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

The contour tree, an abstraction of a scalar field that encodes the nesting relationships of
isosurfaces, can be used to accelerate isosurface extraction, to identify important isovalues …

Large-scale simulations are increasingly being used to study complex scientific and
engineering phenomena. As a result, advanced visualization and data analysis are also …

Topology provides a foundation for the development of mathematically sound tools for
processing and exploration of scalar fields. Existing topology-based methods can be used to …

We study the evolution of the Reeb graph of a time-varying continuous function defined in
three-dimensional space. While maintaining the Reeb graph, we compress the evolving …

The Max-Tree designed for morphological attribute filtering in image processing, is a data
structure in which the nodes represent connected components for all threshold levels in a …

The contour tree is an abstraction of a scalar field that encodes the nesting relationships of
isosurfaces. We show how to use the contour tree to represent individual contours of a …

This work represents the first book to focus on basic algorithms for isosurface construction. It
also gives a rigorous mathematical perspective on some of the algorithms and results. In …

Improved simulations and sensors are producing datasets whose increasing complexity
exhausts our ability to visualize and comprehend them directly. To cope with this problem …

ABSTRACT The Contour Tree of a scalar field is the graph obtained by contracting all the
connected components of the level sets of the field into points. This is a powerful abstraction …