New Models for High-Quality Surface Reconstruction and Rendering

We present an efficient algorithm for approximating huge general\n volumetric data sets, i.e.~the data is given over arbitrarily shaped\n volumes and consists of up to millions of samples. The method is based\n on cubic trivariate splines, i.e.~piecewise polynomials of total\n degree three defined w.r.t. uniform type-6 tetrahedral partitions of\n the volumetric domain. Similar as in the recent bivariate\n approximation approaches, the splines in three variables\n are automatically determined from the discrete data as a result of a\n two-step method, where local discrete least\n squares polynomial approximations of varying degrees are extended by\n using natural conditions, i.e.the continuity and smoothness properties\n which determine the underlying spline space. The main advantages of\n this approach with linear algorithmic complexity are as follows: no\n tetrahedral partition of the volume data is needed, only small\n linear systems have to be solved, the local variation and\n distribution of the data is automatically adapted,\n Bernstein-B{\\'e}zier techniques well-known in Computer Aided\n Geometric Design (CAGD) can be fully exploited, noisy data are\n automatically smoothed. Our numerical examples with huge data sets\n for synthetic data as well as some real-world data confirm the\n efficiency of the methods, show the high quality of the spline\n approximation, and illustrate that the rendered iso-surfaces inherit\n a visual smooth appearance from the volume approximating splines.

An efficient two-level spatial uniform grid structure-based high-quality surface reconstruction method with Marching Cubes (MC) for smoothed particle hydrodynamics (SPH) fluids was presented in this paper. Compared with the traditional way that dividing the simulation domain with uniform grid directly, an enhanced narrow-band approach using the parallel cuckoo hashing method was taken to index the coarse-level surface vertices, hence decrease the memory consumption. Moreover, a two-level spatial uniform grid structure was employed with a scheme of arranging the fine surface vertices, which could preserve the spatial locality property to facilitate the coalesced memory access on the GPU. Our algorithm was designed for parallel architectures, based on which a parallel version of the optimized surface reconstruction was performed on the CUDA platform. In the experiment of comparison to traditional approaches, the results indicated that our surface reconstruction method was more efficient at the same level of quality of the reconstructed surfaces.

Applications in scientific visualization often involve extensive data sets, which represent scalar or vector valued functions resulting from experimental measurements. Ray Casting (RC) is a well-known approach for visualizing a multi-dimensional volume data. It casts a large number of rays from the viewer into the volume and then computes the progressive attenuation along each ray in the volume. It is known that the ray-casting algorithm requires extensive computation time. In this study, we propose two techniques to speed up the ray-casting process. First, we derive an estimation of ray step sizes during its progressive re-sampling without invocating viewing transformation operations. Hence lengthy computations of trigonometric functions and matrix multiplications can be avoided. Furthermore, by exploring the ray coherence property, we propose a scan-line algorithm so that ray/volume intersections can be found efficiently. The proposed algorithm is implemented and compared with the conventional RC algorithm. Experimental results show that the proposed algorithm performs three to four times faster than the conventional RC algorithm.

We present a novel, physically-motivated method for surface reconstruction that can recover smooth surfaces from noisy and sparse data sets, without using orientation information. A new volumetric technique based on regularized-membrane potentials for aggregating the input sample points is introduced, which manages improved noise tolerability and outlier removal, without sacrificing much with respect to detail (feature) recovery. In this method, sample points are first aggregated on a volumetric grid. A labeling algorithm that relies on intrinsic properties of the smooth scalar field emerging after aggregation is used to classify grid points as exterior or interior to the surface. We also introduce a mesh-smoothing paradigm based on a mass-spring system, enhanced with a bending-energy minimizing term to ensure that the final triangulated surface is smoother than piecewise linear. The method compares favorably with respect to previous approaches in terms of speed and flexibility.

An efficient iterative gridding reconstruction method with correction of off-resonance artifacts was developed, which is especially tailored for multiple-shot non-Cartesian imaging. The novelty of the method lies in that the transformation matrix for gridding (T) was constructed as the convolution of two sparse matrices, among which the former is determined by the sampling interval and the spatial distribution of the off-resonance frequencies and the latter by the sampling trajectory and the target grid in the Cartesian space. The resulting T matrix is also sparse and can be solved efficiently with the iterative conjugate gradient algorithm. It was shown that, with the proposed method, the reconstruction speed in multiple-shot non-Cartesian imaging can be improved significantly while retaining high reconstruction fidelity. More important, the method proposed allows tradeoff between the accuracy and the computation time of reconstruction, making customization of the use of such a method in different applications possible. The performance of the proposed method was demonstrated by numerical simulation and multiple-shot spiral imaging on rat brain at 4.7 T.

14th Biennial IEEE Conference on Electromagnetic Field Computation, CEFC2010, Chicago, IL, 9-12 May 2010

In many industrial applications the need for an efficient and high-quality reconstruction of free-form surfaces does exist. Surface Reconstruction - the generation of CAD models from physical objects - has become an independent area of research. The supplementary modification and the automated manufacturing of workpieces represent typical fields of application. Small tolerances in the desired properties result in a very high number of scan points needed. Thus, modern approaches have to be capable of processing, analysing and modelling these amounts of data.There are several studies that use evolutionary algorithms (EA) for surface reconstruction tasks. Until now, these studies only describe the general ability of EA to successfully optimise surfaces. Aspects like runtime as well as comparability to other optimisation techniques have not been considered. Since these aspects are of great importance for integration in applicable software tools, in this paper the ability of a state-of-the-art multi-objective EA to be successfully integrated in surface reconstruction software is analysed. Major drawbacks are disclosed and necessary add-on modules are presented.

Photoacoustic computed tomography (PACT) is a promising imaging modality that combines the advantages of optical contrast with ultrasound detection. Utilizing ultrasound transducers with larger surface areas can improve detection sensitivity. However, when computationally efficient analytic reconstruction methods that neglect the spatial impulse responses (SIRs) of the transducer are employed, the spatial resolution of the reconstructed images will be compromised. Although optimization-based reconstruction methods can explicitly account for SIR effects, their computational cost is generally high, particularly in three-dimensional (3D) applications. To address the need for accurate but rapid 3D PACT image reconstruction, this study presents a framework for establishing a learned SIR compensation method that operates in the data domain. The learned compensation method maps SIR-corrupted PACT measurement data to compensated data that would have been recorded by idealized point-like transducers. Subsequently, the compensated data can be used with a computationally efficient reconstruction method that neglects SIR effects. Two variants of the learned compensation model are investigated that employ a U-Net model and a specifically designed, physics-inspired model, referred to as Deconv-Net. A fast and analytical training data generation procedure is also a component of the presented framework. The framework is rigorously validated in virtual imaging studies, demonstrating resolution improvement and robustness to noise variations, object complexity, and sound speed heterogeneity. When applied to in-vivo breast imaging data, the learned compensation models revealed fine structures that had been obscured by SIR-induced artifacts. To our knowledge, this is the first demonstration of learned SIR compensation in 3D PACT imaging.

There are many techniques that reconstruct continuous 3D surfaces from scattered point data coming from laser range scanners. One of the most commonly used representations are point set surfaces (PSS) defined as the set of stationary points of a moving least squares (MLS) projection operator. One interesting property of the MLS projection is to automatically filter out high frequency noise, that is usually present in raw data due to scanning errors. Unfortunately, the MLS projection also smoothes out any high frequency feature, such as creases or corners, that may be present in the scanned geometry, and does not offer any possibility to distinguish between such feature and noise. The main contribution of this paper, is to present an alternative projection operator for surface reconstruction, based on the enriched reproducing kernel particle approximation (ERKPA), which allows the reconstruction process to account for high frequency features, by letting the user explicitly tag the corresponding areas of the scanned geometry.

In oral and maxillofacial surgery, computer-assisted navigation technologies have been widely used to achieve intraoperative positioning. The traditional methods mainly rely on the experience of doctors and the difference between the locations of key points in the surgical area and the preoperative planning, which have certain limitations. In this paper, a new intraoperative surgical navigation framework based on mobile laser scanner is proposed, which ensures that surgery is performed accurately according to the preoperative planning. The framework mainly includes two parts. First, the real-time surface reconstruction of the anatomy should be realized during the operation. Second, the acquired image is matched to the planned image in real time. Although the most common method of surface reconstruction is to render the volume directly from raw data or render the surface from the segmented data using computed tomography/magnetic resonance (CT/MR) data, this method is too complicated for performing the real-time operation during surgery. Furthermore, a new surface registration technique is proposed for image-guided oral and maxillofacial surgery based on the point sets. To improve the registration accuracy and robustness, the point sets are modeled by Mixed Student’s t-Distribution model. In the experiments, the point sets of CT data are from 10 patients with craniomaxillofacial diseases and the surface point set is from the LRS. The TRE of 10 data was less than 1[Formula: see text]mm. Compared with the paired-point registration method and Iterative Closest Point algorithm, the results demonstrated better performance of the proposed method, the surgical situation can be displayed in real time during the surgical process, and any differences from the surgical plan can also be reflected.

Triple-dexel modeling is a geometric representation method, which depicts the intersection of a solid with rays cast in three orthogonal directions. Due to its fast Boolean operations, simple data structure, and easy implementation, triple-dexel modeling is highly suitable for real-time graphics-based simulation applications such as numerical control (NC) machining verification and virtual sculpting. This paper presents a novel surface reconstruction method from triple-dexel data by first converting the triple-dexel data into contours on three sets of orthogonal slices and then generating the solid’s boundary surface in triangular facets from these contours. The developed method is faster than the voxel-based method, and the reconstructed surface model is more accurate than the surface reconstructed from voxel representation using the marching cube algorithm. Examples are given to demonstrate the ability of surface reconstruction from the triple-dexel model in virtual sculpting.

Over the last eight years, significant scientific effort has been dedicated on the problem of 3-D surface reconstruction for structural systems. However, the critical area of marine structures remains insufficiently studied. The research presented here focuses on the problem of 3-D surface reconstruction in the marine environment. This work is an extension of our previous approach, in which a surface vehicle that was equipped with a powerful laser scanner was designed and used to scan the above-water part of the marine structure of interest. Here we propose the design of a novel surface vehicle that is capable of using laser scanners and a side-looking sonar to scan marine structures both above and below the waterline. We also study the issue of downsampling the dataset in order to perform efficient surface reconstruction of the considered 3-D geometry, and we present a methodology for combining and integrating data from the above- and below-water parts of the structure. To illustrate the proposed robotic platform and validate our algorithms, we present results from a set of experiments in the Singapore Sea. Specifically, we present 2 different maps: the above-water map and the combined above-and below-water map. In both cases, we have two different maps: a lower quality map, that can be generated on-line, and a higher quality map that is generated off-line. To the best of our knowledge, our work is the only one that provides a 3-D model for both above- and below-water parts of marine structures. In this work we assumed a GPS-denied environment, without using any other navigation sensor such as DVL or INS.

We propose efficient signal reconstruction methods such that the reconstructed signal has the same measurements as the underlying original signal if the former was observed by the same system as that for the latter. The reconstructed signal is a linear combination of reconstruction functions, and the main task is to compute the coefficients from the measurements. This generally involves an inversion of the cross-correlation matrix between the sampling functions and the reconstruction functions. We show that the coefficients are computed efficiently using the discrete Fourier transform (DFT) when sampling is shift-invariant and when the reconstruction functions are shift-invariant functions, Fourier basis functions, or Fourier cosine basis functions. Because of the DFT, the proposed methods do not require matrix inversion computation; rather these methods make it possible to obtain the coefficients with an O(N log N) computation, where N stands for the number of samples. We show the effectiveness of the proposed method by experiments using an ECG signal.

In reverse engineering, the point cloud data processing is the key, it will directly affect the quality and efficiency of the subsequent reconstruction of the surface. However, the amount of data obtained by three-dimensional laser scanning is often larger and redundant, which will increase the difficulty of the surface reconstruction, therefore, the point cloud data is needed to streamline. Depth analysis of the efficiency and accuracy of curvature grid method, a secondary streamlined algorithm is proposed, which take use of non-uniform grid streamline law based on octree to streamline to the point cloud, and re-use curvature streamline method based on B-spline surface fitting to streamline it. This method, whose streamline ratio is relatively high, can effectively retain the feature point cloud data, providing a great convenience for the follow-up of reverse engineering.

Direct volume rendering and isosurfacing are ubiquitous rendering techniques in scientific visualization, commonly employed in imaging 3D data from simulation and scan sources. Conventionally, these methods have been treated as separate modalities, necessitating different sampling strategies and rendering algorithms. In reality, an isosurface is a special case of a transfer function, namely a Dirac impulse at a given isovalue. However, artifact-free rendering of discrete isosurfaces in a volume rendering framework is an elusive goal, requiring either infinite sampling or smoothing of the transfer function. While preintegration approaches solve the most obvious deficiencies in handling sharp transfer functions, artifacts can still result, limiting classification. In this paper, we introduce a method for rendering such features by explicitly solving for isovalues within the volume rendering integral. In addition, we present a sampling strategy inspired by ray differentials that automatically matches the frequency of the image plane, resulting in fewer artifacts near the eye and better overall performance. These techniques exhibit clear advantages over standard uniform ray casting with and without preintegration, and allow for high-quality interactive volume rendering with sharp C0 transfer functions.