Showing papers by "Shi-Min Hu published in 2006"

Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes

Abstract: The computation of a rigid body transformation which optimally aligns a set of measurement points with a surface and related registration problems are studied from the viewpoint of geometry and optimization. We provide a convergence analysis for widely used registration algorithms such as ICP, using either closest points (Besl and McKay, 1992) or tangent planes at closest points (Chen and Medioni, 1991) and for a recently developed approach based on quadratic approximants of the squared distance function (Pottmann et al., 2004). ICP based on closest points exhibits local linear convergence only. Its counterpart which minimizes squared distances to the tangent planes at closest points is a Gauss---Newton iteration; it achieves local quadratic convergence for a zero residual problem and--if enhanced by regularization and step size control--comes close to quadratic convergence in many realistic scenarios. Quadratically convergent algorithms are based on the approach in (Pottmann et al., 2004). The theoretical results are supported by a number of experiments; there, we also compare the algorithms with respect to global convergence behavior, stability and running time.

Robust principal curvatures on multiple scales

Abstract: Geometry processing algorithms often require the robust extraction of curvature information. We propose to achieve this with principal component analysis (PCA) of local neighborhoods, defined via spherical kernels centered on the given surface Φ Intersection of a kernel ball Br or its boundary sphere Sr with the volume bounded by Φ leads to the so-called ball and sphere neighborhoods. Information obtained by PCA of these neighborhoods turns out to be more robust than PCA of the patch neighborhood Br∩Φ previously used. The relation of the quantities computed by PCA with the principal curvatures of Φ is revealed by an asymptotic analysis as the kernel radius r tends to zero. This also allows us to define principal curvatures "at scale r" in a way which is consistent with the classical setting. The advantages of the new approach are discussed in a comparison with results obtained by normal cycles and local fitting; whereas the former method somewhat lacks in robustness, the latter does not achieve a consistent behavior at features on coarse scales. As to applications, we address computing principal curves and feature extraction on multiple scales.

Feature sensitive mesh segmentation

Abstract: Segmenting meshes into natural regions is useful for model understanding and many practical applications. In this paper, we present a novel, automatic algorithm for segmenting meshes into meaningful pieces. Our approach is a clustering-based top-down hierarchical segmentation algorithm. We extend recent work on feature sensitive isotropic remeshing to generate a mesh hierarchy especially suitable for segmentation of large models with regions at multiple scales. Using integral invariants for estimation of local characteristics, our method is robust and efficient. Moreover, statistical quantities can be incorporated, allowing our approach to segment regions with different geometric characteristics or textures.

A sweepline algorithm for Euclidean Voronoi diagram of circles

Abstract: Presented in this paper is a sweepline algorithm to compute the Voronoi diagram of a set of circles in a two-dimensional Euclidean space. The radii of the circles are non-negative and not necessarily equal. It is allowed that circles intersect each other, and a circle contains others. The proposed algorithm constructs the correct Voronoi diagram as a sweepline moves on the plane from top to bottom. While moving on the plane, the sweepline stops only at certain event points where the topology changes occur for the Voronoi diagram being constructed. The worst-case time complexity of the proposed algorithm is O((n+m)log n), where n is the number of input circles, and m is the number of intersection points among circles. As m can be O(n^2), the presented algorithm is optimal with O(n^2 log n) worst-case time complexity.

Spherical harmonics scaling

Abstract: In this paper, we present a new SH operation, called spherical harmonics scaling, to shrink or expand a spherical function in the frequency domain. We show that this problem can be elegantly formulated as a linear transformation of SH projections, which is efficient to compute and easy to implement on a GPU. Spherical harmonics scaling is particularly useful for extrapolating visibility and radiance functions at a sample point to points closer to or farther from an occluder or light source. With SH scaling, we present applications to low-frequency shadowing for general deformable object, and to efficient approximation of spherical irradiance functions within a mid-range illumination environment.

Surface fitting based on a feature sensitive parametrization

Abstract: Most approaches to least squares fitting of a B-spline surface to measurement data require a parametrization of the data point set and the choice of suitable knot vectors. We propose to use uniform knots in connection with a feature sensitive parametrization. This parametrization allocates more parameter space to highly curved feature regions and thus automatically provides more control points where they are needed.

Surface mosaics

Abstract: This paper considers the problem of placing mosaic tiles on a surface to produce a surface mosaic. We assume that the user specifies a mesh model, the size of the tiles and the amount of grout, and, optionally, a few control vectors at key locations on the surface indicating the preferred tile orientation at these points. From these inputs, we place equal-sized rectangular tiles over the mesh such as to almost cover it, with controlled orientation. The alignment of the tiles follows a vector field which is interpolated over the surface from the control vectors and also forced into alignment with any sharp creases, open boundaries, and boundaries between regions of different colors. Our method efficiently solves the problem by posing it as globally optimizing a spring-like energy in the Manhattan metric, using overlapping local parameterizations. We demonstrate the effectiveness of our algorithm with various examples.

Skeleton-Based shape deformation using simplex transformations

Abstract: This paper presents a novel skeleton-based method for deforming meshes, based on an approximate skeleton. The major difference from previous skeleton-based methods is that they used the skeleton to control movement of vertices, whereas we use it to control the simplices defining the model. This allows errors, that occur near joints in other methods, to be spread over the whole mesh, giving smooth transitions near joints. Our method also needs no vertex weights defined on the bones, which can be tedious to choose in previous methods.

Rendering Soft Shadows using Multilayered Shadow Fins

Abstract: Generating soft shadows in real time is difficult. Exact methods (such as ray tracing, and multiple light source simulation) are too slow, while approximate methods often overestimate the umbra regions. In this paper, we introduce a new algorithm based on the shadow map method to quickly and highly accurately render soft shadows produced by a light source. Our method builds inner and outer translucent fins on objects to represent the penumbra area inside and outside hard shadows, respectively. The fins are traced into multilayered light space maps to store illuminance adjustment to shadows. The viewing space illuminance buffer is then calculated using those maps. Finally, by blending illuminance and shading, a scene with highly accurate soft shadow effects is produced. Our method does not suffer from umbra overestimation. Physical relations between light, objects and shadows demonstrate the soundness of our approach.

Proceedings of the 2006 ACM symposium on Solid and physical modeling

Abstract: The ACM Symposium on Solid and Physical Modeling is an annual international forum for the exchange of recent research results and applications of spatial modeling and computations in design, analysis and manufacturing, as well as in emerging biomedical, geophysical and other areas. Previous symposia in this series were held in Austin, Texas, 1991; Montreal, Canada, 1993; Salt Lake City, Utah, 1995; Atlanta, Georgia, 1997; Ann Arbor, Michigan in 1999 and 2001; Saarbrucken, Germany, 2002; Seattle, Washington, 2003; Genova, Italy, 2004; and Cambridge, Massachusetts, 2005. For additional information, please visit www.solidmodeling.org, the home page of The Solid Modeling Association that oversees this symposium series.The SPM symposium series started initially with the name "ACM Symposium on Solid Modeling and Applications." To emphasize the fact that solid modeling entails not only handling their geometric shapes, but also their physical properties and behaviors, the name of the symposium was expanded to The ACM Symposium on Solid and Physical Modeling (abbreviated as SPM) in 2005.SPM'06 was held in plenary sessions on the campus of Cardiff University, Wales, United Kingdom from Tuesday June 6 to Thursday June 8, 2006. Fifty six technical papers have been submitted and were reviewed by the international program committee and expert reviewers from around the world. At least three external reviewers and members of the program committee reviewed and discussed each submission. A total of 21 refereed papers have been selected for plenary presentation and publication in the proceedings. The symposium program also includes three invited presentations by Bruno Levy, Sara McMains and Jurgen Weese, all leading researchers in their fi elds. There were also two panels where recent trends and challenges were discussed. These panel sessions were organized by Kenji Shimada (Physical Modeling and Simulation) and Sara McMains (Design, Analysis, and Manufacturing).