Hugues Hoppe

Progressive meshes

Highly detailed geometric models are rapidly becoming commonplace in computer graphics. These models, often represented as complex triangle meshes, challenge rendering performance, transmission bandwidth, and storage capacities. This paper introduces the progressive mesh (PM) representation, a new scheme for storing and transmitting arbitrary triangle meshes. This efficient, lossless, continuous-resolution representation addresses several practical problems in graphics: smooth geomorphing of level-of-detail approximations, progressive transmission, mesh compression, and selective refinement. In addition, we present a new mesh simplification procedure for constructing a PM representation from an arbitrary mesh. The goal of this optimization procedure is to preserve not just the geometry of the original mesh, but more importantly its overall appearance as defined by its discrete and scalar appearance attributes such as material identifiers, color values, normals, and texture coordinates. We demonstrate construction of the PM representation and its applications using several practical models. CR

Surface reconstruction from unorganized points

This thesis describes a general method for automatic reconstruction of accurate, concise, piecewise smooth surfaces from unorganized 3D points. Instances of surface reconstruction arise in numerous scientific and engineering applications, including reverse-engineering--the automatic generation of CAD models from physical objects. Previous surface reconstruction methods have typically required additional knowledge, such as structure in the data, known surface genus, or orientation information. In contrast, the method outlined in this thesis requires only the 3D coordinates of the data points. From the data, the method is able to automatically infer the topological type of the surface, its geometry, and the presence and location of features such as boundaries, creases, and corners. The reconstruction method has three major phases: (1) initial surface estimation, (2) mesh optimization, and (3) piecewise smooth surface optimization. A key ingredient in phase 3, and another principal contribution of this thesis, is the introduction of a new class of piecewise smooth representations based on subdivision. The effectiveness of the three-phase reconstruction method is demonstrated on a number of examples using both simulated and real data. Phases 2 and 3 of the surface reconstruction method can also be used to approximate existing surface models. By casting surface approximation as a global optimization problem with an energy function that directly measures deviation of the approximation from the original surface, models are obtained that exhibit excellent accuracy to conciseness trade-offs. Examples of piecewise linear and piecewise smooth approximations are generated for various surfaces, including meshes, NURBS surfaces, CSG models, and implicit surfaces.

Poisson surface reconstruction

We show that surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial partitioning or blending, and is therefore highly resilient to data noise. Unlike radial basis function schemes, our Poisson approach allows a hierarchy of locally supported basis functions, and therefore the solution reduces to a well conditioned sparse linear system. We describe a spatially adaptive multiscale algorithm whose time and space complexities are proportional to the size of the reconstructed model. Experimenting with publicly available scan data, we demonstrate reconstruction of surfaces with greater detail than previously achievable.

Mesh optimization

We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh M0, produce a mesh M, of the same topological type as M0 , that fits the data well and has a small number of vertices. Our approach is to minimize an energy function that explicitly models the competing desires of conciseness of representation and fidelity to the data. We show that mesh optimization can be effectively used in at least two applications: surface reconstruction from unorganized points, and mesh simplification (the reduction of the number of vertices in an initially dense mesh of triangles). CR

Multiresolution analysis of arbitrary meshes

In computer graphics and geometric modeling, shapes are often represented by triangular meshes. With the advent of laser scanning systems, meshes of extreme complexity are rapidly becoming commonplace. Such meshes are notoriously expensive to store, transmit, render, and are awkward to edit. Multiresolution analysis offers a simple, unified, and theoretically sound approach to dealing with these problems. Lounsbery et al. have recently developed a technique for creating multiresolution representations for a restricted class of meshes with subdivision connectivity. Unfortunately, meshes encountered in practice typically do not meet this requirement. In this paper we present a method for overcoming the subdivision connectivity restriction, meaning that completely arbitrary meshes can now be converted to multiresolution form. The method is based on the approximation of an arbitrary initial mesh M by a mesh MJ that has subdivision connectivity and is guaranteed to be within a specified tolerance. The key ingredient of our algorithm is the construction of a parametrization of M over a simple domain. We expect this parametrization to be of use in other contexts, such as texture mapping or the approximation of complex meshes by NURBS patches. CR

View-dependent refinement of progressive meshes

Level-of-detail (LOD) representations are an important tool for realtime rendering of complex geometric environments. The previously introduced progressive mesh representation defines for an arbitrary triangle mesh a sequence of approximating meshes optimized for view-independent LOD. In this paper, we introduce a framework for selectively refining an arbitrary progressive mesh according to changing view parameters. We define efficient refinement criteria based on the view frustum, surface orientation, and screen-space geometric error, and develop a real-time algorithm for incrementally refining and coarsening the mesh according to these criteria. The algorithm exploits view coherence, supports frame rate regulation, and is found to require less than 15% of total frame time on a graphics workstation. Moreover, for continuous motions this work can be amortized over consecutive frames. In addition, smooth visual transitions (geomorphs) can be constructed between any two selectively refined meshes. A number of previous schemes create view-dependent LOD meshes for height fields (e.g. terrains) and parametric surfaces (e.g. NURBS). Our framework also performs well for these special cases. Notably, the absence of a rigid subdivision structure allows more accurate approximations than with existing schemes. We include results for these cases as well as for general meshes. CR Categories: I.3.3 [Computer Graphics]: Picture/Image Generation Display algorithms; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling surfaces and object representations. Additional

Digital photography with flash and no-flash image pairs

Digital photography has made it possible to quickly and easily take a pair of images of low-light environments: one with flash to capture detail and one without flash to capture ambient illumination. We present a variety of applications that analyze and combine the strengths of such flash/no-flash image pairs. Our applications include denoising and detail transfer (to merge the ambient qualities of the no-flash image with the high-frequency flash detail), white-balancing (to change the color tone of the ambient image), continuous flash (to interactively adjust flash intensity), and red-eye removal (to repair artifacts in the flash image). We demonstrate how these applications can synthesize new images that are of higher quality than either of the originals.

Geometry images

Surface geometry is often modeled with irregular triangle meshes. The process of remeshing refers to approximating such geometry using a mesh with (semi)-regular connectivity, which has advantages for many graphics applications. However, current techniques for remeshing arbitrary surfaces create only semi-regular meshes. The original mesh is typically decomposed into a set of disk-like charts, onto which the geometry is parametrized and sampled. In this paper, we propose to remesh an arbitrary surface onto a completely regular structure we call a geometry image. It captures geometry as a simple 2D array of quantized points. Surface signals like normals and colors are stored in similar 2D arrays using the same implicit surface parametrization --- texture coordinates are absent. To create a geometry image, we cut an arbitrary mesh along a network of edge paths, and parametrize the resulting single chart onto a square. Geometry images can be encoded using traditional image compression algorithms, such as wavelet-based coders.

Piecewise smooth surface reconstruction

We present a general method for automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data. The method can be used in a variety of applications such as reverse engineering—the automatic generation of CAD models from physical objects. Novel aspects of the method are its ability to model surfaces of arbitrary topological type and to recover sharp features such as creases and corners. The method has proven to be effective, as demonstrated by a number of examples using both simulated and real data. A key ingredient in the method, and a principal contribution of this paper, is the introduction of a new class of piecewise smooth surface representations based on subdivision. These surfaces have a number of properties that make them ideal for use in surface reconstruction: they are simple to implement, they can model sharp features concisely, and they can be fit to scattered range data using an unconstrained optimization procedure.

Texture mapping progressive meshes

Given an arbitrary mesh, we present a method to construct a progressive mesh (PM) such that all meshes in the PM sequence share a common texture parametrization. Our method considers two important goals simultaneously. It minimizes texture stretch (small texture distances mapped onto large surface distances) to balance sampling rates over all locations and directions on the surface. It also minimizes texture deviation (“slippage” error based on parametric correspondence) to obtain accurate textured mesh approximations. The method begins by partitioning the mesh into charts using planarity and compactness heuristics. It creates a stretch-minimizing parametrization within each chart, and resizes the charts based on the resulting stretch. Next, it simplifies the mesh while respecting the chart boundaries. The parametrization is re-optimized to reduce both stretch and deviation over the whole PM sequence. Finally, the charts are packed into a texture atlas. We demonstrate using such atlases to sample color and normal maps over several models.