Implicit Surface Reconstruction Research Articles

Computerized segmentation of pulmonary nodules depicted in CT examinations using freehand sketches

To aid a consistent segmentation of pulmonary nodules, the authors describe a novel computerized scheme that utilizes a freehand sketching technique and an improved break-and-repair strategy. This developed scheme consists of two primary parts. The first part is freehand sketch analysis, where the freehand sketching not only serves a natural way of specifying the location of a nodule, but also provides a mechanism for inferring adaptive information (e.g., the mass center, the density, and the size) in regard to the nodule. The second part is an improved break-and-repair strategy. The improvement avoids the time-consuming ray-triangle intersections using spherical bins and replaces the original global implicit surface reconstruction with a local implicit surface fitting and blending scheme. The performance of this scheme, including accuracy and consistence, was assessed using 50 CT examinations in the Lung Image Database Consortium (LIDC). For each of these examinations, a single nodule was selected under the aid of a publically available tool to assure these nodules were diverse in size, location, and density. Two radiologists were asked to use the developed tool to segment these nodules twice at different times (at least three months apart). A Hausdorff distance based method was used to assess the discrepancies (agreements) between the computerized results and the results by the four radiologists in the LIDC as well as the inter- and intrareader agreements in freehand sketching. The maximum and mean discrepancies in boundary outlines between the computerized scheme and the radiologists were 2.73 ± 1.32 mm and 1.01 ± 0.47 mm, respectively. When the nodules were classified (binned) into different size ranges, the maximum errors ranged from 1.91 to 4.13 mm; but smaller nodules had larger percentage discrepancies in term of size. Under the aid of the developed scheme, the inter- and intrareader variability in averaged maximum discrepancy across all types of pulmonary nodules were consistently smaller than 0.15 ± 0.07 mm. The computational cost in time of segmenting a pulmonary nodule ranged from 0.4 to 2.3 s with an average of 1.1 s for a typical desktop computer. The experiments showed that this scheme could achieve a reasonable performance in nodule segmentation and demonstrated the merits of incorporating freehand sketching into pulmonary nodule segmentation.

GPU-Based Sphere Tracing for Radial Basis Function Implicits

Ray tracing of implicit surfaces based on radial basis functions can demand high computational cost in the presence of a large number of radial centers. Recently, it was presented the least squares hermite radial basis functions (LS-HRBF) Implicits, a method for implicit surface reconstruction from Hermitian data (points equipped with their normal vectors) which makes use of iterative center selection in order to reduce the number of centers. In the present work, we propose an antialiazed sphere tracing algorithm fully implemented in OpenGL Shader Language for ray tracing LS-HRBF Implicits, which exploits a regular partition of unity for strong parallelization. We show that interactive frame rates can be achieved for surfaces composed of thousands of centers even when rendering effects such as cube mapping, soft shadows and ambient occlusion are used.

Bilateral Hermite Radial Basis Functions for Contour‐based Volume Segmentation

AbstractIn this paper, we propose a novel contour‐based volume image segmentation technique. Our technique is based on an implicit surface reconstruction strategy, whereby a signed scalar field is generated from user‐specified contours. The key idea is to compute the scalar field in a joint spatial‐range domain (i.e., bilateral domain) and resample its values on an image manifold. We introduce a new formulation of Hermite radial basis function (HRBF) interpolation to obtain the scalar field in the bilateral domain. In contrast to previous implicit methods, bilateral HRBF (B‐HRBF) generates a segmentation boundary that passes through all contours, fits high‐contrast image edges if they exist, and has a smooth shape in blurred areas of images. We also propose an acceleration scheme for computing B‐HRBF to support a real‐time and intuitive segmentation interface. In our experiments, we achieved high‐quality segmentation results for regions of interest with high‐contrast edges and blurred boundaries.

Multi-level hermite variational interpolation and quasi-interpolation

Based on the Hermite variational implicit surface reconstruction presented in Pan et al. (Science in China Series F: Information Sciences 52(2):308---315, 2009), we propose a multi-level interpolation method to overcome the problems resulted from using compactly supported radial basis functions (CSRBFs). In addition, we present a multi-level quasi-interpolation method which directly uses normal vectors to construct non-zero constraints and avoids solving any linear system, a common step of variational surface reconstruction, and leads to a fast and stable surface reconstruction from scattered points. With adaptive support size, our approach is robust and can successfully reconstruct surfaces on non-uniform and noisy point sets. Moreover, as the computation of quasi-interpolation is independent for each point, it can be easily parallelized on multi-core CPUs.

Robust and Efficient Implicit Surface Reconstruction for Point Clouds Based on Convexified Image Segmentation

We present an implicit surface reconstruction algorithm for point clouds. We view the implicit surface reconstruction as a three dimensional binary image segmentation problem that segments the enti...

A Curvature-Adaptive Implicit Surface Reconstruction for Irregularly Spaced Points

A curvature-adaptive implicit surface reconstruction for noisy and irregularly spaced points in 3D is introduced. The reconstructed surface traces the zero crossings of a signed field obtained from the sum of first-derivative anisotropic Gaussians centered at the points. The standard deviations of the anisotropic Gaussians are adapted to surface curvatures estimated from local data. A key characteristic of the formulation is its ability to smooth more along edges than across them, thereby preserving shape details while smoothing noise. The behavior of the proposed method under various density and organization of points is investigated and surface reconstruction results are compared with those obtained by well-known methods in the literature.

Generating smooth surface meshes from multi-region medical images.

Thanks to advances in medical imaging technologies and numerical methods, patient-specific modelling is more and more used to improve diagnosis and to estimate the outcome of surgical interventions. It requires the extraction of the domain of interest from the medical scans of the patient, as well as the discretisation of this geometry. However, extracting smooth multi-material meshes that conform to the tissue boundaries described in the segmented image is still an active field of research. We propose to solve this issue by combining an implicit surface reconstruction method with a multi-region mesh extraction scheme. The surface reconstruction algorithm is based on multi-level partition of unity implicit surfaces, which we extended to the multi-material case. The mesh generation algorithm consists in a novel multi-domain version of the marching tetrahedra. It generates multi-region meshes as a set of triangular surface patches consistently joining each other at material junctions. This paper presents this original meshing strategy, starting from boundary points extraction from the segmented data to heterogeneous implicit surface definition, multi-region surface triangulation and mesh adaptation. Results indicate that the proposed approach produces smooth and high-quality triangular meshes with a reasonable geometric accuracy. Hence, the proposed method is well suited for subsequent volume mesh generation and finite element simulations.

Bipartite Polar Classification for Surface Reconstruction

In this paper, we propose bipartite polar classification to augment an input unorganized point set ℘ with two disjoint groups of points distributed around the ambient space of ℘ to assist the task of surface reconstruction. The goal of bipartite polar classification is to obtain a space partitioning of ℘ by assigning pairs of Voronoi poles into two mutually invisible sets lying in the opposite sides of ℘ through direct point set visibility examination. Based on the observation that a pair of Voronoi poles are mutually invisible, spatial classification is accomplished by carving away visible exterior poles with their counterparts simultaneously determined as interior ones. By examining the conflicts of mutual invisibility, holes or boundaries can also be effectively detected, resulting in a hole-aware space carving technique. With the classified poles, the task of surface reconstruction can be facilitated by more robust surface normal estimation with global consistent orientation and off-surface point specification for variational implicit surface reconstruction. We demonstrate the ability of the bipartite polar classification to achieve robust and efficient space carving on unorganized point clouds with holes and complex topology and show its application to surface reconstruction.

Orienting raw point sets by global contraction and visibility voting

We present a global method for consistently orienting a defective raw point set with noise, non-uniformities and thin sharp features. Our method seamlessly combines two simple but effective techniques—constrained Laplacian smoothing and visibility voting—to tackle this challenge. First, we apply a Laplacian contraction to the given point cloud, which shrinks the shape a little bit. Each shrunk point corresponds to an input point and shares a visibility confidence assigned by voting from multiple viewpoints. The confidence is increased (resp. decreased) if the input point (resp. its corresponding shrunk point) is visible. Then, the initial normals estimated by principal component analysis are flipped according to the contraction vectors from shrunk points to the corresponding input points and the visibility confidence. Finally, we apply a Laplacian smoothing twice to correct the orientation of points with zero or low confidence. Our method is conceptually simple and easy to implement, without resorting to any complicated data structures and advanced solvers. Numerous experiments demonstrate that our method can orient the defective raw point clouds in a consistent manner. By taking advantage of our orientation information, the classical implicit surface reconstruction algorithms can faithfully generate the surface.

Markov Random Field Surface Reconstruction

A method for implicit surface reconstruction is proposed. The novelty in this paper is the adaptation of Markov Random Field regularization of a distance field. The Markov Random Field formulation allows us to integrate both knowledge about the type of surface we wish to reconstruct (the prior) and knowledge about data (the observation model) in an orthogonal fashion. Local models that account for both scene-specific knowledge and physical properties of the scanning device are described. Furthermore, how the optimal distance field can be computed is demonstrated using conjugate gradients, sparse Cholesky factorization, and a multiscale iterative optimization scheme. The method is demonstrated on a set of scanned human heads and, both in terms of accuracy and the ability to close holes, the proposed method is shown to have similar or superior performance when compared to current state-of-the-art algorithms.

Data-Parallel Octrees for Surface Reconstruction

We present the first parallel surface reconstruction algorithm that runs entirely on the GPU. Like existing implicit surface reconstruction methods, our algorithm first builds an octree for the given set of oriented points, then computes an implicit function over the space of the octree, and finally extracts an isosurface as a watertight triangle mesh. A key component of our algorithm is a novel technique for octree construction on the GPU. This technique builds octrees in real time and uses level-order traversals to exploit the fine-grained parallelism of the GPU. Moreover, the technique produces octrees that provide fast access to the neighborhood information of each octree node, which is critical for fast GPU surface reconstruction. With an octree so constructed, our GPU algorithm performs Poisson surface reconstruction, which produces high-quality surfaces through a global optimization. Given a set of 500 K points, our algorithm runs at the rate of about five frames per second, which is over two orders of magnitude faster than previous CPU algorithms. To demonstrate the potential of our algorithm, we propose a user-guided surface reconstruction technique which reduces the topological ambiguity and improves reconstruction results for imperfect scan data. We also show how to use our algorithm to perform on-the-fly conversion from dynamic point clouds to surfaces as well as to reconstruct fluid surfaces for real-time fluid simulation.

Rapid surface reconstruction from a point cloud using the least-squares projection

A new approach for the rapid and robust surface reconstruction from a point cloud is presented based on the distance field and the least-squares projection (LSP) algorithm. This novel approach works directly on the point cloud without any explicit or implicit surface reconstruction procedure. First, a coarse base polygonal model was created directly from the distance field for the given point cloud through the iso-surface extraction. After acquiring a rough base polygonal model, we obtain a quality polygonal model through the iterative refinement and least-squares projection which projects current working polygonal model onto the point cloud in a least-squares sense. The main contribution of this work is the robust and fast surface reconstruction from randomly scattered 3D points only without any further information. We demonstrate the validity and efficiency of this new approach through a number of application examples.

Implicit surface reconstruction from point cloud data based on generalized polynomials neural network

A new type of generalized polynomials neural network was proposed to reconstruct 3D implicit surface from the scattered points. Since its hidden-layer neurons were activated with the different and linear independent generalized polynomials,the proposed neural network could achieve good performance in learning different patterns. Then the weights-updating formula for the new type of neural network was derived based on gradient-descent method. The simulation results on some scattered point models show that this method can obtain good reconstruction quality and denoising effect.

Dual-RBF based surface reconstruction

Surface reconstruction (Bloomenthal and Wyvill, Introduction to Implicit Surfaces, 1997) is a fundamental work in Computer Aided Design (CAD) and Computer Graphics (CG). In this paper, motivated by the physical polar field model (Yuxu Lin Chun Chen in Proceedings of the 3rd Pacific-Rim Symposium on Image and Video Technology, 1997), we propose a novel implicit surface reconstruction approach, named Dual-RBF. Through simulating the physical polar field model, Dual-RBF provides a nice initial reconstruction state firstly. Then, two simple nonlinear methods are introduced to adjust the configurations of Dual-RBF model, so that a more accurate reconstruction is reached. Thirdly, the Dual-RBF becomes even more robust to fill the holes on some flawed input point-clouds by adopting a multi-level strategy. Finally, the visualization of the surface reconstruction is speed up with GPU. Experimental results show that the proposed approach is faster and more robust than previous implicit surface reconstruction techniques.

Hermite variational implicit surface reconstruction

We propose a new technique for reconstructing surfaces from a large set of unorganized 3D data points and their associated normal vectors. The surface is represented as the zero level set of an implicit volume model which fits the data points and normal constraints. Compared with variational implicit surfaces, we make use of surface normal vectors at data points directly in the implicit model and avoid of introducing manufactured off-surface points. Given n surface point/normal pairs, the proposed method only needs to solve an n×n positive definite linear system. It allows fitting large datasets effectively and robustly. We demonstrate the performance of the proposed method with both globally supported and compactly supported radial basis functions on several datasets.

Image piecewise inpainting based on radial basis function

PurposeThe purpose of this paper is to present a novel algorithm for image inpainting, which has been widely used for removing unwanted objects from images or reconstructing damaged photographs.Design/methodology/approachAn image piecewise inpainting technique based on radial basis function (RBF) is used to transform the 2D image inpainting problem into 3D implicit surface reconstruction problem. And a RBF center reduction method is proposed. By RBF resampling, the algorithm can nicely fix the damaged image or remove specific objects.FindingsExperimental results show that the proposed algorithms can prevent the edge blur caused by the isotropic character of RBF, and effectively reduce the RBF centers without a loss in accuracy.Originality/valueThe proposed inpainting approach is interesting for its combination of RBF method and region segmentation that can handle the restoring of high‐variation areas.

Regularized implicit surface reconstruction from points and normals

Abstract We consider the problem of surface reconstruction of a geometric object from a finite set of sample points with normals. Our contribution is to present a new scheme for implicit surface reconstruction. Similarly to the multilevel partition of unity (MPU) method we hierarchically divide the domain obtaining local approximation for the object on each part, and then patch all together obtaining a global description of the object. Our new scheme uses ridge regression and weighted gradient one fitting techniques to get better stability on local approximations. The method behaves reasonably on sparse set of points and data with holes as those which comes from 3D scanning of real objects.

Regularized implicit surface reconstruction from points and normals

Regularized implicit surface reconstruction from points and normals

Implicit surface reconstruction based on mean-shift

Surface reconstruction is one of critical problems in reverse engineering and an approach of implicit surface recon- struction from scattered points is presented based on mean shift procedure, which is a nonparametric and iterative procedure. This needs no solving large linear system and the performance is not reduced when the input data is noisy. With this approach, it is able to repair incomplete data or fill holes, and it is not difficult to create multiresolution representation for the given object, and to apply boolean operation between objects through the techniques of constructive solid geometry. Extensive ex- perimental results and applications show the approach is effec- tive and efficient.

Automatic least-squares projection of points onto point clouds with applications in reverse engineering

A novel method for projecting points onto a point cloud, possibly with noise, is presented based on the point directed projection (DP) algorithm proposed by Azariadis P., Sapidis N. [Drawing curves onto a cloud of points for point-based modelling. Computer-Aided Design 2005; 37(1): 109–22]. The new method operates directly on the point cloud without any explicit or implicit surface reconstruction procedure. The presented method uses a simple, robust, and efficient algorithm: least-squares projection (LSP), which projects points onto the point cloud in a least-squares sense without any specification of the projection vector. The main contribution of this novel method is the automatic computation of the projection vector. Furthermore, we demonstrate the effectiveness of this approach through a number of application examples including thinning a point cloud, point normal estimation, projecting curves onto a point cloud and others.