Differential topology, and specifically Morse theory, provide a suitable setting for formalizing
and solving several problems related to shape analysis. The fundamental idea behind …

Massive simulations and arrays of sensing devices, in combination with increasing
computing resources, have generated large, complex, high-dimensional datasets used to …

Combining concepts from topology and algorithms, this book delivers what its title promises:
an introduction to the field of computational topology. Starting with motivating problems in …

We present DisPerSE, a novel approach to the coherent multiscale identification of all types
of astrophysical structures, in particular the filaments, in the large-scale distribution of the …

Persistent homology is an algebraic tool for measuring topological features of shapes and
functions. It casts the multi-scale organization we frequently observe in nature into a …

An elementary question in porous media research is in regard to the relationship between
structure and function. In most fields, the porosity and permeability of porous media are …

Homology is a powerful tool used by mathematicians to study the properties of spaces and
maps that are insensitive to small perturbations. This book uses a computer to develop a …

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 …

The emerging field of computational topology utilizes theory from topology and the power of
computing to solve problems in diverse fields. Recent applications include computer …

We address the problem of curvature estimation from sampled smooth surfaces. Building
upon the theory of normal cycles, we derive a definition of the curvature tensor for polyhedral …