The Ball-Pivoting Algorithm for Surface Reconstruction

1. Briefly summarize the paper’s contributions. Does it address a new problem? Does it present a new approach? Does it show new types of results?  [AS] This paper presents a new approach to the existing problem of data integration, or generating a surface representation from a given set of sample points. The approach presented in this paper is called the ball-pivot algorithm (BPA), which is a region growing method, resulting in a triangle mesh. This mesh is created roughly, ignoring details, by starting with a seed triangle, pivoting a ball around each edge on the existing mesh boundary, adding new triangles defined by this edge and a point hit by the ball, and repeating with new edge for pivoting. It is simple, efficient in terms of both execution time and storage, and robust to noise in real 3D scanned data.  [DS] Presents a conceptually simple algorithm that is efficient in terms of time (linear) and storage. It presents a new approach to the problem of interpolating a mesh from a point cloud (especially obtained from scanning data). The algorithm is also robust to 3D scanning noise, so it can be used for practical applications.  [FP] It proposes an algorithm for efficiently computing a triangular mesh formed by alphaexposed triangles of an alpha-shape. Since it acts locally, it can be implemented by partitioning the input in slices (reducing memory requirements) and it is able to generate meshes from large data sets (e.g., Pieta).  [JD]  [LF] The paper presents BPA which is a new approach for finding the triangle mesh of an unorganized set of points that actually lends itself to brief explanation. Beginning with any three points, i.e. a seed triangle, a “ball” of a user specified radius pivots around each pair of points until it hits another sample point and that sample point is added to the mesh. That process is repeated on a new edge, formed between one of the pivot points and the new discovery. And so on, until we have our bounded mesh.  [MK] The paper proposes an approach for computing an alpha shape in linear time. Because the value of alpha is fixed, it supports a streaming implementation.