Ernst Peter Mucke

Bio: Ernst Peter Mucke is an academic researcher from University of Illinois at Urbana–Champaign. The author has contributed to research in topics: Alpha shape & Set (abstract data type). The author has an hindex of 7, co-authored 7 publications receiving 4456 citations.

Three-dimensional alpha shapes

Abstract: Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the “shape” of the set. For that purpose, this article introduces the formal notion of the family of a-shapes of a finite point set in R3. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter a e R controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size n in time 0(n2), worst case. A robust implementation of the algorithm is discussed, and several applications in the area of scientific computing are mentioned.

Three-dimensional alpha shapes

Abstract: Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the “shape” of the set. For that purpose, this article introduces the formal notion of the family of a-shapes of a finite point set in R3. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter a e R controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size n in time 0(n2), worst case. A robust implementation of the algorithm is discussed, and several applications in the area of scientific computing are mentioned.

Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms

Abstract: This paper describes a general-purpose programming technique, called Simulation of Simplicity, that can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task of providing a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than those that do not use it. We believe that this technique will become a standard tool in writing geometric software.

Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms

Abstract: This paper describes a general-purpose programming technique, called the Simulation of Simplicity, which can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task to provide a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than those that do not use it. We believe that this technique will become a standard tool in writing geometric software.

Three-dimensional alpha shapes

Abstract: Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the ``shape'' of the set. For that purpose, this paper introduces the formal notion of the family of $\alpha$-shapes of a finite point set in $\Real^3$. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter $\alpha \in \Real$ controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size $n$ in time $O(n^2)$, worst case. A robust implementation of the algorithm is discussed and several applications in the area of scientific computing are mentioned.

A volumetric method for building complex models from range images

Abstract: A number of techniques have been developed for reconstructing surfaces by integrating groups of aligned range images. A desirable set of properties for such algorithms includes: incremental updating, representation of directional uncertainty, the ability to fill gaps in the reconstruction, and robustness in the presence of outliers. Prior algorithms possess subsets of these properties. In this paper, we present a volumetric method for integrating range images that possesses all of these properties. Our volumetric representation consists of a cumulative weighted signed distance function. Working with one range image at a time, we first scan-convert it to a distance function, then combine this with the data already acquired using a simple additive scheme. To achieve space efficiency, we employ a run-length encoding of the volume. To achieve time efficiency, we resample the range image to align with the voxel grid and traverse the range and voxel scanlines synchronously. We generate the final manifold by extracting an isosurface from the volumetric grid. We show that under certain assumptions, this isosurface is optimal in the least squares sense. To fill gaps in the model, we tessellate over the boundaries between regions seen to be empty and regions never observed. Using this method, we are able to integrate a large number of range images (as many as 70) yielding seamless, high-detail models of up to 2.6 million triangles.

Surface reconstruction from unorganized points

Abstract: 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

Abstract: 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.

Three-dimensional alpha shapes

Abstract: Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the “shape” of the set. For that purpose, this article introduces the formal notion of the family of a-shapes of a finite point set in R3. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter a e R controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size n in time 0(n2), worst case. A robust implementation of the algorithm is discussed, and several applications in the area of scientific computing are mentioned.

Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study

Abstract: Numerical models indicate that collective animal behavior may emerge from simple local rules of interaction among the individuals. However, very little is known about the nature of such interaction, so that models and theories mostly rely on aprioristic assumptions. By reconstructing the three-dimensional positions of individual birds in airborne flocks of a few thousand members, we show that the interaction does not depend on the metric distance, as most current models and theories assume, but rather on the topological distance. In fact, we discovered that each bird interacts on average with a fixed number of neighbors (six to seven), rather than with all neighbors within a fixed metric distance. We argue that a topological interaction is indispensable to maintain a flock's cohesion against the large density changes caused by external perturbations, typically predation. We support this hypothesis by numerical simulations, showing that a topological interaction grants significantly higher cohesion of the aggregation compared with a standard metric one.