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### Geometry Analysis

My principal research interest is the study of geometrics shape properties, with a strong focus on 3D acquired point clouds. I have developed during my PhD an approach called Growing Least Squares, which mimic the concept of Scale Space Analysis and extend it for unstructured point clouds. More details can be found in my PhD manuscript.

The GLS framework allows you to:

• Work with point sets: either 2D or 3D (and even 4D or more if you need it), the only (reasonable) requirement is to get the normal vectors associated to each vertex. Indeed, our approach is based on an efficient algebraic sphere fitting procedure valid in any dimension.
• Characterize complex shapes: the algebraic fitted sphere is represented by three different geometric quantities (e.g mean curvature), leading to a discriminative description even for complex shapes.
• Detect pertinent scales: a continuous geometric variation measure can be computed on the object to detect the pertinent interval of scales associated to each point. This information can then be used to for multi-scale shape matching.
• Deal with acquisition data: usual acquisition noise can be handled by your approach thanks to the fitting procedure we rely on. And even better: heuristics can be developed to detect the correct scale that must be used to reconstruct the data and remove noise.
• Compute flows: the original approach has been extended (see details in my PhD manuscript) to compute continuous flows on point set surfaces.

(click on images for more details).

Source code is available through an open source library called Patate, see the Code page.

### Shape matching

I am also interested in shape matching algorithms, mainly for the rigid alignment of acquired objects, either point-cloud or meshes. This is a central and very important topic in computer graphics since acquisition devices are now widely used a produce large datasets that must be processed and aligned before being used.

I have two contributions in that field:

• Super4PCS: an optimisation of the the state-of-the-art 4-Points Congruent Set (4PCS) algorithm by Aiger et al [AMC08]. The main contribution of this work is a method to register point-clouds in linear time without any knowledge on the initial poses (more details on the project page).
• Tangible semi-automatic fragment matching: a semi-automatic system allowing Cultural Heritage expert to manipulate 3D objects using magnetic props and register them using real-time Iterative Closest Point (published at VAST 2010).

(click on images for more details).

### Cultural Heritage applications

The initial topic studied during my PhD was the virtual reassembly of broken artefacts. In addition to the tangible semi-automatic fragment matching system (see Section Matching), I have been involved more recently, in a project leaded by Brett Ridel during his Master thesis (paper published at JOCCH), to develop a Spatial Augmented Reality system to enhance engraved texts and patterns on Cultural Heritage artefacts.

(click on images for more details).

### Rendering

I've worked on a really fun project in early 2013, in a collaboration between Luxology (now associated with The Foundry) and Manao, to compute on-the-fly curvature of 3D objects in a real-time ray tracing engine.

This work has been presented as a Siggraph Talk (2013) in Anaheim (follow this link to go to the publication details). More details will be added soon, in the meantime enjoy some results from our implementation in Modo:

(click on images for more details).

I plan to further investigate this topic, in order to combine on-the-fly geometry analysis and expressive rendering. Preliminary results can be seen in this paper (more details in the Cultural Heritage section).

### 3D Data Acquisition

During my PhD, I've got the chance to take part of the SeARCH project, a French project focusing on the study of the statues that were surrounding the famous Pharos of Alexandria. During this project, we went to Alexandria to define and test a new protocol to acquire broken fragments underwater using photogrammetry. I'm clearly not an expert, but I'm now aware of the practical problems that can occur during 3D acquisitions sessions, and how to address them. Finally, I use to work with acquired data and deal with acquisition noise, unstructured representations, and huge models. This acquisition session has been done in collaboration with Archeovision.

(click on images for more details).