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

We present a computational method for extracting simple descriptions of high dimensional
data sets in the form of simplicial complexes. Our method, called Mapper, is based on the …

Given a shape, a skeleton is a thin centered structure which jointly describes the topology
and the geometry of the shape. Skeletons provide an alternative to classical boundary or …

Curve-skeletons are thinned 1D representations of 3D objects useful for many visualization
tasks including virtual navigation, reduced-model formulation, visualization improvement …

Inspired by recent developments in contraction‐based curve skeleton extraction, we
formulate the skeletonization problem via mean curvature flow (MCF). While the classical …

Reeb graphs are compact shape descriptors which convey topological information related to
the level sets of a function defined on the shape. Their definition dates back to 1946, and …

The Reeb graph is a construction which originated in Morse theory to study a real-valued
function defined on a topological space. More recently, it has been used in various …

Before the availability of digital photography resulting from the invention of charged couple
devices in 1969, the measurement of plant architecture was a manual process either on the …

We propose a metric for Reeb graphs, called the functional distortion distance. Under this
distance, the Reeb graph is stable against small changes of input functions. At the same …

Scalar functions defined on manifold triangle meshes is a starting point for many geometry
processing algorithms such as mesh parametrization, skeletonization, and segmentation. In …