Minimal surfaces based object segmentation

A geometric approach for 3D object segmentation and representation is presented. The segmentation is obtained by deformable surfaces moving towards the objects to be detected in the 3D image. The model is based on curvature motion and the computation of surfaces with minimal areas, better known as minimal surfaces. The space where the surfaces are computed is induced from the 3D image (volumetric data) in which the objects are to be detected. The model links between classical deformable surfaces obtained via energy minimization, and intrinsic ones derived from curvature based flows. The new approach is stable, robust, and automatically handles changes in the surface topology during the deformation     

Shape differentiation of freeform surfaces using a similarity measure based on an integral of Gaussian curvature

Freeform surfaces are popularly used to design and model complex 3D objects. These 3D models are stored as computerized models in databases. To facilitate data retrieval and shape matching, a major challenge lies in defining and computing the level of similarity between two or more freeform surfaces. In order to explore the useful 3D information associated with the surfaces, an integrated approach based on the integral of Gaussian curvature is proposed to develop the measures of similarity of freeform surfaces. Specifically, the integral of Gaussian curvature is mapped into the 2D space, and a shape-based measure is developed using statistical methods to compute the level of similarity. For smooth surfaces, a fast approximation algorithm is developed to calculate the curvature of individual subregions. In cases where the target surface has a complex topological structure or a smooth surface is not available, the integral of Gaussian curvature for the discrete surface is first calculated at each vertex, followed by mapping onto a 2D spherical coordinate. The distance measure focuses on the local geometry, which is critical to investigate models with a certain level of resemblance such as products in a family. This proposed approach can be applied to surfaces under various transformations, as well as 3D data from various sources.     

An efficient and robust algorithm for 3D mesh segmentation

This paper presents an efficient and robust algorithm for 3D mesh segmentation. Segmentation is one of the main areas of 3D object modeling. Most segmentation methods decompose 3D objects into parts based on curvature analysis. Most of the existing curvature estimation algorithms are computationally costly. The proposed algorithm extracts features using Gaussian curvature and concaveness estimation to partition a 3D model into meaningful parts. More importantly, this algorithm can process highly detailed objects using an eXtended Multi-Ring (XMR) neighborhood based feature extraction. After feature extraction, we also developed a fast marching watershed-based segmentation algorithm followed by an efficient region merging scheme. Experimental results show that this segmentation algorithm is efficient and robust.     

三维激光扫描表面数据区域分割

针对现有三维激光扫描数据区域分割算法受原始碎片表面粗糙度影响较大且只适用于形状较规则、表面较平坦及断裂面较少的物体这一问题,提出了区域膨胀策略的三维扫描表面数据区域分割算法,该算法将三维激光扫描表面数据分割成若干个具有相同法矢方向的区域。首先将三维扫描表面数据转化为三维网格模型;然后利用同一区域中相邻网格具有相似法线方向这一性质,使用区域膨胀策略生成若干获选表面区域;最后通过去除候选区域中的噪声区域得到最终表面区域分割结果。通过实物表面扫描数据对上述算法进行仿真验证,结果表明该算法可对三维表面扫描数据进行有效的区域分割。     

Surface feature based mesh segmentation

Mesh segmentation has a variety of applications in product design, reverse engineering, and rapid prototyping fields. This paper presents a novel algorithm of mesh segmentation from original scanning data points, which essentially consists of three steps. Normal based initial decomposing is first performed to recognize plane features. Then we implement further segmentation based on curvature criteria and Gauss mapping, followed by the detection of quadric surface features. The segmentation refinement is finally achieved using B-spline surface fitting technology. The experimental results on many 3D models have demonstrated the effectiveness and robustness of the proposed segmentation method.     

Mean shift denoising of point-sampled surfaces

This paper presents an anisotropic denoising/smoothing algorithm for point-sampled surfaces. Motivated by the impressive results of mean shift filtering on image denoising, we extend the concept to 3D surface smoothing by taking the vertex normal and the curvature as the range component and the vertex position as the spatial component. Then the local mode of each vertex on point-based surfaces is computed by a 3D mean shift procedure dependent on local neighborhoods that are adaptively obtained by a kdtree data structure. Clustering pieces of point-based surfaces of similar local mode provides a meaningful model segmentation. Based on the adaptively clustered neighbors, we finally apply a trilateral point filtering scheme that adjusts the position of sample points along their normal directions to successfully reduce noise from point-sampled surfaces while preserving geometric features.     

Albedo estimation for scene segmentation

Standard methods of image segmentation do not take into account the three-dimensional nature of the underlying scene. For example, histogram-based segmentation tacitly assumes that the image intensity is piecewise constant, and this is not true when the scene contains curved surfaces. This paper introduces a method of taking 3D information into account in the segmentation process. The image intensities are adjusted to compensate for the effects of estimated surface orientation; the adjusted intensities can be regarded as reflectivity estimates. When histogram-based segmentation is applied to these new values, the image is segmented into parts corresponding to surfaces of contant reflectivity in the scene.     

Curvature estimation scheme for triangle meshes using biquadratic Bézier patches

When dealing with triangle meshes, it is often important to compute curvature information for the purposes of feature recognition, segmentation, or shape analysis. Since a triangle mesh is a piecewise linear surface, curvature has to be estimated. Several different schemes have been proposed, both discrete and continuous, i.e. based on fitting surfaces locally. This paper compares commonly used discrete and continuous curvature estimation schemes. We also present a novel method which uses biquadratic Bézier patches as a local surface fitting technique.     

3D reconstruction for featureless scenes with curvature hints

We present a novel interactive framework for improving 3D reconstruction starting from incomplete or noisy results obtained through image-based reconstruction algorithms. The core idea is to enable the user to provide localized hints on the curvature of the surface, which are turned into constraints during an energy minimization reconstruction. To make this task simple, we propose two algorithms. The first is a multi-view segmentation algorithm that allows the user to propagate the foreground selection of one or more images both to all the images of the input set and to the 3D points, to accurately select the part of the scene to be reconstructed. The second is a fast GPU-based algorithm for the reconstruction of smooth surfaces from multiple views, which incorporates the hints provided by the user. We show that our framework can turn a poor-quality reconstruction produced with state of the art image-based reconstruction methods into a high- quality one.     

Robust normal estimation and region growing segmentation of infrastructure 3D point cloud models

Modern remote sensing technologies such as three-dimensional (3D) laser scanners and image-based 3D scene reconstruction are in increasing demand for applications in civil infrastructure design, maintenance, operation, and as-built construction verification. The complex nature of the 3D point clouds these technologies generate, as well as the often massive scale of the 3D data, make it inefficient and time consuming to manually analyze and manipulate point clouds, and highlights the need for automated analysis techniques. This paper presents one such technique, a new region growing algorithm for the automated segmentation of both planar and non-planar surfaces in point clouds. A core component of the algorithm is a new point normal estimation method, an essential task for many point cloud processing algorithms. The newly developed estimation method utilizes robust multivariate statistical outlier analysis for reliable normal estimation in complex 3D models, considering that these models often contain regions of varying surface roughness, a mixture of high curvature and low curvature regions, and sharp features. An adaptation of Mahalanobis distance, in which the mean vector and covariance matrix are derived from a high-breakdown multivariate location and scale estimator called Deterministic MM-estimator (DetMM) is used to find and discard outlier points prior to estimating the best local tangent plane around any point in a cloud. This approach is capable of more accurately estimating point normals located in highly curved regions or near sharp features. Thereafter, the estimated point normals serve a region growing segmentation algorithm that only requires a single input parameter, an improvement over existing methods which typically require two control parameters. The reliability and robustness of the normal estimation subroutine was compared against well-known normal estimation methods including the Minimum Volume Ellipsoid (MVE) and Minimum Covariance Determinant (MCD) estimators, along with Maximum Likelihood Sample Consensus (MLESAC). The overall region growing segmentation algorithm was then experimentally validated on several challenging 3D point clouds of real-world infrastructure systems. The results indicate that the developed approach performs more accurately and robustly in comparison with conventional region growing methods, particularly in the presence of sharp features, outliers and noise.     

三维CAD曲面模型距离-曲率形状分布检索算法

产品三维CAD模型检索对实现产品设计信息的有效重用具有重要意义和作用.针对在工程应用中存在大量含有曲面的产品,提出一种基于距离-曲率形状分布的三维CAD曲面模型检索算法.首先在模型表面随机取点,计算出所取点的曲率以及该点到模型质心的距离;然后以模型质心为球心,统计处在不同半径球壳间所取随机点的曲率分布,分别以球壳半径和曲率为坐标轴构建距离-曲率平面网格,并统计每个网格中随机点出现的频次,从而形成距离-曲率矩阵;最后利用特定的规则计算矩阵的相似值,用该值衡量2个模型的相似程度,实现模型的相似性检索.实验结果表明,文中算法的检索性能比传统的形状分布算法有较大提高,尤其适用于自由曲面模型的检索.     

Patch‐type Segmentation of Voxel Shapes using Simplified Surface Skeletons

We present a new method for decomposing a 3D voxel shape into disjoint segments using the shape's simplified surface‐skeleton. The surface skeleton of a shape consists of 2D manifolds inside its volume. Each skeleton point has a maximally inscribed ball that touches the boundary in at least two contact points. A key observation is that the boundaries of the simplified fore‐ and background skeletons map one‐to‐one to increasingly fuzzy, soft convex, respectively concave, edges of the shape. Using this property, we build a method for segmentation of 3D shapes which has several desirable properties. Our method segments both noisy shapes and shapes with soft edges which vanish over low‐curvature regions. Multiscale segmentations can be obtained by varying the simplification level of the skeleton. We present a voxel‐based implementation of our approach and illustrate it on several realistic examples.     

Segmentation of Three-Dimensional Images with Parametric Active Surfaces and Topology Changes

In this paper, we introduce a novel parametric finite element method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford–Shah and the Chan–Vese functionals and perform a region-based segmentation of 3D image data. An evolution law is derived from energy minimization problems which push the surfaces to the boundaries of 3D objects in the image. We propose a parametric scheme which describes the evolution of parametric surfaces. An efficient finite element scheme is proposed for a numerical approximation of the evolution equations. Since standard parametric methods cannot handle topology changes automatically, an efficient method is presented to detect, identify and perform changes in the topology of the surfaces. One main focus of this paper are the algorithmic details to handle topology changes like splitting and merging of surfaces and change of the genus of a surface. Different artificial images are studied to demonstrate the ability to detect the different types of topology changes. Finally, the parametric method is applied to segmentation of medical 3D images.     

Robust feature detection and local classification for surfaces based on moment analysis

The stable local classification of discrete surfaces with respect to features such as edges and corners or concave and convex regions, respectively, is as quite difficult as well as indispensable for many surface processing applications. Usually, the feature detection is done via a local curvature analysis. If concerned with large triangular and irregular grids, e.g., generated via a marching cube algorithm, the detectors are tedious to treat and a robust classification is hard to achieve. Here, a local classification method on surfaces is presented which avoids the evaluation of discretized curvature quantities. Moreover, it provides an indicator for smoothness of a given discrete surface and comes together with a built-in multiscale. The proposed classification tool is based on local zero and first moments on the discrete surface. The corresponding integral quantities are stable to compute and they give less noisy results compared to discrete curvature quantities. The stencil width for the integration of the moments turns out to be the scale parameter. Prospective surface processing applications are the segmentation on surfaces, surface comparison, and matching and surface modeling. Here, a method for feature preserving fairing of surfaces is discussed to underline the applicability of the presented approach.     

Sampling framework for accurate curvature estimation in discrete surfaces

Accurate curvature estimation in discrete surfaces is an important problem with numerous applications. Curvature is an indicator of ridges and can be used in applications such as shape analysis and recognition, object segmentation, adaptive smoothing, anisotropic fairing of irregular meshes, and anisotropic texture mapping. In this paper, a new framework is proposed for accurate curvature estimation in discrete surfaces. The proposed framework is based on a local directional curve sampling of the surface where the sampling frequency can be controlled. This local model has a large number of degrees of freedoms compared with known techniques and, so, can better represent the local geometry. The proposed framework is quantitatively evaluated and compared with common techniques for surface curvature estimation. In order to perform an unbiased evaluation in which smoothing effects are factored out, we use a set of randomly generated Bezier surface patches for which the curvature values can be analytically computed. It is demonstrated that, through the establishment of sampling conditions, the error in estimations obtained by the proposed framework is smaller and that the proposed framework is less sensitive to low sampling density, sampling irregularities, and sampling noise.     

Reduce the stretch in surface flattening by finding cutting paths to the surface boundary

This paper presents a method for finding cutting paths on a 3D triangular mesh surface to reduce the stretch in the flattened surface. The cutting paths link the surface boundary and the nodes where the Gaussian curvature is high, and their total length is minimized. First, a linear algorithm for computing an approximate boundary geodesic distance map is introduced; the map encapsulates the undirected geodesic distance from every triangular node to the surface boundary approximately. This is followed by determining the undirected shortest paths passing through all the nodes where the Gaussian curvature is larger than a threshold. The cutting paths walk along the triangular edges of the given surface. Compared with other similar approaches, our method reaches a faster speed, and can deal with surfaces with widely distributed curvatures.     

Deep learning-based optimal segmentation of 3D printed product for surface quality improvement and support structure reduction

Large-sized product cannot be printed as one piece by a 3D printer because of the volume limitation of most 3D printers. Some products with the complex structure and high surface quality should also not be printed into one piece to meet requirement of the printing quality. For increasing the surface quality and reducing support structure of 3D printed models, this paper proposes a 3D model segmentation method based on deep learning. Sub-graphs are generated by pre-segmenting 3D triangular mesh models to extract printing features. A data structure is proposed to design training data sets based on the sub-graphs with printing features of the original 3D model including surface quality, support structure and normal curvature. After training a Stacked Auto-encoder using the training set, a 3D model is pre-segmented to build an application set by the sub-graph data structure. The application set is applied by the trained deep-learning system to generate hidden features. An Affinity Propagation clustering method is introduced in combining hidden features and geometric information of the application set to segment a product model into several parts. In the case study, samples of 3D models are segmented by the proposed method, and then printed using a 3D printer for validating the performance.     

破碎刚体三角网格模型的断裂面分割

针对基于断裂面匹配的破碎刚体复原,提出了一种分割断裂面的方法。首先,根据相邻三角片法矢的夹角,将碎块外表面以棱边为界限分割成多张曲面;然后,根据曲面法矢的扰动大小和扰动图像,经过二次分割,将曲面区分为原始面和断裂面。实验结果表明,所提方法能够正确快速地提取出形状较复杂碎块的断裂面。     

Texture mapping on surfaces of arbitrary topology using norm preserving-based optimization

A simple and yet highly efficient, high-quality texture mapping method for surfaces of arbitrary topology is presented. The new method projects the given surface from the 3D object space into the 2D texture space to identify the 2D texture structure that will be used to texture the surface. The object space to texture space projection is optimized to ensure minimum distortion of the texture mapping process. The optimization is achieved through a commonly used norm preserving minimization process on edges of the surface. The main difference here is, by using an initial value approach, the optimization problem can be set up as a quadratic programming problem and, consequently, solved by a linear least squares method. Three methods to choose a good initial value are presented. Test cases show that the new method works well on surfaces of arbitrary topology, with the exception of surfaces with exceptionally abnormal curvature distribution. Other advantages of the new method include uniformity and seamlessness of the texture mapping process. The new method is suitable for applications that do not require precise texture mapping results but demand highly efficient mapping process such as computer animation or video games.