Séminaire IMAGE : « One more step towards the connection between topological data analysis and mathematical morphology » (Nicolas Boutry)

Nous aurons le plaisir d’écouter Nicolas Boutry, enseignant-chercheur au LRDE / EPITA, Paris.

Il donnera un séminaire IMAGE, le jeudi 11 mai 2023, à 14h00, en salle de séminaire F-200.

Some works have shown these last years that topological data analysis (TDA) and mathematical morphology (MM) are very related. Indeed, it has been proven that dynamics, often used to determine seeds to compute watersheds, and the persistence, often used to filter Morse-Smale complexes in TDA, are finally equivalent. It has also been shown that Morse functions, very used in TDA and generally associated with a gradient vector field, are equivalent up to the sign to simplicial stacks used in MM. This allowed us to prove that a combinatorial optimization problem known as the Minimum Spanning Forest (MSF) on the dual graph of a simplicial stack is equivalent to compute the gradient vector field of the corresponding Morse function. Here, we present a new result: the contour tree, also known as Reeb graphs (on simply connected domains) in TDA, is equivalent to the tree of shapes coming from MM (up to a dual cell complex computation). This shows that applications using techniques from TDA could be used in MM and conversely. This new step reinforces the link between TDA and MM.