5 citations · 7 across the 8 of their papers we have counts for
8 papers
Operations on constructible functions and generalized valuations
Andreas Bernig, Vadim Lebovici
Alesker's theory of generalized valuations unifies smooth measures and constructible functions on real analytic manifolds, extending classical operations on functions and measures.…
Topological shape transform for thymus structures
Haochen Yang, Vadim Lebovici, Andreas Tarcevski +5
The Euler characteristic transform (ECT) is an emerging and powerful framework within topological data analysis for quantifying the geometry of shape. The applicability of ECT has…
Efficient computation of topological integral transforms
Vadim Lebovici, Steve Oudot, Hugo Passe
Topological integral transforms have found many applications in shape analysis, from prediction of clinical outcomes in brain cancer to analysis of barley seeds. Using Euler charac…
Local characterization of block-decomposability for multiparameter persistence modules
Vadim Lebovici, Jan-Paul Lerch, Steve Oudot
Local conditions for the direct summands of a persistence module to belong to a certain class of indecomposables have been proposed in the 2-parameter setting, notably for the clas…
Hybrid transforms of constructible functions
Vadim Lebovici
We introduce a general definition of hybrid transforms for constructible functions. These are integral transforms combining Lebesgue integration and Euler calculus. Lebesgue integr…
Local characterizations for decomposability of 2-parameter persistence modules
Magnus Bakke Botnan, Vadim Lebovici, Steve Oudot
We investigate the existence of sufficient local conditions under which poset representations decompose as direct sums of indecomposables from a given class. In our work, the index…
On rectangle-decomposable 2-parameter persistence modules
Magnus Bakke Botnan, Vadim Lebovici, Steve Oudot
This paper addresses two questions: (a) can we identify a sensible class of 2-parameter persistence modules on which the rank invariant is complete? (b) can we determine efficientl…
Reconstruction of piecewise constant functions from X-ray data
Vadim Lebovici
We show that on a two-dimensional compact nontrapping Riemannian manifold with strictly convex boundary, a piecewise constant function can be recovered from its integrals over geod…