Variational Surface Reconstruction Research Articles

Shading‐Based Surface Recovery Using Subdivision‐Based Representation

AbstractThis paper presents subdivision‐based representations for both lighting and geometry in shape‐from‐shading. A very recent shading‐based method introduced a per‐vertex overall illumination model for surface reconstruction, which has advantage of conveniently handling complicated lighting condition and avoiding explicit estimation of visibility and varied albedo. However, due to its discrete nature, the per‐vertex overall illumination requires a large amount of memory and lacks intrinsic coherence. To overcome these problems, in this paper we propose to use classic subdivision to define the basic smooth lighting function and surface, and introduce additional independent variables into the subdivision to adaptively model sharp changes of illumination and geometry. Compared to previous works, the new model not only preserves the merits of the per‐vertex illumination model, but also greatly reduces the number of variables required in surface recovery and intrinsically regularizes the illumination vectors and the surface. These features make the new model very suitable for multi‐view stereo surface reconstruction under general, unknown illumination condition. Particularly, a variational surface reconstruction method built upon the subdivision representations for lighting and geometry is developed. The experiments on both synthetic and real‐world data sets have demonstrated that the proposed method can achieve memory efficiency and improve surface detail recovery.

Quantitative Assessment of Variational Surface Reconstruction from Sparse Point Clouds in Freehand 3D Ultrasound Imaging during Image-Guided Tumor Ablation

Surface reconstruction for freehand 3D ultrasound is used to provide 3D visualization of a VOI (volume of interest) during image-guided tumor ablation surgery. This is a challenge because the recorded 2D B-scans are not only sparse but also non-parallel. To solve this issue, we established a framework to reconstruct the surface of freehand 3D ultrasound imaging in 2011. The key technique for surface reconstruction in that framework is based on variational interpolation presented by Greg Turk for shape transformation and is named Variational Surface Reconstruction (VSR). The main goal of this paper is to evaluate the quality of surface reconstructions, especially when the input data are extremely sparse point clouds from freehand 3D ultrasound imaging, using four methods: Ball Pivoting, Power Crust, Poisson, and VSR. Four experiments are conducted, and quantitative metrics, such as the Hausdorff distance, are introduced for quantitative assessment. The experiment results show that the performance of the proposed VSR method is the best of the four methods at reconstructing surface from sparse data. The VSR method can produce a close approximation to the original surface from as few as two contours, whereas the other three methods fail to do so. The experiment results also illustrate that the reproducibility of the VSR method is the best of the four methods.

Variational Reconstruction of Left Cardiac Structure from CMR Images.

Cardiovascular Disease (CVD), accounting for 17% of overall deaths in the USA, is the leading cause of death over the world. Advances in medical imaging techniques make the quantitative assessment of both the anatomy and function of heart possible. The cardiac modeling is an invariable prerequisite for quantitative analysis. In this study, a novel method is proposed to reconstruct the left cardiac structure from multi-planed cardiac magnetic resonance (CMR) images and contours. Routine CMR examination was performed to acquire both long axis and short axis images. Trained technologists delineated the endocardial contours. Multiple sets of two dimensional contours were projected into the three dimensional patient-based coordinate system and registered to each other. The union of the registered point sets was applied a variational surface reconstruction algorithm based on Delaunay triangulation and graph-cuts. The resulting triangulated surfaces were further post-processed. Quantitative evaluation on our method was performed via computing the overlapping ratio between the reconstructed model and the manually delineated long axis contours, which validates our method. We envisage that this method could be used by radiographers and cardiologists to diagnose and assess cardiac function in patients with diverse heart diseases.

Construction of lunar DEMs based on reflectance modelling

Existing lunar DEMs obtained based on laser altimetry or photogrammetric image analysis are characterised by high large-scale accuracies while their lateral resolution is strongly limited by noise or interpolation artifacts. In contrast, image-based photometric surface reconstruction approaches reveal small-scale surface detail but become inaccurate on large spatial scales. The framework proposed in this study therefore combines photometric image information of high lateral resolution and DEM data of comparably low lateral resolution in order to obtain DEMs of high lateral resolution which are also accurate on large spatial scales. Our first approach combines an extended photoclinometry scheme and a shape from shading based method. A novel variational surface reconstruction method further increases the lateral resolution of the DEM such that it reaches that of the underlying images. We employ the Hapke IMSA and AMSA reflectance models with two different formulations of the single-particle scattering function, such that the single-scattering albedo of the surface particles and optionally the asymmetry parameter of the single-particle scattering function can be estimated pixel-wise. As our DEM construction methods require co-registered images, an illumination-independent image registration scheme is developed. An evaluation of our framework based on synthetic image data yields an average elevation accuracy of the constructed DEMs of better than 20m as long as the correct reflectance model is assumed. When comparing our DEMs to LOLA single track data, absolute elevation accuracies around 30m are obtained for test regions that cover an elevation range of several thousands of metres. The proposed illumination-independent image registration method yields subpixel accuracy even in the presence of 3D perspective distortions. The pixel-wise reflectance parameters estimated simultaneously with the DEM reflect compositional contrasts between different surface units. Specifically, the detected variations of the parameter of the single-particle scattering function indicate small-scale variations of the regolith particle size, possibly as a result of differences in soil maturity.

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.

Surface Reconstruction from Sparse and Arbitrarily Oriented Contours in Freehand 3D Ultrasound

3D reconstruction for freehand 3D ultrasound is a challenging issue because the recorded B-scans are not only sparse, but also non-parallel (actually they may arbitrarily orient in 3D space and may intersect each other). Conventional volume reconstruction methods can’t reconstruct sparse data efficiently while not introducing geometrical artifacts and conventional surface reconstruction methods can’t reconstruct surfaces from contours that are arbitrarily oriented in 3D space. We developed a new surface reconstruction method for freehand 3D ultrasound based on variational implicit function which is presented by Greg Turk for shape transformation. In the new method, we first constructed on- and off-surface constraints from the segmented contours of all recorded B-scans and then used a variational interpolation technique to get a single implicit function in 3D. Finally, the implicit function was evaluated to extract the zero-valued surface as final reconstruction result. Two experiments was conducted to assess our variational surface reconstruction method and the experiment results have shown that the new method is capable of reconstructing surface smoothly from sparse contours which can be arbitrarily oriented in 3D space.

Surface Reconstruction from Sparse & Arbitrarily Oriented Contours in Freehand 3D Ultrasound

3D reconstruction for freehand 3D ultrasound is a challenging issue because the recorded B-scans are not only sparse, but also non-parallel (actually they may arbitrarily oriented in 3D space and may intersect each other). Conventional volume reconstruction methods can’t reconstruct sparse data efficiently while not introducing geometrical artifacts, and conventional surface reconstruction methods can’t reconstruct surfaces from contours that are arbitrarily oriented in 3D space. We developed a new surface reconstruction method for freehand 3D ultrasound based on variational implicit function which is presented by Greg Turk for shape transformation. In the new method, we first constructed on- & off-surface constraints from the segmented contours of all recorded B-scans, then used a variational interpolation technique to get a single implicit function in 3D. Finally, the implicit function was evaluated to extract the zero-valued surface as final reconstruction result. Two experiment was conducted to assess our variational surface reconstruction method, and the experiment results have shown that the new method is capable of reconstructing surface smoothly from sparse contours which can be arbitrarily oriented in 3D space.

Globally optimal estimate for variational surface reconstruction

In this article, we tackle the problem of using globally optimal estimate for variational surface reconstruction. We give an overview of globally optimal method on variational surface when the three-dimensional (3D) surface is represented by a point-based surface and a triangular mesh-based surface, and we detail the variational surface used on surface reconstruction. It can be applied to derive a range of meaningful surface reconstructions from this high dimensional space. We show that using a progression of spatially varying anisotropic weights can achieve significant improvements in surface reconstruction. Simulated surfaces and real model are experimentally studied, and the results validate that the proposed approaches improved the reconstruction. The proposed method improved the reconstruction results significantly for the simulated and real data.

Variational surface reconstruction based on Delaunay triangulation and graph cut

AbstractA novel method for surface reconstruction from an unorganized point set is presented. An energy functional based on a weighted minimal surface model is proposed for surface reconstruction, which is efficiently minimized by graph cut methods. By solving the minimization problem on the graph dual to a Delaunay‐based tetrahedral mesh, the advantages of explicit and implicit methods for surface reconstruction are well integrated. A triangular surface mesh homeomorphic to the original surface can be extracted directly from the tetrahedral mesh provided a sufficient sampling density exists. Difficult cases involving undersampling, non‐uniformity, noises and topological complexities can be handled effectively as well. Furthermore, for the first time, multi‐phase surface reconstruction is realized based on the graph cut methods. Various examples are included for demonstrating the efficiency and effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.

Signal matching through scale space

Given a collection of similar signals that have been deformed with respect to each other, the general signal-matching problem is to recover the deformation. We formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term. The minimization reduces to a dynamic system governed by a set of coupled, first-order differential equations. The dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale. Among the major themes in recent work on visual signal matching have been the notions of matching as constrained optimization, of variational surface reconstruction, and of coarse-to-fine matching. Our solution captures these in a precise, succinct, and unified form. Results are presented for one-dimensional signals, a motion sequence, and a stereo pair.