Multiresolution Surface Research Articles

Multiresolution surface blending for detail reconstruction

While performing mechanical reverse engineering, 3D reconstruction processes often encounter difficulties capturing small, highly localized surface information. This can be the case if a physical part is 3D scanned for life-cycle management or robust design purposes, with interest in corroded areas or scratched coatings. The limitation partly is due to insufficient automated frameworks for handling – localized – surface information during the reverse engineering pipeline. We have developed a tool for blending surface patches with arbitrary irregularities, into a base body that can resemble a CAD design. The resulting routine preserves the shape of the transferred features and relies on the user only to set some positional references and parameter adjustments for partitioning the surface features.

Robotic concrete surface finishing: a moldless approach to creating thermally tuned surface geometry for architectural building components using Profile-3D-Printing

This paper focuses on describing a novel hybrid concrete printing/casting process we term Profile-3D-Printing. Profile-3D-Printing is an additive/subtractive manufacturing process that combines deposition of concrete for rough layup with precision tooling for surface finishing of architectural building components commonly found in the architectural precast industry. Our research team from Architecture, the Robotics Institute, and Material Science invented this novel hybrid manufacturing process for robotically printing architectural facade panels with complex surface geometries. This effort was motivated by previously validated research focused on calibrating the thermal exchange rate of vertical surface geometries for the purpose of improving both the esthetic and thermodynamic performance of passive heating and cooling systems in buildings. Our hybrid approach to concrete 3D printing is unique because it combines high-volume material deposition, multi-resolution surface finishing, and the ability for high customization without significant increases in production time. Our project will significantly advance systems integration between energy-based building performance design and advance additive manufacturing, enabling precast concrete suppliers to design and manufacture innovative architectural products with added value for end users in energy savings. This project serves as a template for other industries to adopt hybrid additive manufacturing systems to transform traditionally mold-based approaches. The goal of our project is to develop and test robotic 3D-printing systems that enable customization for high-resolution parts. Hybrid additive manufacturing (Hybrid-AM) enables automated tooling of soft and phase-changing materials to achieve fine feature resolution and finish quality independent of print nozzle size. Currently, speed of printing, control of finish quality, and flexibility of application are three of the most significant barriers for industries seeking to adopt additive manufacturing for part production. This project highlights how Hybrid-AM techniques, built on robotic work cells, address these challenges to enable customization of value-added products.

Hierarchical grid conversion

Hierarchical grids appear in various applications in computer graphics such as subdivision and multiresolution surfaces, and terrain models. Since the different grid types perform better at different tasks, it is desired to switch between regular grids to take advantages of these grids. Based on a 2D domain obtained from the connectivity information of a mesh, we can define simple conversions to switch between regular grids. In this paper, we introduce a general framework that can be used to convert a given grid to another and we discuss the properties of these refinements such as their transformations. This framework is hierarchical meaning that it provides conversions between meshes at different level of refinement. To describe the use of this framework, we define new regular and near-regular refinements with good properties such as small factors. We also describe how grid conversion enables us to use patch-based data structures for hexagonal cells and near-regular refinements. To do so, meshes are converted to a set of quadrilateral patches that can be stored in simple structures. Near-regular refinements are also supported by defining two sets of neighborhood vectors that connect a vertex to its neighbors and are useful to address connectivity queries.

Shape optimisation with multiresolution subdivision surfaces and immersed finite elements

We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets, multiresolution surfaces represent the domain boundary using a coarse control mesh and a sequence of detail vectors. Based on the multiresolution decomposition efficient and fast algorithms are available for reconstructing control meshes of varying fineness. During shape optimisation the vertex coordinates of control meshes are updated using the computed shape gradient information. By virtue of the multiresolution editing semantics, updating the coarse control mesh vertex coordinates leads to large-scale geometry changes and, conversely, updating the fine control mesh coordinates leads to small-scale geometry changes. In our computations we start by optimising the coarsest control mesh and refine it each time the cost function reaches a minimum. This approach effectively prevents the appearance of non-physical boundary geometry oscillations and control mesh pathologies, like inverted elements. Independent of the fineness of the control mesh used for optimisation, on the immersed finite element grid the domain boundary is always represented with a relatively fine control mesh of fixed resolution. With the immersed finite element method there is no need to maintain an analysis suitable domain mesh. In some of the presented two and three-dimensional elasticity examples the topology derivative is used for introducing new holes inside the domain. The merging or removing of holes is not considered.

Editorial Issue 26.1

Reference EPFL-ARTICLE-207397doi:10.1002/cav.1634View record in Web of Science Record created on 2015-04-13, modified on 2016-08-09

Multiresolution Diffeomorphic Mapping for Cortical Surfaces.

Due to the convoluted folding pattern of the cerebral cortex, accurate alignment of cortical surfaces remains challenging. In this paper, we present a multiresolution diffeomorphic surface mapping algorithm under the framework of large deformation diffeomorphic metric mapping (LDDMM). Our algorithm takes advantage of multiresolution analysis (MRA) for surfaces and constructs cortical surfaces at multiresolution. This family of multiresolution surfaces are used as natural sparse priors of the cortical anatomy and provide the anchor points where the parametrization of deformation vector fields is supported. This naturally constructs tangent bundles of diffeomorphisms at different resolution levels and hence generates multiresolution diffeomorphic transformation. We show that our construction of multiresolution LDDMM surface mapping can potentially reduce computational cost and improves the mapping accuracy of cortical surfaces.

Multiscale geometric modeling of macromolecules I: Cartesian representation

This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace–Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the polarized curvature, for the prediction of protein binding sites.

A Technology to Multi-Resolution Surface Reconstruction

An approach is presented based on scattered data points subdivision surfaces to achieve multi-resolution surface reconstruction techniques. In the surface reconstruction process, based on gray-scale image edge detection ideological eigenvalues scattered data analysis, these features will generate texture characteristic curve values tessellation, thus forming a multi-resolution mesh model structure; After testing, the technology is not only surface reconstruction short time, while the constructed subdivision surfaces can reflect the characteristics of the original details of the data.

Integration method of TINs and Grids for multi-resolution surface modeling

Highly detailed surface models and their real-time applications are increasingly popular in architecture, construction and other design and engineering fields. However, new and related problems have emerged concerning the efficient management of the resulting large datasets and the seamless integration of heterogeneous data. Moreover, the increasingly common requirements of local high-fidelity modeling combined with large-scale landscapes lead to difficulty in the seamless multi-resolution representation of hybrid triangulated irregular networks (TINs) and Grids. This paper presents a hybrid data structure with high-efficiency and a related organizational method for the seamless integration of multi-resolution models. This approach is characterized by (1) a self-adaptive algorithm for feature-preserving surface partitioning, (2) an efficient hybrid index structure for combined Grid and TIN surfaces, and (3) a view-dependent scheduling strategy with access to Grids of necessary resolution, giving priority to the dynamic loading of TINs. Experiments using typical real design datasets of highway constructions are able to achieve accuracy-preserved and real-time availability of results that prove the validity and efficiency of this approach.

An efficient representation of quadtrees and bintrees for multiresolution terrain models

A space-filling curve in 2, 3, or higher dimensions can be thought as a path of a continuously moving point. As its main goal is to preserve spatial proximity, this type of curves has been widely used in the design and implementation of spatial data structures and nearest neighbor-finding techniques. This paper is essentially focused on the efficient representation of Digital Elevation Models (DEM) that entirely fit into the main memory. We propose a new hierarchical quadtree-like data structure to be built over domains of unrestricted size, and a representation of a quadtree and a binary triangles tree by means of the Hilbert and the Sierpinski space-filling curves, respectively, taking into account the hierarchical nature and the clustering properties of this kind of curves. Some triangulation schemes are described for the space-filling-curves-based approaches to efficiently visualize multiresolution surfaces.

Compound Biorthogonal Wavelets on Quadrilaterals and Polar Structures

In geometric models with high-valence vertices, current subdivision wavelets may not deal with the special cases well for good visual effect of multiresolution surfaces. In this paper, we present the novel biorthogonal polar subdivision wavelets, which can efficiently perform wavelet analysis to the control nets with polar structures. The polar subdivision can generate more natural subdivision surfaces around the high-valence vertices and avoid the ripples and saddle points where Catmull-Clark subdivision may produce. Based on polar subdivision, our wavelet scheme supports special operations on the polar structures, especially suitable to models with many facets joining. For seamless fusing with Catmull-Clark subdivision wavelet, we construct the wavelets in circular and radial layers of polar structures, so can combine the subdivision wavelets smoothly for composite models formed by quadrilaterals and polar structures. The computations of wavelet analysis and synthesis are highly efficient and fully in-place. The experimental results have confirmed the stability of our proposed approach.

Safe Control of Hopping in Uneven Terrain

Using a classic problem from robotics of a vertical hopping machine, we demonstrate an approach for investigating the safety of a hybrid discrete/continuous dynamic system operating in an uncertain environment. The challenges imposed by the environment are expressed in terms of constraints imposed in the phase space of the system as it undergoes periodic motion. The approach is demonstrated first with a hopper that has state feedback to govern the timing of thrust and subsequently for a timer-based hopper. The latter case increases the dimensionality of the problem and must be treated numerically. However, the use of a multiresolution surface representation of the feasible regions in state space reduces the computational burden of the approach.

Meshfree Thinning of 3D Point Clouds

An efficient data reduction scheme for the simplification of a surface given by a large set X of 3D point-samples is proposed. The data reduction relies on a recursive point removal algorithm, termed thinning, which outputs a data hierarchy of point-samples for multiresolution surface approximation. The thinning algorithm works with a point removal criterion, which measures the significances of the points in their local neighbourhoods, and which removes a least significant point at each step. For any point x in the current point set Y⊂X, its significance reflects the approximation quality of a local surface reconstructed from neighbouring points in Y. The local surface reconstruction is done over an estimated tangent plane at x by using radial basis functions. The approximation quality of the surface reconstruction around x is measured by using its maximal deviation from the given point-samples X in a local neighbourhood of x. The resulting thinning algorithm is meshfree, i.e., its performance is solely based upon the geometry of the input 3D surface point-samples, and so it does not require any further topological information, such as point connectivities. Computational details of the thinning algorithm and the required data structures for efficient implementation are explained and its complexity is discussed. Two examples are presented for illustration.

A multi-resolution surface distance model for k-NN query processing

A spatial k-NN query returns k nearest points in a point dataset to a given query point. To measure the distance between two points, most of the literature focuses on the Euclidean distance or the network distance. For many applications, such as wildlife movement, it is necessary to consider the surface distance, which is computed from the shortest path along a terrain surface. In this paper, we investigate the problem of efficient surface k-NN (sk-NN) query processing. This is an important yet highly challenging problem because the underlying environment data can be very large and the computational cost of finding the shortest path on a surface can be very high. To minimize the amount of surface data to be used and the cost of surface distance computation, a multi-resolution surface distance model is proposed in this paper to take advantage of monotonic distance changes when the distances are computed at different resolution levels. Based on this innovative model, sk-NN queries can be processed efficiently by accessing and processing surface data at a just-enough resolution level within a just-enough search region. Our extensive performance evaluations using real world datasets confirm the efficiency of our proposed model.

Touch-enabled haptic modeling of deformable multi-resolution surfaces

Currently, interactive data exploration in virtual environments is mainly focused on vision-based and non-contact sensory channels such as visual/auditory displays. The lack of tactile sensation in virtual environments removes an important source of information to be delivered to the users. In this paper, we propose the touch-enabled haptic modeling of deformable multi-resolution surfaces in real time. The 6-DOF haptic manipulation is based on a dynamic model of Loop surfaces, where the dynamic parameters are computed easily without subdividing the control mesh recursively. A local deforming scheme is developed to approximate the solution of the dynamics equations, thus the order of the linear equations is reduced greatly. During each of the haptic interaction loop, the contact point is traced and reflected to the rendering of updated graphics and haptics. The sense of touch against the deforming surface is calculated according to the surface properties and the damping-spring force profile. Our haptic system supports the dynamic modeling of deformable Loop surfaces intuitively through the touch-enabled interactive manipulation.

Multi-level differential surface representation based on local transformations

One crucial issue of multi-resolution surface representations is how to effectively record and reconstruct geometric details among surface levels. Standard multi-resolution techniques encode details directly as local displacements in the vertices, and may produce unplausible results when the base level endures large deformations. In this paper we propose an alternative detail representation and reconstruction scheme, based on local transformations on a per-triangle basis. While more storage is required, recording details as local transformations favors global coupling of geometric details and allows for large-scale surface manipulations. By modeling the scale components of the surface modifications as a set of deforming factors, we achieved detail-preserving reconstruction results naturally under very large deformations. Comprehensive experimental results verify the efficiency and robustness of our approach.

A Multiresolution PDE-Based Deformable Surface for Medical Imaging Applications

We recently developed a multiresolution PDE-based deformable surface whose deformation behavior is governed by partial differential equations (PDEs) such as the weighted minimal surface flow. Comparing with the level-set approach, our new model has better control of the mesh quality and model resolution, and is much simpler to implement since all the computations are local. The new deformable model is very useful for a variety of medical imaging applications including boundary reconstruction, surface visualization, data segmentation, and topology discovery. In this paper, we demonstrate both the accuracy and robustness of our model on areas such as medical image segmentation through a number of experiments on both real (MRI/CT) and synthetic volumetric datasets.

Single-knot wavelets for non-uniform B-splines

We propose a flexible and efficient wavelet construction for non-uniform B-spline curves and surfaces. The method allows to remove knots in arbitrary order minimizing the displacement of control points when a knot is re-inserted. Geometric detail subtracted from a shape by knot removal is represented by an associated wavelet coefficient replacing one of the control points at a coarser level of detail. From the hierarchy of wavelet coefficients, perfect reconstruction of the original shape is obtained. Both knot removal and insertion have local impact. Wavelet synthesis and analysis are both computed in linear time, based on the lifting scheme for biorthogonal wavelets. The method is perfectly suited for multiresolution surface editing, progressive transmission, and compression of spline curves and surfaces.

Multi-resolution surface modeling by using geometry image: Application to a brain atlas

Arbitrary triangle mesh is a collection of 3D triangles without any shape or boundary restrictions. Progressive mesh (PM) is a multiresolution representation that defines continuous level of detail approximations for arbitrary triangle meshes. PM representation of a mesh can be processed to obtain a mesh approximation between the original and the base (simplified) mesh. Furthermore, PM can be refined in a view-dependent fashion to obtain a simpler mesh within a perceptual image quality. In this paper, we introduce an adaptation and improvements in our implementation for view-dependent refinement of progressive meshes. Essentially, we use a similar approach to Hoppe's framework (ACM Comput. Graphics, Proceedings of SIGGRAPH’97, August 1997, pp. 189–198) for view-dependent refinement with a different algorithm for constructing PM representation. Our method is simple to implement and fast enough to achieve interactive frame rates for moderately complex models (models containing hundreds of thousands of polygons) on a machine with polygon rendering hardware. Moreover, our implementation allows changes to topology and achieves a simpler and sometimes more realistic refinements.

Hierarchical Role-Based Viewing for Multilevel Information Security in Collaborative CAD

Information security and assurance are new frontiers for collaborative design. In this context, information assurance (IA) refers to methodologies to protect engineering information by ensuring its availability, confidentiality, integrity, nonrepudiation, authentication, access control, etc. In collaborative design, IA techniques are needed to protect intellectual property, establish security privileges and create “need to know” protections on critical features. This paper provides a framework for information assurance within collaborative design based on a technique we call Role-Based Viewing. We extend upon prior work to present Hierarchical Role-Based Viewing as a more flexible and practical approach since role hierarchies naturally reflect an organization’s lines of authority and responsibility. We establish a direct correspondence between multilevel security and multiresolution surfaces where a hierarchy is represented as a weighted directed acyclic graph. The permission discovery process is formalized as a graph reachability problem and the path-cost can be used as input to a multiresolution function. By incorporating security with collaborative design, the costs and risks incurred by multiorganizational collaboration can be reduced. The authors believe that this work is the first of its kind to unite multilevel security and information clouded with geometric data, including multiresolution surfaces, in the fields of computer-aided design and collaborative engineering.