IPCV (Master Erasmus Mundus)
IPCV - Digital Geometry Processing
Course (Semester 9) of Master Erasmus Mundus IPCVai (Artificial Intelligence for Image Processing and Computer Vision) [Jacques-Olivier Lachaud, November 2025]
Abstract
This course aims at presenting the field of digital geometry and its applications to the analysis and processing of (mainly) 3D images. Digital geometry views shapes as subsets of the lattice grids in arbitrary dimension. 2D shapes are thus sets of pixels, while 3D shapes are sets of voxels. It provides consistent definitions for contours and surfaces, and convergent definitions of tangents, normal vectors, curvatures. It is thus a sound counterpart to Euclidean geometry, but adapted to discrete data as provided by imaging devices. It also develops a sound discrete exterior calculus on digital surfaces, thus providing all the necessary tools for manipulating vector fields on such objects, or doing spectral geometry processing.
The course takes place from December 9 to December 11, 2025, in Bordeaux.
Lectures
Practicals
Practicals will use the DGtal library (https://dgtal.org), an open-source generic C++ library well adapted to digital geometry processing. Coding will be in C++.
Visit and clone repository https://github.com/JacquesOlivierLachaud/IPCV-practicals
- TP1 Filtering and segmentation of 3D CT thoracic image
3d image filtering, digital surfaces, connectedness
- TP2 Homotopic thinning
3d shapes, digital topology, simple points, cubical complexes
- TP3 Geometric estimations on 3d digital surfaces
3d shapes, geometric estimators, multigrid convergence
- TP4 Scale axis transform
3d shapes, distance transform, scale axis, geometry processing
Notes
Featured image represents two distance transforms on digital surfaces, a bunny and a dragon. They were computed using the diffusion of a convergent Laplace-Beltrami operator onto such surfaces.