Theory and Algorithms

Many laser devices acquire directly 3D objects and reconstruct their surface. Nevertheless, the final reconstructed surface is usually smoothed out as a result of the scanner internal de-noising process and the offsets between different scans.

This thesis, working on results from high precision scans, adopts the somewhat extreme conservative position, not to loose or alter any raw sample throughout the whole processing pipeline, and to attempt to visualize them. Indeed, it is the only way to discover all surface imperfections (holes, offsets). Furthermore, since high precision data can capture the slightest surface variation, any smoothing and any sub-sampling can incur in the loss of textural detail.

The thesis attempts to prove that one can triangulate the raw point cloud with almost no sample loss. It solves the exact visualization problem on large data sets of up to 35 million points made of 300 different scan sweeps and more. Two major problems are addressed. The first one is the orientation of the complete raw point set, an the building of a high precision mesh. The second one is the correction of the tiny scan misalignments which can cause strong high frequency aliasing and hamper completely a direct visualization.

The second development of the thesis is a general low-high frequency decomposition algorithm for any point cloud. Thus classic image analysis tools, the level set tree and the MSER representations, are extended to meshes, yielding an intrinsic mesh segmentation method.

The underlying mathematical development focuses on an analysis of a half dozen discrete differential operators acting on raw point clouds which have been proposed in the literature. By considering the asymptotic behavior of these operators on a smooth surface, a classification by their underlying curvature operators is obtained.

This analysis leads to the development of a discrete operator consistent with the mean curvature motion (the intrinsic heat equation) defining a remarkably simple and robust numerical scale space. By this scale space all of the above mentioned problems (point set orientation, raw point set triangulation, scan merging, segmentation), usually addressed by separated techniques, are solved in a unified framework.

- Yves Meyer - CMLA, ENS Cachan - Chairman
- Pierre Alliez - INRIA Sophia Antipolis - Reviewer
- Ron Kimmel - Technion - Reviewer
- Guillermo Sapiro - University of Minnesota - Reviewer
- Jean-Michel Morel - CMLA, ENS Cachan - PhD advisor
- Jacques Blanc-Talon - DGA - Invited member
- Tamy Boubekeur - Télécom ParisTech - Examiner
- Frédéric Chazal - INRIA Saclay - Examiner
- Claire Lartigue - LURPA, ENS Cachan - Examiner

PhD defended on Tuesday, November the 23rd at ENS Cachan.

My thesis was awarded the Hadamard phd award 2012