A fast and efficient projection-based approach for surface reconstruction

Abstract

We present a fast, memory efficient, linear time algorithm that generates a manifold triangular mesh passing through a set of unorganized points. Nothing is assumed about the geometry, topology or presence of boundaries in the data set except that ¡ is sampled from a real manifold surface. The speed of our algorithm is derived from a projection-based approach we use to determine the incident faces on a point. Our algorithm has successfully reconstructed the surfaces of unorganized point clouds of sizes varying from 10,000 to 100,000 in about 3-30 seconds on a 250 MHz, R10000 SGI Onyx2. Our technique is especially suitable for height fields like terrain and range scan data even in the presence of noise. We have successfully generated meshes for scan data of size 900,000 points in less than 40 seconds.

Survey on 3D Surface Reconstruction

“…Gopi and Krishnan [22] present a fast and memory efficient incremental projected-based algorithm for surface reconstruction. This approach builds the surface starting from an arbitrary point.…”

“…Gopi and Krishnan [22] involve three major assumptions on the input dataset. These assumptions reduce the generality of the algorithm due to the unsatisfiability of the assumptions on the real datasets.…”

“…Main impacts of Gopi and Krishnan's work [22] are memory and time efficiency, in addition to high level of noise tolerability in some special occasions. The performance and the results of Gopi and Krishnan's work are displayed in [22].…”

Incremental and batch planar simplification of dense point cloud maps

“…With real-world environment triangulation in mind, the Greedy Projection Triangulation (GPT) algorithm has been developed [10,11]. The algorithm creates triangles in an incremental mesh-growing approach, yielding fast and accurate triangulations.…”

Processing of Terrestrial Laser Scanning Point Cloud Data for Computational Modelling of Building Facades

“…Because of its hierarchical nature, algorithms can operate at a level appropriate to the task, thereby eliminating the execution of processes on out-of-scope data. Weyrich et al [26] comment on the octree's ability to quickly locate a point in space, by exploiting binary locators to address octree cells, which is useful when used in tandem with efficient neighbourhood queries, such as the k-nearest neighbour algorithm as demonstrated by Gopi and Krishnan [27], as will be further discussed later in this paper. Although octree representation can construct the object with less accuracy than the two aforementioned techniques [19], the octree has become popular for modelling and visualizing objects in animations and other applications, such as surface reconstruction from digitized data, because of its ability to model the complex shape of an arbitrary topology [28].…”