Morse theory offers a natural and mathematically‐sound tool for shape analysis and
understanding. It allows studying the behavior of a scalar function defined on a manifold …

In the field of terrain analysis, a primary goal is to effectively identify topographic features for
a better understanding of their associated processes. The relationships among features are …

Terrain feature points, such as the peaks and saddles, are the basic framework of surface
topography and its undulations, which significantly affect the spatial distribution of surface …

Terrain analysis uses different workflows to extract features from terrain models for the
purpose of understanding topographic patterns and processes. However, the results of …

Scalar fields are real-valued functions defined point-wise within a d-dimensional domain.
They appear in many applications, including physics, chemistry, medicine, geography, etc …

We propose a new technique for eliminating flat edges from a Triangulated Irregular
Network (TIN) in a morphologically consistent way. The algorithm is meant to be a …

Terrain simplification is the basis of constructing multi-scale digital elevation models.
However, a definite corresponding relationship between the scales and the hierarchy of …

We address the problem of morphological analysis of real terrains. We describe a
morphological model for a terrain by considering extensions of Morse theory to the discrete …

The basic goal of topological data analysis is to apply topology-based descriptors to
understand and describe the shape of data. In this context, homology is one of the most …

The Morse complex can be used for studying the topology of a function, eg, an image or
terrain height field when understood as bivariate functions. We present an algorithm for the …