In this paper, we propose a normal estimation method for unstructured 3D point clouds. This method, called Nesti-Net, builds on a new local point cloud representation which consists of multi-scale point statistics (MuPS), estimated on a local coarse Gaussian grid. This representation is a suitable input to a CNN architecture. The normals are estimated using a mixture-of-experts (MoE) architecture, which relies on a data-driven approach for selecting the optimal scale around each point and encourages sub-network specialization. Interesting insights into the network's resource distribution are provided. The scale prediction significantly improves robustness to different noise levels, point density variations and different levels of detail. We achieve state-of-the-art results on a benchmark synthetic dataset and present qualitative results on real scanned scenes.

We present an algorithm for registration between a large-scale point cloud and a close-proximity scanned point cloud, providing a localization solution that is fully independent of prior information about the initial positions of the two point cloud coordinate systems. The algorithm, denoted LORAX, selects super-points-local subsets of points-and describes the geometric structure of each with a low-dimensional descriptor. These descriptors are then used to infer potential matching regions for an efficient coarse registration process, followed by a fine-tuning stage. The set of super-points is selected by covering the point clouds with overlapping spheres, and then filtering out those of low-quality or nonsalient regions. The descriptors are computed using state-of-the-art unsupervised machine learning, utilizing the technology of deep neural network based auto-encoders. Abstract This novel framework provides a strong alternative to the common practice of using manually designed key-point descriptors for coarse point cloud registration. Utilizing super-points instead of key-points allows the available geometrical data to be better exploited to find the correct transformation. Encoding local 3D geometric structures using a deep neural network auto-encoder instead of traditional descriptors continues the trend seen in other computer vision applications and indeed leads to superior results. The algorithm is tested on challenging point cloud registration datasets, and its advantages over previous approaches as well as its robustness to density changes, noise, and missing data are shown.

This paper proposes a method for the automatic and simultaneous identification of the body-in-white assembly cell design and motion plan. The method solution is based on an iterative algorithm that looks for a global optimum by iteratively identifying the optimum of three sub-problems. These sub-problems concern system layout design and motion planning for single and multi-robot systems, while collision detection is addressed. The sub-problems are handled through ad-hoc developed Mixed Integer Programming (MIP) models. The proposed solution overcomes the limitations of the current design and motion plan approaches. In fact, the design of body-in-white assembly cell and the robot motion planning are two time-expensive and interconnected activities, up to now generally managed from different human operators. The resolution of these two activities as non-interrelated could lead to an increase of the engineer-to-order time and a reduction of the solution quality. Thus, a test bed is described in order to prove the applicability of the approach.

Bones consist of hierarchical biocomposite materials arranged in multi-scale structural geometry exhibiting complex behavior. This structure is vulnerable to various damaging factors that may cause its degradation, such as accidents, medical operations and diseases. Current technology cannot precisely reconstruct damaged bone tissue and can only roughly approximate such damaged structures. The aim of this research is to develop a method to identify the damaged regions and provide a best fitting scaffold to imitate the original structure, thus offering better rehabilitation. New imaging techniques at the micro-scale level are emerging. Imaging can already provide highly detailed micro-features of a bone sample or even a complete volumetric micro-structure of a bone. A three-dimensional model of the bone can then be reconstructed and analyzed. This study proposes a new method for applying volumetric texture synthesis that can adapt according to location, size and shape. Such 3D volumetric texture may be irregular, but can still imitate the textural behavior of its surroundings. The method has the ability to create a smooth and continuous structure according to topological and geometrical characteristics. Moreover, the texture captures the stochastic and porous nature of the bone micro-structure. In addition, the resulting texture is tested by applying mechanical analysis to the new synthesized structure, thus controlling the mechanical properties of the reconstructed bone. We believe our method will contribute to understanding bone structure and behavior and make it possible to customize the design and fabrication of scaffolds for bone micro-structures. Moreover, such scaffolds can facilitate the process of rehabilitating damaged bone.

This paper proposes a new grid-based method for adaptive anisotropic meshing of implicit surfaces. Grid-based methods are considered the major technique for implicit surface meshing, mainly due to their efficiency and simplicity. However, these methods suffer from a number of inherent drawbacks, resulting from the fact that the imposed Cartesian grid is generally not well adapted to the iso-surface, either in size or in orientation. To overcome the above obstacles, we propose a new implicit surface meshing method. The main idea of this method is first to construct a geometric field which is induced by the shape of the surface. This geometric field represents the natural directions and grid cell size for each point in R/sup 3/. Then, the imposed volumetric grid is deformed toward the object's shape according to the produced geometric field. The iso-surface meshes can be extracted from the resulting adaptive grid by any conventional grid-based contouring technique, since the topology of the grid is not modified during the adaptation process. These meshes provide better approximation of the unknown surface and exhibit anisotropy, which is present in this surface.

The manufacturing industry constantly needs to verify machined objects against their original CAD models. Given a prototype design, an engineer should be able to determine whether the part was manufactured well, that is, whether it fits the CAD model exactly. However, derivative computations are unstable for real data, and the estimated curvature is thus very sensitive to noise. Moreover, in many cases, spatial fitting of corresponding points is not sufficient. The current work utilizes the curvature properties to inspect a manufactured part.

Reverse engineering is an important process in CAD systems today. Yet several open problems lead to a bottleneck in the reverse engineering process. First, because the topology of the object to be reconstructed is unknown, point connectivity relations are undefined. Second, the fitted surface must satisfy global and local shape preservation criteria that are undefined explicitly. In reverse engineering, object reconstruction is based both on parameterization and on fitting. Nevertheless, the above problems are influenced mainly by parameterization. In order to overcome the above problems, the paper proposes a neural network, Self Organizing Map (SOM) method, for creating a 3D parametric grid. The main advantage of the proposed SOM method is that it detects both the orientation of the grid and the position of the sub-boundaries. The neural network grid converges to the sampled shape through an adaptive learning process. The SOM method is applied directly on 3D sampled data and avoids the projection anomalies common to other methods. The paper also presents boundary correction and growing grid extensions to the SOM method. In the surface fitting stage, an RSEC (Random Surface Error Correction) fitting method based on the SOM method was developed and implemented.

Reverse engineering (RE) deals with an enormous number of irregular and scattered digitized points that require intensive processing in order to reconstruct the surfaces of an object. Surface reconstruction of freeform objects is based on geometrical and topological criteria. Current fitting methods reconstruct an object using a bottom-up approach, from points to a dense mesh, and finally into smoothed connected freeform sub-surfaces. This type of reconstruction, however, can cause topological problems that lead to undesired surface fitting results. Such problems are particularly common with concave shapes. To avoid problems of this type, the paper proposes a new method that automatically detects the topological structure of an object as a base for surface fitting. The topological reconstruction method described in the paper is based on two stages: (1) creating 3D non-self-intersecting iso-curves from a 3D triangular mesh and (2) extracting a topological graph. The feasibility of the proposed topological reconstruction method is demonstrated on several examples using freeform objects with complex topologies.

This paper presents a method for adaptive refinement within an integrated mechanically based CAE system. The system uses a mechanical B-spline finite element model for both geometric design and mechanical analysis. A technique for locally refining a solution by B-spline finite elements is presented. The key component in the proposed method is the linear coordinate transformation introduced into the refined element. The transformation is constructed in such a way that the transformed nodal configuration of the refined element is identical to the nodal configuration of the neighbor elements. Therefore, the assembly proceeds in the regular fashion, while the C/sup 0/ continuity is forced along the inter-element boundary exactly. The proposed adaptive refinement method has been implemented both for surface and solid design without substantial differences in technical complexity. Its feasibility as applied to sculptured surface and solid objects is demonstrated by several examples.

Reverse engineering ordinarily uses laser scanners since they can sample 3D data quickly and accurately relative to other systems. These laser scanner systems, however, yield an enormous amount of irregular and scattered digitized point data that requires intensive reconstruction processing. Reconstruction of freeform objects consists of two main stages: parameterization and surface fitting. Selection of an appropriate parameterization is essential for topology reconstruction as well as surface fitness. Current parameterization methods have topological problems that lead to undesired surface fitting results, such as noisy self-intersecting surfaces. Such problems are particularly common with concave shapes whose parametric grid is self-intersecting, resulting in a fitted surface that considerably twists and changes its original shape. In such cases, other parameterization approaches should be used in order to guarantee non-self-intersecting behavior. The parameterization method described in this paper is based on two stages: 2D initial parameterization; and 3D adaptive parameterization. Two methods were developed for the first stage: partial differential equation (PDE) parameterization and neural network self organizing maps (SOM) parameterization. The Gradient Descent Algorithm (GDA) and Random Surface Error Correction (RSEC), both of which are iterative surface fitting methods, were developed and implemented.

This paper proposes a new adaptive parametrization method to overcome the problems of using laser scanners in Reverse Engineering. The method is based on the following stages: (a) Detecting a 3D boundary of the parametric base surface by matching an intensity image from a CCD camera with the scanned data. (b) Adaptively reconstructing a parametric base surface with a non-self intersecting grid, based on a PDE method (c) Calculating the parametrization of the 3D sampled points. (d) Fitting the surface by applying a least square (LSQ) approximation method with boundary constraints. The feasibility of the parametrization algorithm is demonstrated on several examples using sculptured free objects.