morseq — Topological image segmentation
Research at LIGM, CNRS UMR 8049, with Laurent Najman, Gilles Bertrand and Jean Cousty. The project studies image segmentation through discrete Morse sequences: a representation that connects a cell complex, its gradient field and its critical cells.
Contribution
I developed a single-pass basin-labeling algorithm. Instead of repeatedly expanding each basin, the algorithm scans a Morse sequence once. The required faces of a regular pair precede it in the sequence, so labels can be propagated in order.
The labeling pass is linear in the incidence structure, given a Morse sequence. For suitable flooding sequences, the labels restrict consistently to grayscale cuts. Plateaus are handled without perturbing the image values.
Implementation & verification
The public morseq library implements cubical and simplicial complexes, gradient fields, stable and unstable sets, basins and cuts in Python, with no core runtime dependencies. It includes a command-line interface and 2D/3D image-segmentation examples.
The 623-test suite checks the implementation against definitions and structural properties, including:
- Agreement between one-pass basin labeling and explicit closure.
- Independence from the order of allowed expansions.
- Basin disjointness and consistency under prefixes and cuts.
- Boundary composition, path parity and Euler-characteristic identities.
Tests cover cubical and simplicial examples and randomly generated acyclic fields. They check implementation behavior and complement the mathematical reasoning.
Scope
The focus is algorithmic correctness and the structure of discrete Morse sequences. Quantitative benchmarking against learned segmentation models remains a separate evaluation task. The repository includes runnable examples and references to the underlying theory.