LAAS has worked on free form surface modeling
by triangular meshes from multiple viewpoints.
There are different ways to model a surface from sensory data:
(1) 3D segmentation in homogeneous regions, and for each region,
direct parameterized surface fitting,
and (2) generation of a regular or irregular mesh. We select the
representation according to the kind of building we want to model:
typically, mesh for a heritage scene, parametric surfaces for
an industrial scene.
Two types of meshes were evaluated: regular meshes (rectangular, triangular, hexagonal, ...) or irregular ones (triangular, polygonal, ...). Surfaces based on regular meshes are easier to compute, because sensory data could be projected on a pre-computed grid, updated at each step of data acquisitions. But, a multi-resolution model cannot be built without losing the continuity between two levels of different resolution, because of the fixed geometry of meshes.
Irregular meshes are implicitly hierarchical: it is sufficient to
change one parameter (the threshold for the distance between one
perceived point and the mesh) to adapt the mesh size (consequently,
the storage requirements) and the accuracy of the representation.
Their main defect is the complexity of the resulted data structure,
and the difficulty of the direct fusion of such meshes, which has only
been made on triangular meshes, with some simplifications.
The LAAS method is based on irregular triangular meshes. This type of
representation has been chosen because of its properties, i.e. a
hierarchical model, which is compact, local, and suitable to model
either free form or structured objects. Two steps are required:
the construction of a local model from one acquisition, using
a split and merge algorithm, and then the registration and the fusion
of local models built from several viewpoints.
For the Bornholm church images, A. Sappa is working on the registration and fusion of several images, comparing the LAAS method (irregular mesh) with his own method developed previously during his PhD in Barcelona (regular mesh). He is using a three step technique. First, the original range image is cut into a predefined number of stripes (or bands), a stripe is a range image containing a sub-set of the original data points ( e.g. 50x8000 points). Then, each stripe is approximated by means of an adaptive triangular mesh and the meshes generated for every stripe are recombined into a final regular mesh which approximates the given range image. Finally, to obtain a more compact representation, a fine-to-coarse algorithm that removes unuseful vertices of the regular mesh is applied.
In the following figures, we present the model for one stripe (top view) and the simplified irregular mesh obtained by a decimation algorithm (keeping only 15% of the triangles).
