Extracting Geometric Structures in Images with Delaunay Point Processes

Jean-Dominique Favreau (1) , Florent Lafarge (1) , Adrien Bousseau (2) , Alex Auvolat (2)

1 TITANE - Geometric Modeling of 3D Environments
2 GRAPHDECO - GRAPHics and DEsign with hEterogeneous COntent

We introduce Delaunay Point Processes, a framework for the extraction of geometric structures from images. Our approach simultaneously locates and groups geometric primitives (line segments, triangles) to form extended structures (line networks, polygons) for a variety of image analysis tasks. Similarly to traditional point processes, our approach uses Markov Chain Monte Carlo to minimize an energy that balances fidelity to the input image data with geometric priors on the output structures. However, while existing point processes struggle to model structures composed of interconnected components, we propose to embed the point process into a Delaunay triangulation, which provides high-quality connectivity by construction. We further leverage key properties of the Delaunay triangulation to devise a fast Markov Chain Monte Carlo sampler. We demonstrate the flexibility of our approach on a variety of applications, including line network extraction, object contouring, and mesh-based image compression.

Mots clés: Line network extraction; Spatial point process; Object contouring; Geometric structures; Image compression; Delaunay triangulation

Domaines: Mathématique discrète [cs.DM]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Jean-Dominique Favreau, Florent Lafarge, Adrien Bousseau, Alex Auvolat. Extracting Geometric Structures in Images with Delaunay Point Processes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2020, 42 (4), ⟨10.1109/TPAMI.2018.2890586⟩. ⟨hal-01950791⟩