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Computing discrete Morse complexes from simplicial complexes
We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of arbitrary dimension and very large …
Ulderico Fugacci
,
Federico Iuricich
,
Leila De Floriani
PDF
DOI
Computing multiparameter persistent homology through a discrete Morse-based approach
Persistent homology allows for tracking topological features, like loops, holes and their higher-dimensional analogues, along a …
Sara Scaramuccia
,
Federico Iuricich
,
Leila De Floriani
,
Claudia Landi
PDF
DOI
Discrete Morse versus Watershed Decompositions of Tessellated Manifolds
With improvements in sensor technology and simulation methods, datasets are growing in size, calling for the investigation of efficient …
Leila De Floriani
,
Federico Iuricich
,
Paola Magillo
,
Patricio D. Simari
PDF
DOI
Efficient Computation and Simplification of Discrete Morse Decompositions on Triangulated Terrains
We consider the problem of efficient computing and simplifying Morse complexes on a Triangulated Irregular Network (TIN) based on …
Riccardo Fellegara
,
Federico Iuricich
,
Leila De Floriani
,
Kenneth Weiss
PDF
DOI
Efficient Homology-Preserving Simplification of High-Dimensional Simplicial Shapes
Simplicial complexes are widely used to discretize shapes. In low dimensions, a 3D shape is represented by discretizing its boundary …
Riccardo Fellegara
,
Federico Iuricich
,
Leila De Floriani
,
Ulderico Fugacci
PDF
DOI
Efficient topology-aware simplification of large triangulated terrains
A common first step in the terrain processing pipeline of large Triangulated Irregular Networks (TINs) is simplifying the TIN to make …
Yunting Song
,
Riccardo Fellegara
,
Federico Iuricich
,
Leila De Floriani
PDF
DOI
Fast and Scalable Mesh Superfacets
In the field of computer vision, the introduction of a low-level preprocessing step to oversegment images into superpixels - relatively …
Patricio Simari
,
Giulia Picciau
,
Leila De Floriani
PDF
DOI
Generalized Extrinsic Distortion and Applications
Curvature is a key feature in shape analysis and its estimation on discrete simplicial complexes benefits many geometry processing …
Patricio Simari
,
Leila De Floriani
,
Federico Iuricich
,
Mohammed M. Mesmoudi
PDF
DOI
Hierarchical Forman Triangulation: A multiscale model for scalar field analysis
We consider the problem of analyzing the topology of scalar fields defined on a triangulated shape by using a multi-scale approach, …
Federico Iuricich
,
Leila De Floriani
PDF
DOI
Homological Shape Analysis Through Discrete Morse Theory
Homology and persistent homology are fundamental tools for shape analysis and understanding that recently gathered a lot of interest, …
Leila De Floriani
,
Ulderico Fugacci
,
Federico Iuricich
DOI
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