This system paper presents the Topology ToolKit (TTK), a software platform designed for the
topological analysis of scalar data in scientific visualization. While topological data analysis …

Topological persistence has proven to be a key concept for the study of real-valued
functions defined over topological spaces. Its validity relies on the fundamental property that …

Solving optimization tasks based on functions and losses with a topological flavor is a very
active and growing field of research in data science and Topological Data Analysis, with …

We present a novel approach for optimizing real‐valued functions based on a wide range of
topological criteria. In particular, we show how to modify a given function in order to remove …

Presents an implementation of symbolic regression which is based on genetic programming
(GP). Unfortunately, standard implementations of GP in compiled languages are not usually …

We define notions of differentiability for maps from and to the space of persistence barcodes.
Inspired by the theory of diffeological spaces, the proposed framework uses lifts to the space …

We present a combinatorial algorithm for the general topological simplification of scalar
fields on surfaces. Given a scalar field f, our algorithm generates a simplified field g that …

We present an approach to incorporate topological priors in the reconstruction of a surface
from a point scan. We base the reconstruction on basis functions which are optimized to …

This book is adapted from my habilitation thesis manuscript, which reviewed my research
work since my Ph. D. thesis defense (2008), as a postdoctoral researcher at the University of …

Given a function f on a surface and a tolerance δ> 0, we construct a function f δ subject to‖ f
δ− f‖∞≤ δ such that f δ has a minimum number of critical points. Our construction relies on …