incremental_solid_modelling_sfm.md

Incremental Solid Modeling from Sparse and Omnidirectional Structure-from-Motion Data

Author: Maxime Lhuillier

Notes:

• 2 Manifold surface reconstruction using a sparse pc from sfm algorithm
• advantages of sparse surface rec: quality of 3D points, low computationnal cost
• manifold = list of 3D triangle so that every the neighbourhood of every surface point is locally a disk
• the 3D delaunnay triangulation of a set of 3D point P is such that: each tetrahedra is on the convex hull of P, its vertex set is P, the circumscribing sphere of every tetrahedron does not contain any vertex.
• the genus of the surface is always zero (i.e. it has no hole)
• define a general test to see if a surface is manifold: if for every vertex, all the triangles that has this vertex can be ordered in a chain that link every triangle pair with an edge (i.e. the graph of v opposite edges must be a cycle)
• it also defines a substraction test and an addition test
• The length of the ray is bounded: the point uncertainty increases with the square of the length
• The size of the triangles is bounded (formally, the circumscribing sphere of each tetrathedron has a diameter bounded by a thresh)
• A rigorous sculpting method to add new point in the mesh so that it remains "Manifold"

@inproceedings{Litvinov2013IncrementalSM, title={Incremental Solid Modeling from Sparse and Omnidirectional Structure-from-Motion Data}, author={Vadim Litvinov and Maxime Lhuillier}, booktitle={British Machine Vision Conference}, year={2013} }