. The proposed method detects the vertical points, adjust their normal vectors by analyzing surface normals of nearest neighbors. As a result, we have found almost all vertical points through point type classification, detected the points with wrong normal vectors and corrected the direction of the normal vectors. We compared the quality of mesh models generated with corrected surface normals and uncorrected surface normals. Result of comparison showed that our method could correct wrong surface normal successfully of vertical points and improve the quality of the mesh model.

Surface reconstruction based on point cloud data has been extensively studied. In this paper, the original data has a lot of noise and without normal vector information, so we use Poisson surface reconstruction algorithm to create 3D heart model, which has good robustness for noisy and irregular point cloud data. Then correct the shape by removing or adding points from the model surface to perfect the heart model, and reconstruct the new model by Power Crust algorithm based on the correctional surface point cloud data with normal vector, which is quick, accurate and efficient and very suitable for fast model correction. The results not only accurately display the spatial relationship of the heart, but also can be discretionary scaling and rotation in 3D space. The visual 3D graphical structures of the reconstructed heart model can display diseases (cardiopathy & arrhythmia) and enable catheter navigation in real time, which can help doctors to detect and diagnose diseases effectively, and improve the accuracy and security of medical diagnosis.

The Moving Least Squares (MLS) and Moving Total Least Squares (MTLS) method are widely used for approximating discrete data in many areas such as surface reconstruction. One of the disadvantages of MLS is that it only considers the random errors in the dependent variables. The MTLS method achieves a better fitting accuracy by taking into account the errors of both dependent and independent variables. However, both MLS and MTLS suffer from a low fitting accuracy when applied to the measurement data with outliers. In this work, an improved method named as α-MTLS method is proposed, which uses the Total Least Square (TLS) method based on singular value decomposition (SVD) to fit the nodes in the influence domain and introduces a geometric characteristic parameter α to associated with the abnormal degree of nodes. The generated fitting points are used to construct the parameter and quantify the abnormal degree of the nodes. The node with the largest parameter value is eliminated and the remaining nodes are used to determine the local coefficients. By trimming only one node per influence domain, multiple outliers of measurement data can be effectively handled. There is no need to set threshold values subjectively or assign weights which avoids the negative influence of manual operation. The performance of the improved method is demonstrated by numerical simulations and measurement experiment. It is shown that the α-MTLS method can effectively reduce the influence of the outliers and thus has higher fitting accuracy and greater robustness than that of the MLS and MTLS method.

Abstract. Leaf detection through automated segmentation of 3D data is becoming a crucial technique in many applications of digital agriculture. Some 3D segmentation techniques that can be mentioned are based on normal differences and median normalised vector growth. However, applying these approaches to high canopy density data remains challenging. In this study, we propose a processing flow for leaf detection in high canopy density LiDAR-RGB point clouds. First, a noise removal technique inspired by Moving Least Squares (MLS) was applied to the LiDAR point cloud, and a RGB colour was assigned to each point by combining computer vision and photogrammetric methods. Moreover, once the data were suitable for leaf detection, the branches were filtered using the Statistical Outlier Removal (SOR) filter based on an analysis of the statistical behaviour of the neighbourhood. Afterwards, an unsupervised DBSCAN (Density-Based Clustering Non-Parametric Algorithm) method was used to segment similar points. Finally, the points within each cluster were identified as leaf or non-leaf using the RGB values implemented by our method; ground points were filtered out using a maximum height threshold. As a result, the leaf, non-leaf, and ground point identifiers were correct in 98.9% of cases, with the branch filtering technique SOR proving effectiveness in removing branches with low information loss and without additional complex point densification steps in reconstruction. This SOR-based solution overcomes major challenges in semantic segmentation (leaves and branches) in high-density data and potentially contributes to precision agriculture.