Multi-level Partition Of Unity Research Articles

A Hybrid Method for 3D Reconstruction of MR Images.

Three-dimensional surface reconstruction is a well-known task in medical imaging. In procedures for intervention or radiation treatment planning, the generated models should be accurate and reflect the natural appearance. Traditional methods for this task, such as Marching Cubes, use smoothing post processing to reduce staircase artifacts from mesh generation and exhibit the natural look. However, smoothing algorithms often reduce the quality and degrade the accuracy. Other methods, such as MPU implicits, based on adaptive implicit functions, inherently produce smooth 3D models. However, the integration in the implicit functions of both smoothness and accuracy of the shape approximation may impact the precision of the reconstruction. Having these limitations in mind, we propose a hybrid method for 3D reconstruction of MR images. This method is based on a parallel Marching Cubes algorithm called Flying Edges (FE) and Multi-level Partition of Unity (MPU) implicits. We aim to combine the robustness of the Marching Cubes algorithm with the smooth implicit curve tracking enabled by the use of implicit models in order to provide higher geometry precision. Towards this end, the regions that closely fit to the segmentation data, and thus regions that are not impacted by reconstruction issues, are first extracted from both methods. These regions are then merged and used to reconstruct the final model. Experimental studies were performed on a number of MRI datasets, providing images and error statistics generated from our results. The results obtained show that our method reduces the geometric errors of the reconstructed surfaces when compared to the MPU and FE approaches, producing a more accurate 3D reconstruction.

Adaptive Meshing Based on the Multi-level Partition of Unity and Dynamic Particle Systems for Medical Image Datasets

Adaptive Meshing Based on the Multi-level Partition of Unity and Dynamic Particle Systems for Medical Image Datasets

Robust multi‐level partition of unity implicits from triangular meshes

ABSTRACTThis paper presents a new robust multi‐level partition of unity (MPU) method, which constructs an implicit surface from a triangular mesh via the new error metric between the mesh and the implicit surface. The new error metric employs a weighted function of inner points and vertices of a triangle to fit an implicit surface, which can control the approximation error between the surface and vertices of the triangle. Furthermore, it is applied to the MPU method by utilizing the dual graph of a triangular mesh, and the general quadric implicit surface is used for surface representation. Compared with the MPU method, the new method generates fewer subdivision cells with the same approximation error and performs more steadily especially when given triangular mesh with fewer vertices. Copyright © 2013 John Wiley & Sons, Ltd.

Data fitting independent of grid structure using a volumic version of MPU

Volume graphics is a key technology in fields such as fluid dynamics and medical science. The visualization of volume data requires the creation of a continuous scalar field to exactly or approximately interpolate scalar values assigned to the discrete voxels. In the present paper, we propose a method that we refer to as the volumic version of the multi-level partition of unity (volumic MPU). The method approximately interpolates the scalar values with good precision to generate a scalar field that is continuous up to second-order differentiation. The volumic MPU, being independent of grid structures of input volume data, is applicable to both irregular-grid data and regular grid data. The volumic MPU can also be used as an effective data-compression technique. The speed to evaluate the created scalar field is almost as high as that of trilinear interpolation.

3D Face Landmarking Method under Pose and Expression Variations

A robust method is presented for 3D face landmarking with facial pose and expression variations. This method is based on Multi-level Partition of Unity (MPU) Implicits without relying on texture, pose, orientation and expression information. The MPU Implicits reconstruct 3D face surface in a hierarchical way. From lower to higher reconstruction levels, the local shapes can be reconstructed gradually according to their significance. For 3D faces, three landmarks, nose, left eyehole and right eyehole, can be detected uniquely with the analysis of curvature features at lower levels. Experimental results on GavabDB database show that this method is invariant to pose, holes, noise and expression. The overall performance of 98.59% is achieved under pose and expression variations.

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.

B215 MPU法に基づいたボリュームデータの補間と圧縮

Volume visualization is widely used in medical, scientific, and other fields. Since volume data are generally large, data compression techniques become important. In addition, volume data are usually discrete, and must be interpolated to execute volume-visualization algorithms. For high-quality visualization, higher-order smooth interpolation is required. But it is difficult to make such interpolation compatible with the data compression. Recently, the MPU (multi-level partition of unity) method has been developed to reconstruct a smooth implicit surface from a large number of 3D points. Our purpose is to construct a new version of the MPU method that is applicable to interpolate discrete volume data, generating a highly-smooth scalar field described with small-size data. It is demonstrated that the data size is reduced drastically, keeping the smooth feature of the interpolated scalar field.

B214 MPU法による陰関数曲面の多重解像度表現

Recently, the Multi-level Partition of Unity (MPU) method has been used as a technique to create an implicit surface from a large number of points. In this study, we propose multi-resolution representation of the implicit surface based on the MPU method. If the concept of the multi-resolution representation is incorporated into the MPU method, the implicit surfaces become tunable in various situations. Furthermore, the evaluation time of the implicit function can also be shortened. In proposed approach, we create and save the small domains and the local quadratic functions recursively until the given limit precision. For the case with the evaluation of the implicit function, we select quadratic functions satisfying the given precision that should be more moderate than the limit precision. As the result, the implicit surface of arbitrary resolution can be generated quickly.

Contour-based surface reconstruction using MPU implicit models

This paper presents a technique for creating a smooth, closed surface from a set of 2D contours, which have been extracted from a 3D scan. The technique interprets the pixels that make up the contours as points in R 3 and employs multi-level partition of unity (MPU) implicit models to create a surface that approximately fits to the 3D points. Since MPU implicit models additionally require surface normal information at each point, an algorithm that estimates normals from the contour data is also described. Contour data frequently contains noise from the scanning and delineation process. MPU implicit models provide a superior approach to the problem of contour-based surface reconstruction, especially in the presence of noise, because they are based on adaptive implicit functions that locally approximate the points within a controllable error bound. We demonstrate the effectiveness of our technique with a number of example datasets, providing images and error statistics generated from our results.